Description of Mechanical Systems by the Use of Quadripole ParametersHarald KammererThe author expects that this worksheet will only be used for teaching and educational purposes and not for commercial profit without contacting the author for a licensed agreement. The following numerical values are only academic examples and have no reference to real structures.MotivationLet's consider a mechanical device defined with an input gate and an output gate. At the input gate there are two values of the force NiMmJSJGRzYjIiIi and the velocity NiMmJSJ2RzYjIiIi. At the output gate there are the two values of the force NiMmJSJGRzYjIiIj and the velocity NiMmJSJ2RzYjIiIj. So we have all in all two gates and four items. This system can be described in the equivalent manner as an electrical quadripole. So we call this system a mechanical quadripole. Such a quadripole is shown in Figure 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For example in [2] there is some more detailed description of this method. Here we will give a first introduction in this theory.We can consider it as a black box. It is not important of what the device consists. It is only important how it works. In this worksheet we will see how we can use this method to work with some special dynamical systems. But first we have to give some conditions for the mechanical systems. Perhaps not all of the following conditions are necessary, but they will help to understand this idea.restart:with(linalg):with(plots):We define a helpful procedure first. This procedure is used in the following to convert complex values into the standard form NiMvJSJ6RywmJSJhRyIiIiomJSJJR0YnJSJiR0YnRic=. complexextension:=proc(a)local z,n,zr,nr,zi,ni,zbr,zbi,nb,b;z:=numer(a);n:=denom(a);zi:=coeff(z,I);zr:=simplify(z-zi*I);ni:=coeff(n,I);nr:=simplify(n-ni*I);zbr:=(zr*nr+zi*ni);zbi:=(zi*nr-zr*ni);nb:=(nr**2+ni**2);b:=simplify(zbr/nb)+simplify(zbi/nb)*I;end:ConditionsAt first we assume that all motions are harmonic vibrations. All other kind of motions must be analyzed by use of a Fourier transformation. Further, the devices should be a straight line. There is only one input gate and one output gate. That means for example that no rocking of the foundation is possible. We consider devices with linearly dependantence between the force and the displacement, velocity or the acceleration is possible. For example no Duffing device is considered.All the following relations are defined by use of the angular frequency NiMlJk9tZWdhRw==. For practical use it is usual to consider the frequency NiMlImZH. The relation between NiMlJk9tZWdhRw== and NiMlImZH isNiM+JSVzdWIxRy8lJk9tZWdhRyooIiIjIiIiJSNQaUdGKSUiZkdGKQ==Description of the motionEvery motion, especially every harmonic vibration, can be described by the displacement, the velocity or the acceleration. Of course there are some constants of integration, but in our consideration they are not important.
We describe here the motion by the velocity, as shown in Figure 1. The velocity should be given as a harmonic vibration in complex notation.NiM+LSUidkc2IyUidEcqJiUjdjBHIiIiLSUkZXhwRzYjKiglIklHRiolJk9tZWdhR0YqRidGKkYqThe displacement is can be integrated from the velocityNiM+LSUieEc2IyUidEctJSRpbnRHNiQtJSJ2R0YmRic=And the acceleration is derived from the velocityNiM+LSUiYUc2IyUidEctJSVkaWZmRzYkLSUidkdGJkYnHere we express the displacement and the acceleration by the velocity. This allows us to generate a formalism to describe any device. For example the displacement NiMtJiUieEc2IyIiIjYjJSJ0Rw== and acceleration NiMtJiUiYUc2IyIiIjYjJSJ0Rw== are expressed by the velocity NiMtJiUidkc2IyIiIjYjJSJ0Rw==NiM+LSYlInhHNiMiIiI2IyUidEcqKC1GJkYpRigtJSJ2R0YpISIiLSZGLkYnRilGKA==NiM+LSYlImFHNiMiIiI2IyUidEcqKC1GJkYpRigtJSJ2R0YpISIiLSZGLkYnRilGKA==ImpedanceWe have assumed that the forces are linearly dependant on the displacement, velocity or the acceleration. Additionally we assumed that only harmonic vibrations are considered. This means that we can write for the relation between force and velocityNiMvLSUiRkc2IyUidEcqJiUiUkciIiItJSJ2R0YmRio=orNiMvJSJSRyomLSUiRkc2IyUidEciIiItJSJ2R0YoISIiR is called the impedance of a device or a structure.Impedances of Standard DevicesLet's consider some typical devices and their impedances. SpringFirst consider the spring in Figure 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2The displacement at the upper end of the spring should be given by NiMtJiUieEc2IyIiIjYjJSJ0Rw==, the velocity is NiMtJiUidkc2IyIiIjYjJSJ0Rw==.The force which is neededed to produce this displacement isNiM+LSYlI0YxRzYjJSdzcHJpbmdHNiMlInRHKiYlImtHIiIiLSYlInhHNiNGLUYpRi0=For the impedance of the spring we getNiM+JiUiUkc2IyUnc3ByaW5nRyomLSYlI0YxR0YmNiMlInRHIiIiLSYlInZHNiNGLkYsISIiDamperWe repeat the same consideration for a viscous damper.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 3The displacement and the velocity are again given by NiMtJiUieEc2IyIiIjYjJSJ0Rw== and NiMtJiUidkc2IyIiIjYjJSJ0Rw==.The Force on the damper is nowNiM+LSYlI0YxRzYjJSdkYW1wZXJHNiMlInRHKiYlImRHIiIiLSYlInZHNiNGLUYpRi0=NiM+JiUiUkc2IyUnZGFtcGVyRyomLSYlI0YxR0YmNiMlInRHIiIiLSYlInZHNiNGLkYsISIiMassThe third standard device is a rigid body with mass m.MFNWtKUb<ob<R=MDLCdNB^>ZJ@[<Zb_^owW@ka`N\\@Nd\\QgqxHqQ`Pslik]yJ>]LK\\LDdRJdRGPtTUOLUx_mv\\eocMnpqjR]sTAUeMPUdtYdqfmt`eWPqtYdkPqTUXWehxAuyZamgeOd]TPqlGAmgeoFqlO`NRLV\\LjLMN>MxuAXxxQhhmK`MgyLWXxvtqhXwIxVIYwstswuYiYwoqqhYwCEMV\\MF`j>pYyiyqapn`pN`lNXKXlkZpqxpqCTL`<p_qmkUv@IuSHj;HJHAu[TQwiywIwcIw[Ew>`pB=Yb]yrIxfUmTPmxlyrYVtEYCQl_ToPeoTdw`atNat[pv?AnoXWQqopp`whqwxhVIhAipQqeeXxJVaaysYxtwq[RAmKwcIwcPodPfuWAuRAyVYhIIZ:gggggSGeSAgFIZt@rZ?fZ>cXqiuiwIvavA\\HV_dN_<>`j`y]ykynr?G[`g[E>fcHf;^_mV`M_]mYuiwq;plRp^x@_=V]gGbeOv>IkgiwgieWge:v[dQ\\^Pq;AiQIZUVtQfklCq;fr=wYISMoFWMViSxZKxMATSsE_?U[=E\\cGXkF:AvaKyWks:gGJ?VaqsWWImmvF[ilKuwArZcG_CtaWHfYrN_Ih;Cs[BH=HECDZEfKIVl?wNYsTQRSCESCXXCBjCWcCk:lr[<SmXVa=uKlVhXr@qm>qLbAPp`Xn]YHAL^LqS=M]DK_TJ;HULETt@Xntr:IJuYuLANTywRxKfEvO@yvDPRdnfawf]Rb@v;MLlatZAPSySkURR=ue\\fmOh:a]jv^A^sCIZm?rV`]jvnyo\\j^aUXhaqsSI^Xvk?pdi>cawsXhli^orHlwfvJ`e>I]WVoYNcCGc;y[?V`pOtMYtOvr=ydoHgaH\\nFgLa^pP[qXZU>yGgmtfhnXmWprX>pYwiwihlavCQkW^r\\@aT?\\;>ltQytAfc>hDwkL@uH?btfy]Q^KGvY>f:o`d>wAq`H?sAXcSGeS?n?v\\H@fuvn>?hRPncAk>gc[_]t^hbpohpw^IsMP[:nySp\\h^erAw]xkTawNwcIwssYxaynFGm\\Al^>[jpuXquF`kF`wfagWNZRqkWValOhl_gT_f>fv`qvpxpqxsTh`EGek>kM_jdXvK@a:agTvdlA\\[qdJ?djQtEw_O_dN_ejqinx\\rFrO?gl^nbvk]F^Wvk>IwjV\\w_xxN^KhwkXfAAp;Od@G^hyamovF^wOHmSHkxVtNa\\<Ht[FcVXvfnuLx__HqZ?dKasM>rbaap?njHk>Wxd_vtHu^@hlGmFQxu>up_hn_ajAr=vwvXxHp_cF_;WyY^ijIrWxhXIsRQwdQwLI]GWlpohpojF>`sOsl`xHx]yn_HHnkA_afvAnmxfiTXobg`;xrS^hX>`Yfat_\\``whqwHOxZicGgtrHZsneRFxjqwuxw\\w`cQ\\A``Jp^n^`n^\\Qv\\m^wJAtZ@[n`kvn[MV`TqrL>`tfeF^ZX>uNVhaqs?n]_f_c_vDA[^hsapcWPdxakLgtDPkDP^=IkfGca>d[_^;nZp_wQyeygy=y[y>kaa^jnqyqyuysyvyvGylivQhepG]gQZ?aqv`asHnn^^;FlTH`mNaRVgvhqCv`TqtVauvasmvsfquwX]=PZjnisivQ>x=xvbYkQwewglPQgZVhmy^Y`i<paUwqxgqx_^SOxJCPOG<KGoixoywywyxQh_Us:EdpEttwxXYYIsukEx\\irLetLodI]IkaBx[Svuim;X:GGd_Re_HRcFPIDQsgyoytKHJoRD;HRSgj?hjUt`gSnuBt;BjQUTMUhiiqquQwUxEUGwSP;V]KyToT:yx:Sheuth[dSkwASbCGtpWXaqsdOgd_yvaYTKrb[vFqhgUuxGy`YE_;wa;F]mWfcstMiU]S]?cNahcUtpwWYqYYiYqICR?uk_sOMuIIsiuiwqx?yDY]YpIuaETZ=feCxL_GLAeMqT`YWsEYsSBhuwXii:_rjWumwVIKxvqtUuW_ueP=V_]ipQueedOgdbeHJQhOiD[At[=f?Af]icc=Hr=FGIJ<puflRBdJhDq;imjMLV=ycynYPvYUPHEVu<tLtU`DtbAPoeNqPXKQn?UwPio=qT^]Q[hnZuooXWQqUqeuoMsLeWgeW?uSidUt`LIXPk<WGHXfDTPUJ]=lKyrxPPgEMdPr@XlQxUxEqnTPJLXBqy`isUHVoLMF@V>ls^LuWlpXLRHIkTLruYr:=oRyOx@y<<YTTMUTOdLObEWY]lDUSEEqDAq^=rcEWM=m\\dM`yrBaLNaXQ\\m^Tp\\lLCDsVTtS\\POHre<QM@sXmLcHp:\\pTLjhhVFiqsqvU`qaTvf`of`SdPm=EuG=K@dpkDPmURcXVBpLgmvOySV@Q;tKCqXBxu@drcilkeOalNxamaMTBpjvdxNYTGeSGUypiwUQp_UkvHLSMrnxle`kKeNuUOLqLT<rbYWCaJvEVjMl`<kiYSTxt<ATG<NNmPd@T]]PGTtcUv@ikT\\VTMT`_g^^j_VwApb^NgO?k?f\\kgkKh\\AqkWVkmAko>mhAfJPu\\oT_SpAv=wC\\IG\\uxDwbnORJgEHMH:EdJKWEMBLaxAAYter:SRsSFhiV_kUNAeXWHamcPMR@;Dg[vXkUQYRIcI^ofSsFceU?_Ya=UJUs^mGTGxY;nCdO;qN;uKTMsU<qbYpRmrn`mx@jAUjp@ML=SJQKUPTQaU>PN_@M`<K@<yIEueDKruyk`MH<v^EntePclQTmvr`SWPQOmpSO`S`e=WmqI\\=FgegbB>\\Opp\\H_nnbA>[;X\\BFfJYt@@yEgw\\gyXfcU?^X?tAFZVox=Pk<I^EisGivGfL=WsMd<scnOyv]drssOAH;kVtqDXEdvUi>uiAmKt@rLYK>DnV<UGIqbeUQhOmmL:qL=MpaPVGqSgloOPvKySCxwkdjriSEUm^Qt?eOWDQ^Mm[EP_dOgiry@P@ex\\EkCPj@lW>UOW=rF]V^hVfAj:hY_dmntVg@VD@L_xqZeJZ=RBHoqDqdTrOXb=HvDqk<nfTGhEhnhVvp^bca^;XZFOcXgugH_WopVHdYPrx@pBPvU?a=^m^Xq;FcPqp\\OpLg_V`vp>pQ_s?xe=h\\>Qjj_[yHsS`mV`]J_vXXck`k<NbcGZ>^[^N`mV`anbCX`gf_g>[kNyWp_`wvuxwxXZ^FmdgggggKHvtFZGisGypWqhUHiky^Iom>nchyZ]?XkrLaDTYuUYUUUUIcEt[BlMCGaDOcD?[Vtax\\Qga;eOMGbYW[gRAutPqtPytQYcgad@KVkIuRMrUMumwVIaisUx^ouJcYocHoKSDAhSMIcSEkWn^=L:?fS?rmGlrypFAg:HlTHr\\oujHf=nbT`rZnl^`cJ?m=otGHm]hv_ivmwvHivFnu?Ndh@nZ@nn`pNnu\\qZcIap_`[`oFR\\ODSAi_UsP?DOOwBKfKIVvCfZaF<ogtOiTQWb?WpUBuQRxYbHysTgHeOf\\ORwqg>uRbqyuywYeiteHq;Up;II?HN\\qnXNPyJbxTOeTseL;xyW@vC<VJ=QOTx;Ul^UkQtOPTS?mjeuRCqqQEOUlxcaxlPpl<YBXoBqRSMNBxrepotPKXXt=@NaEJIIsKMwfawf=Wb=KQMJe=LAmLWQW`Um`DsplWVAk>YlJTvL<j;hNj<jDTQr<XemtfHlctOUuU[yYReWuqhaySYxZ_f\\Oxq_VmMrHWSP_G;cG^aVBot_gb@]DvKxBYFmsVHabgavAGB@SQIlq;]x;PkVdPs`sLeUlPxqtWXaW;UUHAovPkF<lOUoPeUyeyoAw?ALgXC;Hf;C:Sdw?RiYFaCuDAe>QWj_wWSkJhNCiKbqPJEl^\\P_mjpQOf\\Ov]ykyr;hOkDqRtyt<rjhPXQYeiOrqRxtOWusPDoruxWyXi<Uj@NLTlq]OyUSdQKcEkWHO`TprMLU]pQeV_eNF@KuEkgaMjHP`LYpmrFHMqaumuKPyJfERQTJXLsC<P\\Tr[`VmPL_Lvf<v>pyuHw`Xm\\EQFTnyIwaxmPmW[]rE\\UxYL^`MRhpeut\\=t=HMfiRqUtcAN;<PnAqOLpn@qmPNZ<QTAK:]mslsEXxrhwCyNY`lItLthTOIV<\\KYPYwQyoipohpldvkUlK]W]\\r`LxJaUc]O:=x:Es;hKLXLxTTdXLPLKAPXZaLsxSFmjTyqE<PsaqnuPwqoDPYelTf@qeqou`O=UkU\\l=QKaDJ@<MBMRdMp@dSpPX_QSwaLfin>]kB]Xp<RHMRRMy[djkpj\\ptLOcPvcGPdJQx[SUKbMKFkAr;WBggggWhausxGx@YE]aTc\\N:Iov]VR`kAmKX\\QB`yvPvDXODMSD=Wf`SveOj\\KT`WNhKFYmm\\MKyuDHKNitOiKWUMkTx@un><X>Iw_dLxApMHxepKREqJlJYls:HkDO[fP^q?`eNllqvtWbEwb:vlIpatA_GQ^SAurPkH>`bQZRwrWoZ?PZFPsnqfAF`rNuuOc`?]qOgLgclVlYFkGOvIh[^yZA`^di^a^olYikGhkOmt@jQiohpoPXyS@p^ntyP]iPdxOov>`oYiV@lLP\\<^nLad@We_Ni^qocQlDpcbyhNvxD^\\ZOm:NfyilQoeKQbJqkHpk[hj[d[=yPatNaUwexOIbOmhB[X?uHbQY_Ud?yyDAbnYDb?ulWI_sEb]XTME^Odu[x_KbZmHVwHViiuuxcWTa_djYxYEdB[X`wCNuIb;WkATEsBUee]CHDAWL?rrwrHSVoEVfoWQwCQ[hpQxDMCPOHjocVCI<UHsUx[GE<UXxihbQemCbGEDN]sCxpEujc<yNtuPQT@yjPAMdDWAqTeQKa@u^]o:ElodSMDSTxVBUtdiUCQY>qkl`l\\aT[US\\AkEhwSen;MstAqZiybLWG]XwIuyDPMITyToOMT;USO@TXYNUEyxawJQn[HY\\dqk\\rkaxcYtO`pNt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4 Now we define the displacement and the velocity again with NiMtJSN4MUc2IyUidEc= and NiMtJSN2MUc2IyUidEc=. Additionally we use now the acceleration NiMtJSNhMUc2IyUidEc=.The force which is needed to move the body isNiM+LSYlI0YxRzYjJSVtYXNzRzYjJSJ0RyomJSJtRyIiIi0mJSJhRzYjRi1GKUYtNiM+JiUiUkc2IyUlbWFzc0cqJi0mJSNGMUdGJjYjJSJ0RyIiIi0mJSJ2RzYjRi5GLCEiIg==Elastic Half-SpaceAt last we give the Impedance for an elastic half-space as an example as shown in Figure 5.
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 5Such an elastic half-space is used to describe the soil under a foundation. It is not so easy to deduce the impedance of this half-space. It is given for example in [1] byNiM+JiUiUkc2IyUzRUxBU1RJQ19IQUxGX1NQQUNFRyksJiosIiM+IiIiIiQrIiEiIiwmRixGLCUjbXVHRi5GLCUmT21lZ2FHIiIjKiYlIkdHRiwtJSVzcXJ0RzYjKiZGNEYsJSRyaG9HRi5GLEYuRiwqLiUiSUdGLEYvRiwlI1BpR0YuRjFGLEY0Ri4lImFHRi5GLCwkRixGLg==In this relation NiMlIkdH is the shear modulus, NiMlI211Rw== is the Poisson's ratio and NiMlJHJob0c= is the specific mass of the soil. NiMlJk9tZWdhRw== is the angular frequency of the harmonic vibration. NiMlImFH is the radius of the area where the force is acting.Quadripole ParametersIn practice two different ways to describe a quadripole as shown in Figure 1 are common. The first form is the chain form, the second is the impedance form.Chain FormIn this form we describe the values of the input gate dependent on the values of the output gate:NiMvJiUiRkc2IyIiIi0mJSJmR0YmNiQmRiU2IyIiIyYlInZHRi0=NiMvJiUidkc2IyIiIi0mJSJmRzYjIiIjNiQmJSJGR0YrJkYlRis=Due to the condition that all forces are linearly dependantent on the displacement, velocity or the acceleration and the condition that we only consider harmonic vibrations, it followsNiMvJiUiRkc2IyIiIiwmKiYmJSJBRzYkRidGJ0YnJkYlNiMiIiNGJ0YnKiYmRis2JEYnRi9GJyYlInZHRi5GJ0YnNiMvJiUidkc2IyIiIiwmKiYmJSJBRzYkIiIjRidGJyYlIkZHNiNGLUYnRicqJiZGKzYkRi1GLUYnJkYlRjBGJ0YnThe values NiMmJSJBRzYkIiIiRiY=, NiMmJSJBRzYkIiIiIiIj, NiMmJSJBRzYkIiIjIiIi and NiMmJSJBRzYkIiIjRiY= are called the quadripole parameter of the chain form.In matrix form we can write NiMvLSUnbWF0cml4RzYjNyQ3IyYlIkZHNiMiIiI3IyYlInZHRisqJi1GJTYjNyQ3JCYlIkFHNiRGLEYsJkY2NiRGLCIiIzckJkY2NiRGOkYsJkY2NiRGOkY6RiwtRiU2IzckNyMmRio2I0Y6NyMmRi9GRUYsImpedance FormIn this form we describe all forces dependent on the velocities:NiMvJiUiRkc2IyIiIi0mJSJnR0YmNiQmJSJ2R0YmJkYtNiMiIiM=NiMvJiUiRkc2IyIiIy0mJSJnR0YmNiQmJSJ2RzYjIiIiJkYtRiY=Same as in the chain form, this yieldsNiMvJiUiRkc2IyIiIiwmKiYmJSJaRzYkRidGJ0YnJiUidkdGJkYnRicqJiZGKzYkRiciIiNGJyZGLjYjRjJGJ0YnNiMvJiUiRkc2IyIiIywmKiYmJSJaRzYkRiciIiJGLSYlInZHNiNGLUYtRi0qJiZGKzYkRidGJ0YtJkYvRiZGLUYtThe values NiMmJSJaRzYkIiIiRiY=, NiMmJSJaRzYkIiIiIiIj, NiMmJSJaRzYkIiIjIiIi and NiMmJSJaRzYkIiIjRiY= are called the quadripole parameter of the impedance form.In matrix form we can write NiMvLSUnbWF0cml4RzYjNyQ3IyYlIkZHNiMiIiI3IyZGKjYjIiIjKiYtRiU2IzckNyQmJSJaRzYkRixGLCZGNzYkRixGMDckJkY3NiRGMEYsJkY3NiRGMEYwRiwtRiU2IzckNyMmJSJ2R0YrNyMmRkVGL0YsIn this worksheet we use the impedance form only as an aid. So when we say "quadripole parameter" we mean the quadripole parameter of the chain form.ConversionOf course both forms can be converted to the other. It is practical to make this by use of procedures.Calculate the quadripole parameter of the impedance form from the quadripole parameter of the chain form (chain form -> impedance form)chain2impedance:=proc(A)local Z,F1,v1,F2,v2,eq1,eq2;Z:=matrix(2,2);eq1:=F1=evalm(A&*vector(2,[F2,v2]))[1];eq2:=v1=evalm(A&*vector(2,[F2,v2]))[2];assign(solve({eq1,eq2},{F1,F2}));Z[1,1]:=coeff(F1,v1);Z[1,2]:=coeff(F1,v2);Z[2,1]:=coeff(F2,v1);Z[2,2]:=coeff(F2,v2);evalm(Z);end:Calculate the quadripole parameter of the chain form from the quadripole parameter of the impedance form (impedance form -> chain form)impedance2chain:=proc(Z)local A,F1,v1,F2,v2,eq1,eq2;A:=matrix(2,2);eq1:=F1=evalm(Z&*vector(2,[v1,v2]))[1];eq2:=F2=evalm(Z&*vector(2,[v1,v2]))[2];assign(solve({eq1,eq2},{F1,v1}));A[1,1]:=coeff(F1,F2);A[1,2]:=coeff(F1,v2);A[2,1]:=coeff(v1,F2);A[2,2]:=coeff(v1,v2);evalm(A);end:Quadripole Parameter of Standard DevicesNow we will give the quadripole parameter for some typical devices.SpringFirst we consider the spring shown in Figure 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 6To get the quadripole parameter we first consider the forces NiMmJSJGRzYjIiIi and NiMmJSJGRzYjIiIj. To fulfill the condition for the equilibrium, the forces must be equal.NiMvJiUiRkc2IyIiIiZGJTYjIiIjNext we know that the spring will be stretched byNiMvKiYlJkRlbHRhRyIiIiUieEdGJiwmJkYnNiNGJkYmJkYnNiMiIiMhIiI=With the displacement on the input gate we getNiMvJiUieEc2IyIiIiwkKiglIklHRiclJk9tZWdhRyEiIiYlInZHRiZGJ0Ysand on the output gateNiMvJiUieEc2IyIiIywkKiglIklHIiIiJSZPbWVnYUchIiImJSJ2R0YmRitGLQ==For the relation between the stretching of the spring and the force we assume linearly dependenceNiMvKiYsJiYlInhHNiMiIiJGKSZGJzYjIiIjISIiRiklImtHRikmJSJGR0YrThis yields for the relation between the force and the velocities at the input gate and the output gateNiMvKiYmJSJGRzYjIiIjIiIiJSJrRyEiIiwmKiglIklHRikmJSJ2RzYjRilGKSUmT21lZ2FHRitGKyooRi5GKSZGMEYnRilGMkYrRik=or after rearrangementNiMvJSN2MUcsJioqJSJJRyIiIiUmT21lZ2FHRiglImtHISIiJiUiRkc2IyIiI0YoRigmJSJ2R0YuRig=Now we have the four quadripole parameter for the matrix NiMmJSJBRzYjJSdzcHJpbmdHNiM+JiUkQTExRzYjJSdzcHJpbmdHIiIiNiM+JiUkQTEyRzYjJSdzcHJpbmdHIiIhNiM+JiUkQTIxRzYjJSdzcHJpbmdHKiglIklHIiIiJSZPbWVnYUdGKiUia0chIiI=NiM+JiUkQTIyRzYjJSdzcHJpbmdHIiIiIn matrix form we getNiM+JiUiQUc2IyUnc3ByaW5nRy0lJ21hdHJpeEc2JSIiI0YrNyYmJSRBMTFHRiYmJSRBMTJHRiYmJSRBMjFHRiYmJSRBMjJHRiY=DamperNext consider the damper in Figure 7.MFNWtKUb<ob<R=MDLCdNBR>ZFA[<Z=^^kNY<\\C_b;_drOugimu?pOgfsyrq@kQQ\\KFqYaZK^Z?FbBFbH?gVQ\\^?\\KN^MPjhVrg_`@W]gH[@^tNNfLqf>VcEAbBH\\iF^>On<p`;G`pV^^@]ZWrb>sW?vjwjFWqqYynxayXxFQ[uV[HIwVhrs>pQy]uotXWigipXyxuqaqyxswmqakygyeyes`cHxqwiwig`d_trYwYwytouswvkosuwsxVyfy[y^yjaymysyYxYxyVW`y_y_y_yGaaammoyeyusxyFX`HAkMX^AokV?i[ijS^`upf_wqZy]yAyAfe\\Xxagmoo\\YwliveX_eV_ibAt[Pn\\PnhgutHavrsUxSwVXGUTYXP]gREh[Ur@;dgQuoWGyiBPmG`?BTeW:KfIyyByEV_EwKYnmsVGIEmdfCbHoYjYbY[XfAuK]trayayIyIeH;DqyijQrE;tHafCUd:;C>IiREubayu=xl;fLEB\\afPegT=xN;wjmYZAr;;YGkG]aehUBG[t[SDOor\\]I^ywyuyuwxjAdf]b=ecF;tKmiBGdB_UjEr?CRf;v\\ISDKIVsevavaCfQ;WGMu[ywcyxQUMOAOs<l>AVkIrAtMjExIxYvYnwaJodJpMQyEXVlQv=MCXrGAlX@nmET@aoXAJKiNtlrCIqaqmEAy=UQbuMRXShHSDIlnMkbXUqpwalQkIKY@LJMy^QwG<LvdvrTO>=tY=LKyRYdY>dSkeyFayK<tBqjyixRYqquwYpynyNxQNgANF@yN<wduO^HnWxYeYsvurJXtZ@N\\trjalrelpALnQqRPK\\mP<<O]fdeYN[T:;g:;T;;f<P[tff;Nra^r??xVvyZYvPOpPAh@n\\gIstNgXvtHnkm__wgcR?^=qxMiZoynFNrHfdHPjZxl=xZInjKwy[yjYNwjOZDnko@t:we[YkYpH=y>gXdatKiR:QiqKh?Cv:OExCdqAXKMDuKX^AscAs\\=sQwdXMYcUwPigAucXcIusYbCXrCbpmCYkIVUipewXiiuuXbAt[SejAXOWBB[U`usXgirEx\\QYoQw[yYUKs;Gtj]DoAEUwHimsaUh`es:Mwn]BBAuGUv@icYwYxIYv?XBsBPSR^cyesYbguT_HcMBt;ISIDruIG?B<=B=sBlivTYWigxDOyEkyDcwp]sn_rc]F^Gb@CEFsVcgumEyreCbAxCKI[]EWSDssbecICECweTfIRuCtjwCw[xJQyoYwOmi@yvNmiUmhfEexcYtggD?yfsFxQg\\kGa@TXmrLxsutwvLU:YRoTK_llj@jxQmy<yCUPLlSnQn:dYVqpf@YP<oSUlK]UqpWWYsitqFYSKTKvMMr]nSTxaysYeqtePtmNQxmAEyyqQQAoKltCtpkUXDaJCeknmL=LMbpR]<Ke=trlMjymsmvSxjHdMDHKLmU=Us<qmH@nttLm<N\\LMjEs_tlf@UknvGYmOpjV^``@qr@yoxtXWq[qjUnotPwd@p`gn]ngJ@kvQmLvmFWl;?pR>bZVjX_ikibRf[rr\\YGWqrP]vQqIwMy^ceFwuwqwqegTehd]tbGD>urbOxYmwCAFpKYxIyayCWKInEwLifesTh_Bccv];X:UIusXhawRIh]sUkguZoWTUsguHYaYmGdlECGYdLarbEg:Ct=MyCcdhIumwVdatcWepcWl]gNKtBAFX]yuyuyqE^oxiyuYuhheuawexME]GWnAwKABNWsAWtswFBEgLuC@MfWUipeGT]hR=hZErQmiliDgqYXYIamsVoGWMincWTaD=cbpMRl;g]yrYsYv?gb?C=iFSsy`qB?WRS\\v>HJILrRImkTV@`j:ptAXp:HK<PvD<LjQMJIurHX]qxgYuSlOxiLmiv@QweTyjiXvXWrWrypyoyomnfWXaqoj`pthheuQsevofVep`[:`mTien@gKVbuXfAqkZ_iMw^ZhmJ_b_Wfk>kBNx[hZjHprWmSG\\J>cS`kFavCYl;FxwyxYyrfNvDv_xV^y_^WNuDOa<geH>]j>newth@\\ByxxxxwXkhNqBNh@FopfgTAxMnwKf];Xs@h[Unx>Y\\I?al?cFfrmOyfOcG`lQVbH^qcvdlva]ausNQcE@OBl_TWtoaumwmp;Uj@Typiw=TNhmVR=yitNS<xQHum<Ol=Y^]tbHTi\\qjQJLMXGQmoTp`estxvXXYjPX_YJr=XZAr;@tHTnh@S<mQ<yXnAsedV`@N?YpD`SjHr?dpwEx?yLe\\kNhjaevI@We<lcPPmTSh<VrmsGyMVxxbIt=ptxdxNYTnhkhURJMY?MtldOqXNKLqkDsB<mDYN^HNJlyVAp[URXXK>LU@HOdUmq=RoLWDLmEULcEU@DyulKIPt>DXmUugupwQwQuq<DLbiJoEVqXrVynC]XDeN=UToIpKDLc\\lXMOEHjetmBpUrpRCXmHMknLrVaLMLj^HrZloD]X?LxJ<mSTrCyLy@y?]oGxQvIvI<NO`kpISAER`DssTwnAXbMmF@J`mrYHV;PPoHkL=SKxmrxMX\\KLHs:`Y\\]y[EMT<rUDVe\\QA]RILKXmSQlNt@nF]RZUWVqNc=PlYyDqVADxNHp]ur\\dl_\\j^YRylYjQjEqOu`SS=V]XpkurndpnpmcU`:alcVdZi]r>s:YjgW[A_[cg[d_kVHaM@nPpuiPmcqZRN[xFgl^nCVpTh`Av[X^[@GfyXhyoZ>_rmYfvi\\_fauoxNHusp]iwdu?hkqwuxw@Oi>_kn^kOP`EA^s`d@qZlWeJp];pr_Ip;G``Fm_Afr^^vhe;PnqA\\lYarAkMpwWYqeWn_FtCvvx`gHQoSfaLPlkqtNNhji]K^mpa^WPie^vBfsgFmJad_qcnIu:?g^G^KY^^gn^VZTpmNX\\ZnmbN^Aansfl@QftQ^\\VomWsEhdpQlXpZavhlWrkFlJnw^hoKnclxsK>njNg]?_dn]_ooJPiMIsbn]eAelwcFhcwQyoYl^asGFv=frrwnrgboN_J@soGifYmCHtvOuZFoW_qFH`[GimnpnaZYw`\\vbBodvgaRPbDitbflLV^IHtZhm[v^OV\\`GpX_pJ>`XFwcqkOn\\lg_YhaL`vjgp[_rF`jIOhZQq`p\\xp_Y@yn>rAwunog<WbEQoVIoGP[p_u=YxsIkMfvhIv=yjsafF^fk@kdidh?soPn<HnJV[da_`N]eatcXbei`GIa^oyWXaqOogHfFAkSP_hw_Fy]vIhiquwHrSOh\\HZvne;xjFY_^>oFWjpiv:_^RFj`qiNxax@x?x_:i`@pnZAnQyeyge?IpjGv<ulgVR]X@gikwtkEL>`l<hPvdXdatgUupHrr<Ud@tBYQiaq=YL:]jyeoUupHxX;IU@LQXHY`IMxiNQTXkPVmTQemTZ`KLqlQ`qOlLVXJ;QuoXWkEUNMjlyLjiqwqxUISWIt[XRAdMZUJoeMulXvPydYoQeoTepausX<VGDvGIpxeytypXQYe<yTLxKqn?]m;IkKAjdtr\\MxyMpk]Kc\\nKyoYuqJDpTik\\AKtLkUlW=HRX\\YjIr:LUq@vTXWhHTBEkH\\P\\PtK=rsQNX`yRYVIHna@yCuJWeYNEjMEvO\\O=`XSeTjqUshvPXUTepdeLKlJ_ToDMKPYt=qJ>YwixqXE^UA\\e>Z>ir\\Pn\\vy?>kBq^i?hWx[jFn]QqoWwpIoIgiDgk`_^i^^Qg\\?>sBYcf@ojAinItAG][wn@_tuFvS>aQqtaxcYNqNFp^nsGW^SpawOqj?xM`t>`kQPa:_ZeFgRAp[g[Un`>pkNvsD`nFp^HV_jAbDqutWwgpZqFlinsVWZ\\^d@wyiXqhQq[YrAXc`Ng_F_KXjXQZ;`haHbFx_hVfPYoQwwmwmuauBILQSIsf^=BJcyVSH`]cmgE[[fnyFcIyrGX]AHTcT:Ev=KxCygoWWQqy@yHxGt\\gRECUIWGVuR]GxouuxgY=oBGLuN]RoMJBEV>`n:mn>LKtPuVdQt]xjQYLMk?]oPxyXmXSiVVYvYdPrdp=TQqmwVypiuuFlRqPt;LtmQR@=rHdOUmpF@J?`QodVDaL_`KnEVJYsCEl^]oi]rBHL`IujuQ<<s_IkvITL`QO<UFesWYqquw;XJAlN]=NJpRIqmwdXu\\jCMXElPNuoYAY]ikRUm`XqcqqquwXiM?tVFYxN=JBuKU\\UJlrgXUqptP]n=YvAykQYoZxmVAjPyTlUQWen?AN>TjAtK@iVMykA@thuqwqX?eX@TXMhlH<l[pYM<R[DmpdWTAsA=l:At[XRKLq[@m\\moKEYFIvvmKqyUuewo@NeiWYhyfyV[lRaenHeJPTkc]SmXtxMyMym\\ULMyVtIO?=xOAUA=yeIq>aYcHl]mqxDy^YlvMrneqtex<iY;AK<aUDAVCmV_xsvmRVtKpIQatY:AWRdPYmylylOAwTxQkdJF@PDmNaxR>qKP`MwLigVep@bx>ZGH]W`cnWo@UYsI@qcWSSaIhFGB<Ci=usGsT<_thiuuGXfoXgQuOagSUhRwUMMR;QYRST:[X_idQMxqegjaCTUeKPlKPmhhUuPMBmknPKRQkMhoUupH]mrDtrPwvHYmQX_DmTMpatUUuvIDMGAu:MsvmToMt\\EqLHK\\MQYTXFDPIDNv]Xo@qr@ySxVXHYhtYbHwNyxxmRd<mHiQFMYF=wlPq<\\lFEVBHsYAmGMTEXMHmXwxP^`rwDlSDvipJU`s>=TPXNdPpSeJKHlJplQ\\xydKqAkN]NSPnBakT=R\\]u`]T>ur\\DsX@Neanb]smemDlj\\mo^mQ=EneaWN=xT`jZpkEljl<X;IqxXMyEPFaLqAQuhm;lRoTpNHRLQjKhMr]rHmRN=SwpKBpSuIuy]yoUTMpye@sydL^=TouQD<JO^DKG:[T:;g:b]AUCGiL?Xw]RsMsWSYE_dA_WvGyFOcvgvDmVPexyOsQoEfgufQdwUTAm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7The situation is equivalent to that for the spring. To fulfill the equilibrium condition, NiMmJSJGRzYjIiIi and NiMmJSJGRzYjIiIj must be equal.NiMvJiUiRkc2IyIiIiZGJTYjIiIjThe damper is stretched byNiMvKiYlJkRlbHRhRyIiIiUieEdGJiwmJkYnNiNGJkYmJkYnNiMiIiMhIiI=and the difference of the velocities on both sides isNiMvKiYlJkRlbHRhRyIiIiUidkdGJiwmJkYnNiNGJkYmJkYnNiMiIiMhIiI=For the relation between the relative velocity and the damping force we assume linearityNiMvKiYsJiYlInZHNiMiIiJGKSZGJzYjIiIjISIiRiklImRHRikmJSJGR0YrAfter rearrangement we getNiMvJSN2MUcsJiomJiUiRkc2IyIiIyIiIiUiZEchIiJGKyYlInZHRilGKw==Now we have the four quadripole parameter for the matrix NiMmJSJBRzYjJSdkYW1wZXJHNiM+JiUkQTExRzYjJSdkYW1wZXJHIiIiNiM+JiUkQTEyRzYjJSdkYW1wZXJHIiIhNiM+JiUkQTIxRzYjJSdkYW1wZXJHKiYiIiJGKSUiZEchIiI=NiM+JiUkQTIyRzYjJSdkYW1wZXJHIiIiIn matrix form we getNiM+JiUiQUc2IyUnZGFtcGVyRy0lJ21hdHJpeEc2JSIiI0YrNyYmJSRBMTFHRiYmJSRBMTJHRiYmJSRBMjFHRiYmJSRBMjJHRiY=MassAs the last standard device, we consider the rigid body in Figure 8.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 8for a rigid body, the displacement and the velocity at the input gate and at the output gate are the same.NiMvJiUidkc2IyIiIiZGJTYjIiIjIn the equilibrium condition, we have to consider the inertiaNiMvJiUiRkc2IyIiIiwmJkYlNiMiIiNGJyomJSJtR0YnJiUiYUdGKkYnRic=We replace the acceleration by the velocity and getNiMvJiUiRkc2IyIiIiwmJkYlNiMiIiNGJyoqJSJtR0YnJSJJR0YnJSZPbWVnYUdGJyYlInZHRipGJ0YnNow we have the four quadripole parameters for the matrix NiMmJSJBRzYjJSVtYXNzRw==NiM+JiUkQTExRzYjJSVtYXNzRyIiIg==NiM+JiUkQTEyRzYjJSVtYXNzRyooJSJtRyIiIi0mJSJhRzYjRio2IyUidEdGKi0mJSJ2R0YuRi8hIiI=NiM+JiUkQTIxRzYjJSVtYXNzRyIiIQ==NiM+JiUkQTIyRzYjJSVtYXNzRyIiIg==In matrix form we getNiM+JiUiQUc2IyUlbWFzc0ctJSdtYXRyaXhHNiUiIiNGKzcmJiUkQTExR0YmJiUkQTEyR0YmJiUkQTIxR0YmJiUkQTIyR0YmQuadripole Parameter of a Vibration SourceIn some structures the vibration source is a very complex system that cannot easily be described analytically. But sometimes the impedance NiMmJSJSRzYjJSJzRw== of the vibration source is known, for example from the constructer of the machine.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 9For such a structure, we assume that the force NiMmJSJGRzYjIiIi which will be transmitted to the connected device at the output gate 1 can be measured. Additionally we assume that the structure is rigid. So we know that NiMvJiUidkc2IyIiISZGJTYjIiIi.The force that generates the vibration is thenNiM+JiUiRkc2IyIiISwmJkYlNiMiIiJGKyomJiUiUkc2IyUic0dGKyYlInZHRipGKyEiIg==In matrix form this yieldsNiMvLSUnbWF0cml4RzYjNyQ3IyYlIkZHNiMiIiE3IyYlInZHRisqJi1GJTYjNyQ3JCYmJSJBRzYjJSJzRzYkIiIiRjsmRjY2JEY7IiIjNyQmRjY2JEY+RjsmRjY2JEY+Rj5GOy1GJTYjNyQ3IyZGKjYjRjs3IyZGL0ZJRjs=The matrix of the quadripole parameter is thenNiM+JiUiQUc2IyUic0ctJSdtYXRyaXhHNiUiIiNGKzcmIiIiJiUiUkdGJiIiIUYtCombination of Standard DevicesA lot of different devices can be described by combinations of the standard devices spring, damper and mass. There are two principal ways to combine two devices.Serial ConnectionFirst the devices can be combined as a chain one behind the other as shown in Figure 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10This is called a serial connection.We have two devices.The device 1 has the input gate NiMtJSdtYXRyaXhHNiM3JDcjJiUiRkc2IyIiIjcjJiUidkdGKg== and the output gate NiMtJSdtYXRyaXhHNiM3JDcjJiUiRkc2IyIiIzcjJiUidkdGKg==.At the same time NiMtJSdtYXRyaXhHNiM3JDcjJiUiRkc2IyIiIzcjJiUidkdGKg== is the input gate of the device 2 and NiMtJSdtYXRyaXhHNiM3JDcjJiUiRkc2IyIiJDcjJiUidkdGKg== is the output gate of device 2.So we get the relationsNiMvLSUnbWF0cml4RzYjNyQ3IyYlIkZHNiMiIiI3IyYlInZHRisqJi1GJTYjNyQ3JCYmJSJBR0YrNiRGLEYsJkY2NiRGLCIiIzckJkY2NiRGO0YsJkY2NiRGO0Y7RiwtRiU2IzckNyMmRio2I0Y7NyMmRi9GRkYsNiMvLSUnbWF0cml4RzYjNyQ3IyYlIkZHNiMiIiM3IyYlInZHRisqJi1GJTYjNyQ3JCYmJSJBR0YrNiQiIiJGOSZGNjYkRjlGLDckJkY2NiRGLEY5JkY2NiRGLEYsRjktRiU2IzckNyMmRio2IyIiJDcjJkYvRkZGOQ==with the quadripole parameter NiMmJiUiQUc2IyIiIjYkJSJpRyUiakc=of device 1 and NiMmJiUiQUc2IyIiIzYkJSJpRyUiakc=of device 2. Joining both equations yieldsNiMvLSUnbWF0cml4RzYjNyQ3IyYlIkZHNiMiIiI3IyYlInZHRisqKC1GJTYjNyQ3JCYmJSJBR0YrNiRGLEYsJkY2NiRGLCIiIzckJkY2NiRGO0YsJkY2NiRGO0Y7RiwtRiU2IzckNyQmJkY3NiNGO0Y4JkZGRjo3JCZGRkY+JkZGRkBGLC1GJTYjNyQ3IyZGKjYjIiIkNyMmRi9GUUYsThe matrix of the quadripole parameter of the serial connection of two devices is the product of the matrices of the quadripole parameter of both single devices.NiMvJSJBRyomJkYkNiMiIiJGKCZGJDYjIiIjRig=.This function is defined in the following procedure for several serial connected devices.serialconnection:=proc()local AB,i;AB:=matrix(2,2,[1,0,0,1]);for i from 1 by 1 to nargs doAB:=multiply(AB,args[i]);od:end:Parallel ConnectionNow we consider the situation of two devices combined in parallel as shown in Figure 11.MFNWtKUb<ob<R=MDLCdNBpRhKb:RkOiSE\\ZRLCTJcDXoHuuxWsWQEU_iCvAEkmrk]EE;DtCCW?T<uC>cfq]fBuRcAFLaB>wd\\KbDeddObnED;cRK;d`;C\\_XJou[[t:CbJYcNcrlKI]wwqsxQWiVquuus;_rE[vlCuy]eIIIuawwadooYegI_eIY;yuyuyquT;vQyYyyxyuyuyiyYyYuytytIcYbYRoUxiuYuYuAKihwivivisypyWyqvaAf;UblIuh_eUyWygYkgrPSxDYEi]ikIxIwYvyYxyvymfROVDoYfuVD[S[AsxurWsXF?EkKfoCydQi@cCnqCvIxIwY>iUb[xWsXyuyuyuuQBv=BayGRcyYXyypwvpytYwxiw:PruuwwxXGhPPAudUogpyjyjy^\\qOd`waXG_JGvd@dKPwNOaSNjspnR>wW>yBybxNvMP]E>slYlD^xsymyIyYhxRalMoccYxIwitYty_yAyinIeHyiwytygqvQxEalPou<ve?`xJQpyQ^Df\\b@uInijYjd@dK<xxCpRFPmcdTAhsimqsqNXTyHExJ=lymymymS]VTILBLu[@t_ioIpYnYn=mjFDxWhx>\\L?ErquYoXTKMKN]o<iyNEldaTtDM<xwMdkBUV;\\MYDlsljm\\yxAWQiJpEtguYeQq\\HO[QpWPL<<WtQxSxVXHTHyrxlxkxygQqtItA]TN]t[PrOEn\\dtoYqoymfHLYYvZeJUHRgDX@ywxuxu`uaaL<AOpYt=eVyUuOLJDYjAtK@@VBqTHPJcPtrylwQXcLS;PkO=qd\\T^PQOpS@@vuaR]LJS]yylrqqwuxwXqVUhWjTyOyTYer]=kVEY_ilIAQ]aKTPL\\tmymysIQ`Am]hUs\\osPLLtU==p<MmhlvypY?iPFUj[ET?MoEXKkDytum:DLb=msLOAXvoLV>AkiuYuYuMqSudWxijy<O>QXZ<mwmxSYQNXvY=rwewoxtZlRKEMLLjBqylULM]TNxpd\\T^fmU``Sa`I^neYrYnyjxcbWfiAaX?lAfjCHd\\Im?awta_Mhuaiv?wmfnfSOwx_b[OjOfZPh_Hgbc`pAhZAndlghlIsaVixN_Mpny`vLXcTxkKWUYEwAwy[S@Kv>yUjsbW?E=CdMeSocDHuixQyeaY;uIYMYciFyCHOoBdeXG;vGMb]wxwWeNGXrYeimisidQmU[yRtWRAysvSxFighGtJAVq=tZGRoQVyKSEaVMaIkyT\\yCT]Bi=uuWCh;i:SCkUCumbIsExmysyvMmdyGyGyWhEi_qdgwhXQELuFG=FP;elkC_yvTUWggx]wEwAWQgUpEYvIxAIyOSCg[hJccxYrYkyjeyoytI=UPmvx;fV;wj]EjAR^yy[]CGyrPSrSyvxsxsWdHMIcCV;?w^YVYSyRkIC_C>[HM?FDSeTCHBMCjOB>iCp;uZYcY]y\\iDQ]UkostSwj[rJCsDsisqvUgHh_rH[RSytQGs`GywSi\\YC@IU>afkWVAQR[mraqfYoYtyivivi;etSufUhwGx@YERmICkcUixPaV;Lrm@s\\TkV=Y[ijNIy<TKf<JsUXHIQaXQJ=UD]xw=pH=vwYJ>MoHxLBIY\\PMchkI]Y\\YLyatwHR=pUwexOIoapmtlrexq`YwtYl;dUQum@hXmhspTQkarMtjGTMpTvFXPpPq`]Os\\rOlwNao`Yy:eMxxMFUXeXWleNmuXRTpRQVEhVtaNeqMDhWf]PvPYlxYQ\\tvXnTpmD\\yFyVxTx?xOvEN[tQ:Iw?poOxMStwjXxLPnCARvulhpv\\eosxvXXY[ijQlsqmngivQxUHaw?lnh`pLQchIcVYnioZh^bEh\\XyiyULctdQUFIfUWXFIHAmfkSwk_CywSHOeaCbH[Hn[UIGiJ_cw]rw]e_mdSmFwqinAdM?EVag^KSqSV]WeIsYjWwT_w]kSxoFYUd;?IsQeF[rCHsQaVZlSxpN=JsQmF\\rCyt^[xpuSYgDP]JnyuyuyqyaxawIsqa[VghrpytytypijYjY^]n>gJx_SWyXIv[aojfwwWdCfqaFat^g_nwwyl<oanInIfhX`dBQhbqvBWepnv_Wpmxm]orFHa`Am]oalIlI`ypypyhdNicqfunXyhYqyiwiwiUxfXHip?u[wZIHirpvJatRh`?h]pXpnv\\<adgvIayayCy=y=QgxoxTYWi?i\\QcQoUtEwhYiiqy>yFxCXJIRAcSwcxNQSUyVYgY@_CSKxAwIvIFU[ydUbEeDeyV`=TtscTkVWOfDeH]iGqaurmRI_hp?ENeddEYmex^mtxkTcEE?us^uhaYgq=WOwwwKEYaiZ]SkGvTUhPGGdWdheVAGtUmUoSVUkFcERAgClEg`SwwSh>suU=GOkWsuHRExRmXD_hO?ehix`CUAKuVoieaFaUTFwwZ]baOsioGFQHEaGhmEx=y[IysuWQixKycx]xfYhIqYmisqShZQg`UCUWxvgwd]sYEubSTIgVoqgXuSoctNuvWwXXYXIiIQgIYMWkuyMuetadlYhUYGEQHxAyAyIteRCCusiDxuXP=DSqXRgtLCW@YUHmVtmFGSS?EUACeyOghcwcOfJIBHahVcET?IECHowuQ_DRIBBgSV_fP?Rb=TPmguagoodTgdgMwwmUb]voseraDScTVubgMeDUCjIHOCf]cCOIvFUDAmbvkTeocuuUdWtd_GV=X_weTGthIYIstTUEokvgOUqAvEOEYEY_iDYmtVUXGqEUOg@gCUkhvQxEYb]]BQUeKyRQ[HiywWuTiidOiIdicbebJqE@yincXxGy`YUsevOgxNOVBOYmAutUwgwHMaSmcfoGVaKUsyHPIw=imf=V:=xHQNQMUAekTUu;pQbImCYrPutnaSN\\RLeLntXGhPQxYu]S=AxepLU]nwDv?=rmylhXom@JrOm^GlDGwNx[xgweweEN`Dv]sYnWa[`Ntb@qpPq?NgGiZ=iah`wHno<ixm>qFNxdX]sorqqh_ajiH_^n_>?dOIvsQ\\DQebP\\?amO`dOOrNXdHGsPoukwrWF\\FvxIpatAw?v\\V?\\_PjTAm`Afqi_cYltWf_NjX@_mfbc>\\QflvOycyn]o`k`tRHv=yjY^ijIrYvyryrOYytYwiXbyPwZ`npYgAGdOQ^WphoqneGwN?dOFxuWmnI_?oa?wtON\\??]<OqJaqXG_c@sHXp`VnmAeuPi]I_?@^kXZyAwZ_wW_dQps>vnY>gmgbV_qLapOHhoNyvPeGhuiin<vygXwDqbMxi>icWYkDOyvPcS^ncI\\Aao>qgQwoH`ysXw<atLvub>vJH_D`]Bn`RAf=@_Ov\\iAhwixQyko^kZxtL>rBGllOpFIpIY_N`kwfw[Xr\\Iy:iy@W]g_tdqeCGq?q\\U_fQwieXioHat>y<FlK^qfAphO`lh]wOsYwsUO]SV]LqkxFdFIdmqaAIuAqgHgr`a\\RPpvaoVVagvklNd]o`Yaj>oyL?kAHnmhew`jGgnw^xN?by>o<GZwvkSN[=Nyv@hk`tUOwEXxNqwsa^T?o_hwSgmtyjhXoc?kMQmrIlwoe[HgDFkcPtFNc_humIZPWthh`]p\\wftj^\\CHxTGh?i\\;Nbu_`ZARYBMqef=SGYUcOiFST\\GbxsgRGIOOYWur=iGoerTwVOqtqkikic>cFEcGn?dRAGJssu_Xm]C?ohO;cEaD\\KRuOY]Sux?wK=ydOW:ow:uebQb:yHXcgEUBDUDO=xJkfQ[X\\ACtYwowtXUGasGtmsOgC=ewdiD\\GyQUFmgvvyE`SGyKsGsCiMv_ahM_FOyvu]CnUgeUTIUiaihfcY:YvbKDieyautO[rAesNswUidMUGeMsyeTcEiRiii_Vh=SYMrO_w`aWoeW[mS:CbGCVpKtiQhEqGduUfEh?qIuIuIQhFGSFKxkwcw]gccGjaDQQSCiEdisuGx=QwWahYYBDavKKXFeHcUtGLmAQOlHMv<Yj]OWEq\\uyMiX?lkClmtaqXeYogfhNh?@dgqmI_^Joc^gZSVtFW`Gnq>@dkXs[GebI]:IifNhoIsIoilnk>Ouf>[EYkW>xMnl_>fBArE_wOa\\_>h>GvTYgihqgqpUapIpqgh^riqA>[JAkkG]sNh^_stnrVYhIiayRpYhpuseefx;WtAt[WRcqeKSF@=V@]irYuiuiwQsesgVSIp]wAMih_X]wsEYcVayyQwt_yvwyxYyIIIaaEKqRu?wFcVOwgFibQkURYim[sjSRSIu=mCs[FKyUbkCy=yK_SIKusWrHSIr]SYcTnwuxUyOAw@oRXmXSiVqiuquUnaUu?i;EstGC[UhIqIuMhDGdUYCi[ijIfAoEtiwiuYUch;CgDyr:GT]oRgahMqScMGOExfYhIqwmwsxSxIyIymrw]xhqtUuWwGy`YeWyS:ME?OuaeinKI<QGysCvqvqsiKkeAqbpWcXeH=SF>awEiGq_ejmIhGFH_UkerOhqqqUWyjm<N=MnyAwt`YIUPv@wCiVPHU`emomtKyr>pTxiQxAy]ipSLrNYuh=UGPyRMYcinyTxSxsj=STXunmnRUVGhP`Am]mK?=q?<ka`mlMSLDVoXKZexMUnkuLJTrL\\TuXyhYqImQsavpusqTQiiUj@K;eprIrAtMNepHhRHAt\\hM[hQjpxTYWQMYhdyKUV@tyTiQY`JV]lVxLEdmBQy=xMvAJ]YN_QmNHlg@qrtOv@x<<kaIVBMumuswTWaXpitnXPYdlK[`c]_w:wmRNiWIs\\auEp_t@wLYcifwsvlj>gJImaomSojlVr\\VohPqd>^@qdrXjjxuvqvqVxj?_Mqoy@dbnwch[x?^hhptHuhIyNpZg?[<F]oNwCP]YiyhUTEg<GtJauaoc^Urr=e?SXVGwTsFpqwksrVSDyySmKIbKhUsWvGdnwVBirowwxWyx[yjYrY;rCgRQcUN[BOoI`]sR[gGQqgqR[PN[U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11This is called a parallel connection. Again we have two devices. But now the situation is a bit more complicated.Device 1 has the input gate NiMtJSdtYXRyaXhHNiM3JDcjJiUiRkc2IyUjYTFHNyMmJSJ2R0Yq and the output gate NiMtJSdtYXRyaXhHNiM3JDcjJiUiRkc2IyUjYTJHNyMmJSJ2R0Yq.Device 2 has the input gate NiMtJSdtYXRyaXhHNiM3JDcjJiUiRkc2IyUjYjFHNyMmJSJ2R0Yq and the output gate NiMtJSdtYXRyaXhHNiM3JDcjJiUiRkc2IyUjYjJHNyMmJSJ2R0Yq.At last ,the input gate of the total device should be NiMtJSdtYXRyaXhHNiM3JDcjJiUiRkc2IyIiIjcjJiUidkdGKg== and the output gate NiMtJSdtYXRyaXhHNiM3JDcjJiUiRkc2IyIiIzcjJiUidkdGKg==.The velocities at the input gate must all be equal. That means NiMvJiUidkc2IyUjYTFHJkYlNiMiIiI= and NiMvJiUidkc2IyUjYjFHJkYlNiMiIiI=. The same is valid for the output gate: NiMvJiUidkc2IyUjYTJHJkYlNiMiIiM= and NiMvJiUidkc2IyUjYjJHJkYlNiMiIiM=The force on both gates of the parallel connection is the sum of the forces at all single devices. That means NiMvJiUiRkc2IyIiIiwmJkYlNiMlI2ExR0YnJkYlNiMlI2IxR0Yn and NiMvJiUiRkc2IyIiIywmJkYlNiMlI2EyRyIiIiZGJTYjJSNiMkdGLA==.Now we use the impedance form of our quadripoles. We can use the above defined procedure chain2impedance to convert the quadripole parameter of the chain form NiMmJSJBRzYjJSJhRw== and NiMmJSJBRzYjJSJiRw== into the quadripole parameter of the impedance form NiMmJSJaRzYjJSJhRw== and NiMmJSJaRzYjJSJiRw==.NiMvJiUiWkc2IyUiYUctJTBjaGFpbjJpbXBlZGFuY2VHNiMmJSJBR0YmNiMvJiUiWkc2IyUiYkctJTBjaGFpbjJpbXBlZGFuY2VHNiMmJSJBR0YmWith this we can writeNiMvLSUnbWF0cml4RzYjNyQ3IyYlIkZHNiMlI2ExRzcjJkYqNiMlI2EyRyomLUYlNiM3JDckJiYlIlpHNiMlImFHNiQiIiJGPCZGNzYkRjwiIiM3JCZGNzYkRj9GPCZGNzYkRj9GP0Y8LUYlNiM3JDcjJiUidkc2I0Y8NyMmRko2I0Y/Rjw=NiMvLSUnbWF0cml4RzYjNyQ3IyYlIkZHNiMlI2IxRzcjJkYqNiMlI2IyRyomLUYlNiM3JDckJiYlIlpHNiMlImJHNiQiIiJGPCZGNzYkRjwiIiM3JCZGNzYkRj9GPCZGNzYkRj9GP0Y8LUYlNiM3JDcjJiUidkc2I0Y8NyMmRko2I0Y/Rjw=Remember that all velocities at the input gate are the same, and the same holds at the output gate. Combination of theses equations yieldsNiMvLCYtJSdtYXRyaXhHNiM3JDcjJiUiRkc2IyUjYTFHNyMmRis2IyUjYTJHIiIiLUYmNiM3JDcjJkYrNiMlI2IxRzcjJkYrNiMlI2IyR0YyLCYqJi1GJjYjNyQ3JCYmJSJaRzYjJSJhRzYkRjJGMiZGRTYkRjIiIiM3JCZGRTYkRkxGMiZGRTYkRkxGTEYyLUYmNiM3JDcjJiUidkc2I0YyNyMmRlc2I0ZMRjJGMiomLUYmNiM3JDckJiZGRjYjJSJiR0ZJJkZcb0ZLNyQmRlxvRk8mRlxvRlFGMkZSRjJGMg==orNiMvLSUnbWF0cml4RzYjNyQ3IyYlIkZHNiMiIiI3IyZGKjYjIiIjKiYtRiU2IzckNyQmJSJaRzYkRixGLCZGNzYkRixGMDckJkY3NiRGMEYsJkY3NiRGMEYwRiwtRiU2IzckNyMmJSJ2R0YrNyMmRkVGL0Yswith the matrix of the quadripole parameter of the impedance form of the total device as the sum of the matrices of the quadripole parameter of the impedance form of all the single devicesNiMvLSUnbWF0cml4RzYjNyQ3JCYlIlpHNiQiIiJGLCZGKjYkRiwiIiM3JCZGKjYkRi9GLCZGKjYkRi9GLywmLUYlNiM3JDckJiZGKjYjJSJhR0YrJkY7Ri43JCZGO0YyJkY7RjRGLC1GJTYjNyQ3JCYmRio2IyUiYkdGKyZGR0YuNyQmRkdGMiZGR0Y0Riw=.Finally we get the quadripole parameter of the chain form of the total device by convert ing the quadripole parameter of the impedance form by use of the procedure impedance2chain.NiMvJSJBRy0lMGNoYWluMmltcGVkYW5jZUc2IyUiWkc=This process is also defined in the following procedure for several parallel connected devices.parallelconnection:=proc()local ZA,AB,i;ZA:=matrix(2,2,[0,0,0,0]):for i from 1 by 1 to nargs doZA:=matadd(ZA,chain2impedance(args[i]),1,1);od:AB:=impedance2chain(ZA);end:Some typical combinations of standard devicesThere are several combination of the above defined standard devices often used in practice. Some of them are shown here.KELVIN-VOIGT ModelThis model is used to describe visco-elastic devices as parallel connection of an ideal elastic spring with an ideal viscous damper as shown in Figure 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Figure 12The quadripole parameters of this model are calculated by use of the procedure parallelconnection.The input parameters for this procedure are the matrices of the quadripole parameter of the damperevalm(A[damper]);and the springevalm(A[spring]);The matrix of the quadripole parameter of the KELVIN-VOIGT model is consequentlyA[KELVINVOIGT]:=parallelconnection(A[damper],A[spring]);Additionally we will consider the impedance of such a device. This can be derived different ways. First we can consider the quadripole parameter for the case that the velocity at the output gate is NiMmJSJ2RzYjIiIj=0.We will not do this here but we consider the relation between the force and the velocity. The force which passes through the KELVIN-VOIGT model is given byNiM+LSYlIkZHNiMlLEtFTFZJTlZPSUdURzYjJSJ0RywmLSYlI0YxRzYjJSdzcHJpbmdHRikiIiItJkYuNiMlJ2RhbXBlckdGKUYxAnd the impedance is the quotient of the force and the velocityNiM+JiUiUkc2IyUsS0VMVklOVk9JR1RHLSUnZXhwYW5kRzYjKiYtJiUiRkdGJjYjJSJ0RyIiIi0mJSJ2RzYjRjFGLyEiIg==We see this is the sum of the impedances of the two single devices.MAXWELL ModelThis is another model which is used to describe viscous elastic devices. Here an ideal elastic spring and an ideal viscous damper are connected as a chain in series as shown in Figure 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Figure 13Such a device is only able to transmit dynamic forces.The quadripole parameter of this model are calculated by use of the procedure serialconnection.The input parameters for this procedure are again the matrices of the quadripole parameter of the damperevalm(A[damper]);and the springevalm(A[spring]);The matrix of the quadripole parameter of the MAXWELL model is consequentlyA[MAXWELL]:=serialconnection(A[damper],A[spring]);Again we will also consider the impedance of such a device. We assume for this that the velocity on the output gate of this device is NiMvJiUidkc2IyIiIyIiIQ==. The force must go directly through the device. That means that the force on the spring and the force on the damper are eqaul: NiMvJiUiRkc2IyUnZGFtcGVyRyZGJTYjIiIi and NiMvJiUiRkc2IyUnc3ByaW5nRyZGJTYjIiIi. The velocity of the damper is then given byNiM+LSYmJSJ2RzYjIiIiNiMlL01BWFdFTExfZGFtcGVyRzYjJSJ0RyomLSYlIkZHRihGLEYpJSJkRyEiIg==The displacement of the spring isNiM+LSYmJSJ4RzYjIiIiNiMlL01BWFdFTExfc3ByaW5nRzYjJSJ0RyomLSYlIkZHRihGLEYpJSJrRyEiIg==Because we assume harmonic motion, we get for the velocity in the springNiM+LSYmJSJ2RzYjIiIiNiMlL01BWFdFTExfc3ByaW5nRzYjJSJ0RyooLSYmJSJ4R0YoRipGLEYpJSJJR0YpJSZPbWVnYUdGKQ==The velocity at the input gate of the total device is the sum of the single velocitiesNiM+LSYmJSJ2RzYjIiIiNiMlKE1BWFdFTExHNiMlInRHLCYtJkYmNiMlL01BWFdFTExfc3ByaW5nR0YsRiktJkYmNiMlL01BWFdFTExfZGFtcGVyR0YsRik=And the impedance is the quotient of the force and the velocityNiM+JiUiUkc2IyUoTUFYV0VMTEctJSlzaW1wbGlmeUc2IyomLSYlIkZHNiMiIiI2IyUidEdGMC0mJiUidkdGL0YmRjEhIiI=Spring-Damper-Mass-SystemNext we consider how a simple spring-damper-mass-system is typically used to describe the simplest structural dynamic system as a single-degree-of-freedom system. This system is shown in Figure 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Figure 14This model is the parallel connection of a spring and a damper and these two devices together in series with the mass. The above formalism yields the following for the total deviceA[spring_damper_mass]:=simplify(serialconnection(A[mass],parallelconnection(A[spring],A[damper])));The impedance of this device can be deduced when we assume that the velocity at gate 2 must be 0NiM+JiYlInZHNiMiIiM2IyUzc3ByaW5nX2RhbXBlcl9tYXNzRyIiIQ==From the definition of the quadripole parameter we know the relationNiMvLSUnbWF0cml4RzYjNyQ3IyYlIkZHNiMiIiI3IyYlInZHRisqJi1GJTYjNyQ3JCYlIkFHNiRGLEYsJkY2NiRGLCIiIzckJkY2NiRGOkYsJkY2NiRGOkY6RiwtRiU2IzckNyMmRio2I0Y6NyMmRi9GRUYsor written for this special case as two equationsNiM+JSVyZWwxRy8mJiUiRkc2IyIiIjYjJTNzcHJpbmdfZGFtcGVyX21hc3NHLCYqJiYmJSJBR0YrNiRGKkYqRiomJkYoNiMiIiNGK0YqRioqJiZGMDYkRipGNkYqJiYlInZHRjVGK0YqRio=NiM+JSVyZWwyRy8mJiUidkc2IyIiIjYjJTNzcHJpbmdfZGFtcGVyX21hc3NHLCYqJiYmJSJBR0YrNiQiIiNGKkYqJiYlIkZHNiNGM0YrRipGKiomJkYwNiRGM0YzRiomJkYoRjdGK0YqRio=The solution of this two equations yields the force at the output gate NiMmJiUiRkc2IyIiIzYjJTNzcHJpbmdfZGFtcGVyX21hc3NH and the velocity at the input gate NiMmJiUidkc2IyIiIjYjJTNzcHJpbmdfZGFtcGVyX21hc3NH, both dependent on the force at the input gate NiMmJiUiRkc2IyIiIjYjJTNzcHJpbmdfZGFtcGVyX21hc3NH.sols:=solve({rel1,rel2},{F[2][spring_damper_mass],v[1][spring_damper_mass]});assign(sols);At last we calculate the relation between the force and the velocity at the input gate to get the impedanceR[spring_damper_mass] := simplify(F[1][spring_damper_mass]/v[1][spring_damper_mass]);4-Parametrical MAXWELL ModelAt last we consider a model which is composed by four single standard devices as shown in Figure 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Figure 15This model is the parallel connection of two MAXWELL models, which are themselves serial connections of a spring and a damper. The damper on the left line has damping resistance NiMmJSJkRzYjJSJhRw==, the spring on the left line has stiffness NiMmJSJrRzYjJSJhRw==. The damper and the spring on the right line have the damping resistance NiMmJSJkRzYjJSJiRw== and the stiffness NiMmJSJrRzYjJSJiRw==. We use the information about the MAXWELL model for the two partial devices on the left and on the right line to get the matrices of the quadripole parameterA[a]:=subs({k=k[a],d=d[a]},evalm(A[MAXWELL]));A[b]:=subs({k=k[b],d=d[b]},evalm(A[MAXWELL]));The matrix of the quadripole parameter for the total device is now easy to calculate as a parallel connection of NiMmJSJBRzYjJSJhRw== and NiMmJSJBRzYjJSJiRw==A[MAXWELL2]:=simplify(parallelconnection(A[a],A[b]));The impedance of this device is the sum of the impedance of the MAXWELL device on the left line and that on the right line, same as in the parallel connection of a damper with a springR[a]:=simplify(subs({k=k[a],d=d[a]},R[MAXWELL]));R[b]:=simplify(subs({k=k[b],d=d[b]},R[MAXWELL]));NiM+JiUiUkc2IyUpTUFYV0VMTDJHLSUpc2ltcGxpZnlHNiMsJiZGJTYjJSJhRyIiIiZGJTYjJSJiR0YvExampleNow we will consider an example. As shown in Figure 16 we have a a special machine as the source of the vibration. All values here and in the following are given in N, m, kg and s. Consequently the impedances are given in Ns/m. Please note: These numerical values are academic examples 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 16We have the input gate given byinput:=matrix([[F[0]],[v[0]]]);and the output gate given byoutput:=matrix([[F[2]],[v[2]]]);The impedance of the source shall be given by its real partNiM+JiUncmVhbF9SRzYjJSJzRyoqIicrK0QiIiIqJCUjUGlHIiIjRiolImZHRi0sKCIoKytEJ0YqKigiJXZcRipGK0YqRi5GLSEiIiomRiwiIiVGLkY1RipGMw==and its imaginary partNiM+JiUnaW1hZ19SRzYjJSJzRywkKiwiJisrJiIiIiUjUGlHRislImZHRissJiIlK0QhIiIqJkYsIiIjRi1GMkYrRissKCIoKytEJ0YrKigiJXZcRisqJEYsRjJGK0YtRjJGMComRiwiIiVGLUY5RitGMEYwSo the impedance NiMmJSJSRzYjJSJzRw== isNiM+JiUiUkc2IyUic0csJiYlJ3JlYWxfUkdGJiIiIiomJSJJR0YrJiUnaW1hZ19SR0YmRitGKw==Let's consider graphs of these functions.PRsr:=plot(Re(R[s]),f=0..100,color=red,legend="real part"):PRsi:=plot(Im(R[s]),f=0..100,color=green,legend="imaginary part"):PRsa:=plot(abs(R[s]),f=0..100,color=blue,thickness=2,legend="absolute value"):PRsp:=plot(argument(R[s]),f=0..100,color=cyan,legend="argument"):Most of the time, the absolute value is the most interesting, so we draw it with a thick line.display(PRsr,PRsi,PRsa,title="Impedance of the Vibration Source");The argument of this function is shown in the next picturedisplay(PRsp,title="Impedance of the Vibration Source");The matrix of the quadripole parameter of the vibration source follows from aboveA[s]:=matrix(2,2,[1,R[s],0,1]);Next we consider the foundation, the recipient. We assume the following numerical values and use the definition for the elastic half-space defined above.NiM+JSVzb2lsRzYmLyUiR0ciKisrKysjLyUjbXVHKiYiIiMiIiIiIzUhIiIvJSRyaG9HIiUrPy8lImFHRiw=The impedance of the recipient is thenR[r]:=complexextension(subs({soil,sub1},R[ELASTIC_HALF_SPACE]));This result is best shown graphically. The first picture shows the real part, the imaginary part and the absolute value.vw:=-2E7..2E7:PEr:=plot(Re(R[r]),f=0..100,vw,color=red,legend="real part"):PEi:=plot(Im(R[r]),f=0..100,vw,color=green,legend="imaginary part"):PEa:=plot(abs(R[r]),f=0..100,vw,color=blue,thickness=2,legend="absolute value"):PEp:=plot(argument(R[r]),f=0..100,-Pi..Pi,color=cyan,legend="argument"):display(PEr,PEi,PEa,title="Impedance of the Ground");The next picture shows the angle between the real part and the imaginary part of the impedance.display(PEp,title="Impedance of the Ground");Now we consider some devices which are arranged between the machine and the soil for vibration control. Here we assume that the excitation force NiMmJSJGRzYjIiIh for all the following examples is identical. That means that there is no feedback interaction from the structure to the source of the excitation. Otherwise this problem would be much more complicated and not so easily solved without more details about the excitation.Rigid ConnectionRigid connection means that the machine stands on the ground without any device. So we have the relationNiMvLSUnbWF0cml4RzYjNyQ3IyYlIkZHNiMiIiI3IyYlInZHRisqJi1GJTYjNyQ3JEYsIiIhNyRGNUYsRiwtRiU2IzckNyMmRio2IyIiIzcjJkYvRjxGLA==That means for the matrix of the quadripole parameterA[rigid]:=matrix([[1,0],[0,1]]);The total structure is a serial connection of the source with a rigid connection.A[1]:=serialconnection(A[s],A[rigid]);Of course this is the same as the matrix of the quadripole parameter of the source itself. The relation between the values of the input gate NiMmJSJGRzYjIiIh, NiMmJSJ2RzYjIiIh and the values at the output gate NiMmJSJGRzYjIiIj, NiMmJSJ2RzYjIiIj iseq[1]:=input=A[1]&*output;evalm(eq[1]);This yields for the values of the output gatesol[1]:=linsolve(A[1],input);This meansF_rigid[2]:=sol[1][1,1];v_rigid[2]:=sol[1][2,1];At last we use our information about the impedance of the output gateNiM+JiUjZXFHNiMiIiMvJiUoRl9yaWdpZEdGJiomJiUiUkc2IyUickciIiImJSh2X3JpZ2lkR0YmRjA=The solution of this equation yields the velocity at the input gate dependent on the force at the input gatesol[2]:=simplify(solve(eq[2],v[0]));For the velocity on the output gate we get v_r[2]:=simplify(subs(v[0]=sol[2],v_rigid[2]));We use this derivation later again, so it makes sense to define this in form of a proceduretrans:=proc(A,input,R)local sol1,sol2,v1,F1,F2,v2,vs2,eq;F1:=input[1,1]:v1:=input[2,1]:sol1:=linsolve(A,input);F2:=sol1[1,1];v2:=sol1[2,1];eq:=F2=R*v2;sol2:=simplify(solve(eq,v1));vs2:=simplify(subs(v1=sol2,v2));end:We show the result for the ground velocity graphicallyPErr:=plot(Re(v_r[2]/F[0]),f=0..100,color=red,legend="real part"):PEri:=plot(Im(v_r[2]/F[0]),f=0..100,color=green,legend="imaginary part"):PEra:=plot(abs(v_r[2]/F[0]),f=0..100,color=blue,thickness=2,legend="absolute value"):display(PErr,PEri,PEra,title="Ground Velocity in m/s");Vibration Isolation by a SpringNext we consider the situation that a spring is set between the machine and the ground . Then we have the matrix of the quadripole parameter of the spring with the stiffnessNiM+JiUia0c2IyIiIyImKysiA[ex]:=subs({sub1,k=k[2]},evalm(A[spring]));and the matrix of the quadripole parameter of the serial connection of the vibration source and the springA[2]:=serialconnection(A[s],A[ex]);We get the velocity at the output gate by use of the above defined procedurev_s[2]:=trans(A[2],input,R[r]);The most important point is now the comparison between the velocity in the case of the rigid position of the machine on the ground with the velocity with the spring between machine and ground.In blue, the velocity of the case of the rigid connection is displayed.PEsa:=plot(abs(v_s[2]/F[0]),f=0..100,color=cyan,thickness=2,legend="absolute value spring"):display(PEsa,PEra,title="Ground Velocity in m/s");Most interesting is normally the question, what is the relation between the absolute value of the velocity at the output gate in case of the rigid support and the isolated support by use of a spring. This is usually shown in a special logarithmic scale. For details please see the literature, for example [1]. We calculate the quotient between the velocity of the ground in case of rigid connection and that in case of supporting by use of any device, here the spring. Then we have to calculate the logarithm and multiply by 20. This result has no physical dimension. It is called the insertion loss for the inserted device. To emphasize this kind of presentation, we use the pseudo dimension dB (decibel). Although this property belongs to the inserted device, it depends on the impedance of the vibration source and the impedance of the recipient, here the ground. Strictly speaking, it is not possible to give the insertion loss of a pure device but only in combination with its use.Here we calculate the insertion loss of the spring.dv_rs:=simplify(20*log[10](abs(v_r[2]/v_s[2])));PErsa:=plot(dv_rs,f=0..100,color=cyan,legend="spring",title="Insertion Loss in dB",thickness=2):display(PErsa);Vibration Isolation by a DamperNext we consider the situation that a damper is set between the machine and the ground . Of course this idea is more theoretically interesting, because the damper itself cannot carry the static load of a machine. In reality there must be some device that can do that. We have the matrix of the quadripole parameter of the damper with the damping residenceNiM+JiUiZEc2IyIiJCIjSQ==A[fx]:=subs({sub1,d=d[3]},evalm(A[damper]));and the matrix of the quadripole parameter of the serial connection of the vibration source and the damperA[3]:=serialconnection(A[s],A[fx]);We get the velocity at the output gate by use of the above defined procedurev_d[2]:=trans(A[3],input,R[r]);The following diagram shows the ground velocities for all the previously considered situationsPEda:=plot(abs(v_d[2]/F[0]),f=0..100,color=magenta,thickness=2,legend="absolute value damper"):display(PEda,PEsa,PEra,title="Ground Velocity in m/s");Again we calculate the insertion loss of the damperdv_rd:=simplify(20*log[10](abs(v_r[2]/v_d[2])));PErda:=plot(abs(dv_rd),f=0..100,color=magenta,legend="damper",title="Insertion Loss in dB",thickness=2):display(PErda,PErsa);It seems that the damper, especially in the range of lower frequencies, gives the better reduction of the vibration. Only for higher frequencies, in this example from about 50 Hz, the spring support yields a higher insertion loss than the spring. Unfortunately the damper itself cannot carry the static load, so we need something as a spring. Let's consider what happens when we use a combination of a spring and a damper.Vibration Isolation by a KELVIN-VOIGT DeviceNext we consider the situation that a combination of a spring and a damper according the KELVIN-VOIGT model is set between the machine and the ground . Then we have the matrix of the quadripole parameter of the device with the spring stiffness NiMmJSJrRzYjIiIj and the damping residence NiMmJSJkRzYjIiIk.A[gx]:=subs({sub1,d=d[3],k=k[2]},evalm(A[KELVINVOIGT]));and the matrix of the quadripole parameter of the serial connection of the vibration source and the KELVIN-VOIGT device isA[4]:=serialconnection(A[s],A[gx]);We get again the velocity at the output gate by use of the above defined procedurev_KV[2]:=trans(A[4],input,R[r]);The following diagram shows the ground velocitiesPEKVa:=plot(abs(v_KV[2]/F[0]),f=0..100,color=brown,thickness=2,legend="absolute value KELVIN-VOIGT"):display(PEKVa,PEda,PEsa,PEra,title="Ground Velocity in m/s");Again we calculate the insertion loss of the devicedv_rKV:=simplify(20*log[10](abs(v_r[2]/v_KV[2])));PErKVa:=plot(dv_rKV,f=0..100,color=brown,legend="KELVIN-VOIGT",title="Insertion Loss in dB",thickness=2):display(PErKVa,PErda,PErsa);As expected this solution is somewhere between the support by a spring and the support by a damper. The advantage of the KELVIN-VOIGT device against the single spring is the fact that there is not so big an incursion in the insertion loss.Vibration Isolation by a MAXWELL DeviceNext we consider the situation that a combination of a spring and a damper according the MAXWELL model with the spring stiffness NiMmJSJrRzYjIiIj and the damping residence NiMmJSJkRzYjIiIk is set between the machine and the ground . As with the single damper, this device cannot carry static loads and is not capable for practical use of supporting a machine.We have the matrix of the quadripole parameter of the deviceA[hx]:=subs({sub1,d=d[3],k=k[2]},evalm(A[MAXWELL]));and the matrix of the quadripole parameter of the serial connection of the vibration source and the springA[5]:=serialconnection(A[s],A[hx]);The velocity at the output gate is nowv_MW[2]:=trans(A[5],input,R[r]);The following diagram shows the ground velocitiesPEMWa:=plot(abs(v_MW[2]/F[0]),f=0..100,color=green,thickness=2,legend="absolute value MAXWELL"):display(PEMWa,PEKVa,PEda,PEsa,PEra,title="Ground Velocity in m/s");We calculate the insertion loss of the devicedv_rMW:=simplify(20*log[10](abs(v_r[2]/v_MW[2])));PErMWa:=plot(dv_rMW,f=0..100,color=green,legend="MAXWELL",title="Insertion Loss in dB",thickness=2):display(PErMWa,PErKVa,PErda,PErsa);Up to now this model is the best one for elimating ground vibrations. Unfortunately it cannot be used because it cannot carry static loads.Vibration Isolation by Double Spring Device with one DamperNext we consider the situation that a combination of a spring, an additional mass and a second spring in series and parallel to this damper is set between the machine and the ground . This device is shown in Figure 17.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 17The spring stiffness shall beNiM+JiUia0c2IyUjYTZHKiYiIiMiIiImRiU2I0YpRio=NiM+JiUia0c2IyUjYjZHKiYiIiMiIiImRiU2I0YpRio=and the damping resistance is again NiMmJSJkRzYjIiIk.The mass shall beNiM+JiUibUc2IyIiJyIiIg==The matrices of the single quadripole parameter arefirst spring:Am:=subs(k=k[a6],evalm(A[spring]));massAn:=subs(m=m[6],evalm(A[mass]));second springAo:=subs(k=k[b6],evalm(A[spring]));damperAp:=subs(d=d[3],evalm(A[damper]));The matrix of the quadripole parameter of the serial connection of the spring, the mass and the second spring isAmno:=serialconnection(Am,An,Ao);And the parallel connection from this with the damper isAmnop:=parallelconnection(Amno,Ap);This yields with the source in seriesA[6]:=subs(sub1,serialconnection(A[s],Amnop));The velocity at the output gate isv_m[2]:=trans(A[6],input,R[r]);The following diagram shows the ground velocities for all the up to now situationsPEma:=plot(abs(v_m[2]/F[0]),f=0..100,color=red,thickness=2,legend="absolute value double spring with one damper"):display(PEma,PEMWa,PEKVa,PEda,PEsa,PEra,title="Ground Velocity in m/s");We calculate the insertion loss of the devicedv_rm:=simplify(20*log[10](abs(v_r[2]/v_m[2])));PErma:=plot(dv_rm,f=0..100,color=red,legend="double elastic support",title="Insertion Loss in dB",thickness=2):display(PErma,PErMWa,PErKVa,PErda,PErsa);This devise is not so easy to classify, because to do this we must consider a lot of different combinations of spring stiffness, damping resistances and Additionally masses. The combination we used in this example seems not to be a very good solution.Vibration Isolation by Double Spring-Damper DeviceNext we consider the situation that a combination of a KELVIN-VOIGT device, an additional mass and a second KELVIN-VOIGT device in series is set between the machine and the ground as shown in Figure 18. 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18The spring stiffness shall beNiM+JiUia0c2IyUjYTdHKiYiIiMiIiImRiU2I0YpRio=NiM+JiUia0c2IyUjYjdHKiYiIiMiIiImRiU2I0YpRio=and the damping resistance isNiM+JiUiZEc2IyUjYTdHKiYiIiMiIiImRiU2IyIiJEYqNiM+JiUiZEc2IyUjYjdHKiYiIiMiIiImRiU2IyIiJEYqThe mass shall bem[7]:=1;The matrices of the single quadripole parameter arefirst KELVIN-VOIGT device:Aq:=subs({k=k[a7],d=d[a7]},evalm(A[KELVINVOIGT]));massAr:=subs(m=m[7],evalm(A[mass]));second KELVIN-VOIGT deviceAs:=subs({k=k[b7],d=d[b7]},evalm(A[KELVINVOIGT]));The matrix of the quadripole parameter of the serial connection of the fist KELVIN-VOIGT device, mass and the second KELVIN-VOIGT device isAqrs:=serialconnection(Aq,Ar,As);This yields with the source in seriesA[7]:=subs(sub1,serialconnection(A[s],Aqrs));The velocity at the output gate isv_z[2]:=trans(A[7],input,R[r]);The following diagram shows the ground velocitiesPEza:=plot(abs(v_z[2]/F[0]),f=0..100,color=maroon,thickness=2,legend="absolute value double spring-damper device"):display(PEza,PEma,PEMWa,PEKVa,PEda,PEsa,PEra,title="Ground Velocity in m/s");We calculate the insertion loss of the devicedv_rz:=simplify( 20*log[10](abs(v_r[2]/v_z[2])) ):
PErza:=plot(dv_rz,f=0..100,color=maroon,legend="double spring-damper device",title="Insertion Loss in dB",thickness=2):display(PErza,PErma,PErMWa,PErKVa,PErda,PErsa);Consider that this device has the same additional mass as the device above. The only difference between both models is the fact that the damper here is divided in two, just as the spring, so the motion of the additional mass is directly damped in this model. The advantage is easy to see in the insertion loss. We get with this device for frequencies higher than about 60 Hz the best values for the insertion loss. Such devices are often used for the isolation of machines in very sensitive areas, for example, in ships. The vibration of the motor of a ship otherwise can easily be transmitted through all the ship.But once again: Remember that all numerical values are only academic examples. Real devises have more complicated properties than we can show here. For exdample, the spring itself is a mass, every real damper has a certain stiffness, and I don't believe that one can find in reality a vibration source with such a simple form of the impedancethe as described here .Literature[1] M. Heckl, H.A. M\374ller, Taschenbuch der Technischen Akustik, p. 571-595, Springer-Verlag, 2nd Edition, Berlin 1994[2] E. Seidel, Wirksamkeit von Konstruktionen zur Schwingungs- und K\366rperschalld\344mmung in Maschinen und Ger\344ten, Schriftenreihe der Bundesanstalt f\374r Arbeitsschutz und Arbeitsmedizin, Dortmund/Berlin 1999