Engineering: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=164
en-us2014 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemMon, 21 Apr 2014 07:17:13 GMTMon, 21 Apr 2014 07:17:13 GMTNew applications in the Engineering categoryhttp://www.mapleprimes.com/images/mapleapps.gifEngineering: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=164
Collision detection between toolholder and workpiece on ball nut grinding
http://www.maplesoft.com/applications/view.aspx?SID=153477&ref=Feed
<p>In this worksheet a collision detection performed to determine the minimum safety distance between a tool holder and ball nut on grinding manufacturing. A nonlinear quartic equation system have to be solved by <em>Newton's</em> and <em>Broyden's</em> methods and results are compared with <em>Maple fsolve()</em> command. Users can check the different results by embedded components and animated 3D surface plot.</p><img src="/view.aspx?si=153477/Collision_Detection_image1.jpg" alt="Collision detection between toolholder and workpiece on ball nut grinding" align="left"/><p>In this worksheet a collision detection performed to determine the minimum safety distance between a tool holder and ball nut on grinding manufacturing. A nonlinear quartic equation system have to be solved by <em>Newton's</em> and <em>Broyden's</em> methods and results are compared with <em>Maple fsolve()</em> command. Users can check the different results by embedded components and animated 3D surface plot.</p>153477Mon, 23 Dec 2013 05:00:00 ZGyörgy HegedûsGyörgy HegedûsClassroom Tips and Techniques: Mathematical Thoughts on the Root Locus
http://www.maplesoft.com/applications/view.aspx?SID=153452&ref=Feed
Under suitable assumptions, the roots of the equation <em>f</em>(<em>z, c</em>) = 0, namely, <em>z</em> = <em>z</em>(<em>c</em>), trace a curve in the complex plane. In engineering feedback-control, such curves are called a <em>root locus</em>. This article examines the parameter-dependence of roots of polynomial and transcendental equations.<img src="/view.aspx?si=153452/thumb.jpg" alt="Classroom Tips and Techniques: Mathematical Thoughts on the Root Locus" align="left"/>Under suitable assumptions, the roots of the equation <em>f</em>(<em>z, c</em>) = 0, namely, <em>z</em> = <em>z</em>(<em>c</em>), trace a curve in the complex plane. In engineering feedback-control, such curves are called a <em>root locus</em>. This article examines the parameter-dependence of roots of polynomial and transcendental equations.153452Tue, 29 Oct 2013 04:00:00 ZDr. Robert LopezDr. Robert LopezSymmetry of two-dimensional hybrid metal-dielectric photonic crystal within MAPLE
http://www.maplesoft.com/applications/view.aspx?SID=151383&ref=Feed
<p>Hybrid structures were made by assembling monolayers (MLs) of closely packed colloidal microspheres on a metal-coated glass substrate . In fact, this architecture is one of several realizations of hybrid plasmonic-photonic crystals (PHs), which differ in photonic crystals dimensionality and metal ﬁlm corrugation [1,2].</p>
<p>The main challenge to us were exploring of those properties of structures which are caused by their space symmetry. In particular, it was necessary to establish the so-called "rules of selection", i.e. the list of the allowed transitions between electronic states of different symmetry and energy that can be induced by light of varying polarization. Additional interest for us was to demonstrate the possibilities of MAPLE within this specific field.</p><img src="/view.aspx?si=151383/440fb9a2994e797b26c18564d860131b.gif" alt="Symmetry of two-dimensional hybrid metal-dielectric photonic crystal within MAPLE" align="left"/><p>Hybrid structures were made by assembling monolayers (MLs) of closely packed colloidal microspheres on a metal-coated glass substrate . In fact, this architecture is one of several realizations of hybrid plasmonic-photonic crystals (PHs), which differ in photonic crystals dimensionality and metal ﬁlm corrugation [1,2].</p>
<p>The main challenge to us were exploring of those properties of structures which are caused by their space symmetry. In particular, it was necessary to establish the so-called "rules of selection", i.e. the list of the allowed transitions between electronic states of different symmetry and energy that can be induced by light of varying polarization. Additional interest for us was to demonstrate the possibilities of MAPLE within this specific field.</p>151383Thu, 05 Sep 2013 04:00:00 ZOlga V. DvornikOlga V. DvornikWavelet analysis of the blood pressure and pulse frequency measurements with Maple
http://www.maplesoft.com/applications/view.aspx?SID=149420&ref=Feed
<p>A significant part of medical signals, or observations, is non-stationary, discrete time sequences. Thus, the computer methods analysis, as well as refinement and compression, are very helpful as for the problems of recognition and detection of their key diagnostic features. We are going to illustrate here this statement with examples of very common, and even routine medical measurements of blood pressure as well as pulse rate and with possibilities of Maple.<br />The package of Discrete Wavelet transforms (DWT) within Maple 16 [1] was recently added as new research software just for such tasks. The practical testing of this package was additional goal of present study.</p><img src="/view.aspx?si=149420/4b9024ee653d2c7be8febb717b1df52a.gif" alt="Wavelet analysis of the blood pressure and pulse frequency measurements with Maple" align="left"/><p>A significant part of medical signals, or observations, is non-stationary, discrete time sequences. Thus, the computer methods analysis, as well as refinement and compression, are very helpful as for the problems of recognition and detection of their key diagnostic features. We are going to illustrate here this statement with examples of very common, and even routine medical measurements of blood pressure as well as pulse rate and with possibilities of Maple.<br />The package of Discrete Wavelet transforms (DWT) within Maple 16 [1] was recently added as new research software just for such tasks. The practical testing of this package was additional goal of present study.</p>149420Sun, 14 Jul 2013 04:00:00 ZIrina A. DanishewskaIrina A. DanishewskaDispersion of arterial pulse waves
http://www.maplesoft.com/applications/view.aspx?SID=145362&ref=Feed
<p>In this paper, we are primarily focusing on the arterial pulse waves, more exactly even their dispersion. It is important because presence of this together with the non-linearity generates the conditions of existence of localized waveforms. Thus, we would like to obtain here the dispersion law for pulse waves with Maple.</p><img src="/view.aspx?si=145362/arterialpulsewaves_thumb.png" alt="Dispersion of arterial pulse waves" align="left"/><p>In this paper, we are primarily focusing on the arterial pulse waves, more exactly even their dispersion. It is important because presence of this together with the non-linearity generates the conditions of existence of localized waveforms. Thus, we would like to obtain here the dispersion law for pulse waves with Maple.</p>145362Tue, 02 Apr 2013 04:00:00 ZShiyan S.I.Shiyan S.I.Fuzzy Sets in Examples
http://www.maplesoft.com/applications/view.aspx?SID=141714&ref=Feed
<p>This worksheet has been created first as a practical part of short course on the pattern recognition theory for my students. It had intended to their introduce, including visually impressions, with fuzzy sets and basic rules of simple operations with them. MAPLE tools were extremely comfortable for such a task and this experience may be useful for community colleagues.</p><img src="/view.aspx?si=141714/fuzzy-sets.jpg" alt="Fuzzy Sets in Examples" align="left"/><p>This worksheet has been created first as a practical part of short course on the pattern recognition theory for my students. It had intended to their introduce, including visually impressions, with fuzzy sets and basic rules of simple operations with them. MAPLE tools were extremely comfortable for such a task and this experience may be useful for community colleagues.</p>141714Sat, 22 Dec 2012 05:00:00 ZProf. Gennady P. ChuikoProf. Gennady P. ChuikoGeneration and Interaction of Solitons
http://www.maplesoft.com/applications/view.aspx?SID=141102&ref=Feed
<p>Classic computer experiments demonstrating the generation of solitons first time, has been published by N. J. Zabusky and M. D. Kruskal in 1965. Considered that was an earlier idea of Enrico Fermi. In 2006, Frank Wang has created a demonstration on the same subject with Maple tools . We would like to show both the origin and the interaction of Korteweg de Vries solitons as a development of approach of above cited publications.</p><img src="/view.aspx?si=141102/fig.jpg" alt="Generation and Interaction of Solitons" align="left"/><p>Classic computer experiments demonstrating the generation of solitons first time, has been published by N. J. Zabusky and M. D. Kruskal in 1965. Considered that was an earlier idea of Enrico Fermi. In 2006, Frank Wang has created a demonstration on the same subject with Maple tools . We would like to show both the origin and the interaction of Korteweg de Vries solitons as a development of approach of above cited publications.</p>141102Tue, 04 Dec 2012 05:00:00 ZS.I. ShyanS.I. ShyanClassroom Tips and Techniques: Fourier Series and an Orthogonal Expansions Package
http://www.maplesoft.com/applications/view.aspx?SID=134198&ref=Feed
The OrthogonalExpansions package contributed to the Maple Application Center by Dr. Sergey Moiseev is considered as a tool for generating a Fourier series and its partial sums. This package provides commands for expansions in 17 other bases of orthogonal functions. In addition to looking at the Fourier series option, this article also considers the Bessel series expansion.<img src="/view.aspx?si=134198/thumb.jpg" alt="Classroom Tips and Techniques: Fourier Series and an Orthogonal Expansions Package" align="left"/>The OrthogonalExpansions package contributed to the Maple Application Center by Dr. Sergey Moiseev is considered as a tool for generating a Fourier series and its partial sums. This package provides commands for expansions in 17 other bases of orthogonal functions. In addition to looking at the Fourier series option, this article also considers the Bessel series expansion.134198Mon, 14 May 2012 04:00:00 ZDr. Robert LopezDr. Robert LopezVan der Waals equation of state (I)
http://www.maplesoft.com/applications/view.aspx?SID=134131&ref=Feed
<p>This is the first of a series of Maple worksheets developed for teaching chemical thermodynamics.</p>
<p>Given the van der Waals' constants, this worksheet plots: a) the PV van der Waals' isotherms as-given by the equation, b) the PV isotherms based on Maxwell's construction, c) the compressibility factor isotherms based on the low pressure series expansion, and d) the compressibility factor isotherms based on Maxwell's construction. All procedures are independent and were developed to work with the classic interface.</p><img src="/view.aspx?si=134131/436827\41b8ef0a763a603085145e0cf8cd9b47.gif" alt="Van der Waals equation of state (I)" align="left"/><p>This is the first of a series of Maple worksheets developed for teaching chemical thermodynamics.</p>
<p>Given the van der Waals' constants, this worksheet plots: a) the PV van der Waals' isotherms as-given by the equation, b) the PV isotherms based on Maxwell's construction, c) the compressibility factor isotherms based on the low pressure series expansion, and d) the compressibility factor isotherms based on Maxwell's construction. All procedures are independent and were developed to work with the classic interface.</p>134131Sat, 12 May 2012 04:00:00 ZChristian Viales MonteroChristian Viales MonteroAnalysis of basic equations of state (II)
http://www.maplesoft.com/applications/view.aspx?SID=134136&ref=Feed
<p>This is the second of a series of Maple worksheets developed for teaching chemical thermodynamics.</p>
<p>Given a two-constant equation of state (the worksheet includes the most common), this worksheet calculates its critical point, reduced form, volumetric coefficients, Boyle's temperature, virial expansion and internal pressure.</p><img src="/view.aspx?si=134136/436839\ae00ea34ed62fd64822a9ee2652b3c1c.gif" alt="Analysis of basic equations of state (II)" align="left"/><p>This is the second of a series of Maple worksheets developed for teaching chemical thermodynamics.</p>
<p>Given a two-constant equation of state (the worksheet includes the most common), this worksheet calculates its critical point, reduced form, volumetric coefficients, Boyle's temperature, virial expansion and internal pressure.</p>134136Sat, 12 May 2012 04:00:00 ZChristian Viales MonteroChristian Viales MonteroClassroom Tips and Techniques: An Undamped Coupled Oscillator
http://www.maplesoft.com/applications/view.aspx?SID=129521&ref=Feed
<p>Even for just three degrees of freedom, an undamped coupled oscillator modeled by the ODE system <em>M</em> ü + <em>K</em> u = 0 is difficult to solve analytically because, ultimately, a cubic characteristic equation has to be solve exactly. Instead, we simultaneously diagonalize <em>M</em> and <em>K</em>, the mass and stiffness matrices, thereby uncoupling the equations, and obtaining an explicit solution.</p><img src="/view.aspx?si=129521/thumb.jpg" alt="Classroom Tips and Techniques: An Undamped Coupled Oscillator" align="left"/><p>Even for just three degrees of freedom, an undamped coupled oscillator modeled by the ODE system <em>M</em> ü + <em>K</em> u = 0 is difficult to solve analytically because, ultimately, a cubic characteristic equation has to be solve exactly. Instead, we simultaneously diagonalize <em>M</em> and <em>K</em>, the mass and stiffness matrices, thereby uncoupling the equations, and obtaining an explicit solution.</p>129521Tue, 10 Jan 2012 05:00:00 ZDr. Robert LopezDr. Robert LopezClassroom Tips and Techniques: Simultaneous Diagonalization and the Generalized Eigenvalue Problem
http://www.maplesoft.com/applications/view.aspx?SID=128444&ref=Feed
<p>This article explores the connections between the generalized eigenvalue problem and the problem of simultaneously diagonalizing a pair of <em>n × n</em> matrices.</p>
<p>Given the <em>n × n</em> matrices <em>A</em> and <em>B</em>, the <em>generalized eigenvalue problem</em> seeks the eigenpairs <em>(lambda<sub>k</sub>, x<sub>k</sub>)</em>, solutions of the equation <em>Ax = lambda Bx</em>, or <em>(A - lambda B) x = 0</em>. If <em>B</em> is nonsingular, the eigenpairs of <em>B<sup>-1</sup> A</em> are solutions. If a matrix <em>S</em> exists for which<em> S<sup>T</sup> A S = Lambda</em>, and <em>S<sup>T</sup> B S = I</em>, where <em>Lambda</em> is a diagonal matrix and <em>I</em> is the <em>n × n</em> identity, then <em>A</em> and <em>B</em> are said to be <em>diagonalized simultaneously</em>, in which case the diagonal entries of <em>Lambda</em> are the generalized eigenvalues for <em>A</em> and <em>B</em>. Such a matrix <em>S</em> exists if <em>A</em> is symmetric and <em>B</em> is positive definite. (Our definition of positive definite includes symmetry.)</p><img src="/view.aspx?si=128444/thumb.jpg" alt="Classroom Tips and Techniques: Simultaneous Diagonalization and the Generalized Eigenvalue Problem" align="left"/><p>This article explores the connections between the generalized eigenvalue problem and the problem of simultaneously diagonalizing a pair of <em>n × n</em> matrices.</p>
<p>Given the <em>n × n</em> matrices <em>A</em> and <em>B</em>, the <em>generalized eigenvalue problem</em> seeks the eigenpairs <em>(lambda<sub>k</sub>, x<sub>k</sub>)</em>, solutions of the equation <em>Ax = lambda Bx</em>, or <em>(A - lambda B) x = 0</em>. If <em>B</em> is nonsingular, the eigenpairs of <em>B<sup>-1</sup> A</em> are solutions. If a matrix <em>S</em> exists for which<em> S<sup>T</sup> A S = Lambda</em>, and <em>S<sup>T</sup> B S = I</em>, where <em>Lambda</em> is a diagonal matrix and <em>I</em> is the <em>n × n</em> identity, then <em>A</em> and <em>B</em> are said to be <em>diagonalized simultaneously</em>, in which case the diagonal entries of <em>Lambda</em> are the generalized eigenvalues for <em>A</em> and <em>B</em>. Such a matrix <em>S</em> exists if <em>A</em> is symmetric and <em>B</em> is positive definite. (Our definition of positive definite includes symmetry.)</p>128444Tue, 06 Dec 2011 05:00:00 ZDr. Robert LopezDr. Robert LopezPlastic method of structural analysis
http://www.maplesoft.com/applications/view.aspx?SID=102534&ref=Feed
<p>This worksheet contains a step-by-step method for the analysis of 2D frames with all kind of boundary conditions or joints between elements.</p>
<p>In each step, determined by the creation of a new plastic hinge, numeric information (displacements, reactions and stresses) and graphic information (beam diagrams and deformed shape) are obtained.</p>
<p>Finally, accumulated beam diagrams and accumulated deformed shapes are also obtained.<br /><br /></p><img src="/view.aspx?si=102534/Image1.PNG" alt="Plastic method of structural analysis" align="left"/><p>This worksheet contains a step-by-step method for the analysis of 2D frames with all kind of boundary conditions or joints between elements.</p>
<p>In each step, determined by the creation of a new plastic hinge, numeric information (displacements, reactions and stresses) and graphic information (beam diagrams and deformed shape) are obtained.</p>
<p>Finally, accumulated beam diagrams and accumulated deformed shapes are also obtained.<br /><br /></p>102534Mon, 14 Mar 2011 04:00:00 ZAntolín Lorenzana IbánAntolín Lorenzana IbánLead and Lag Root Locus Design
http://www.maplesoft.com/applications/view.aspx?SID=87682&ref=Feed
<p>Root locus plots can provide a great deal of information about a system. Maple's DynamicSystems package provides the RootContourPlot and the RootLocusPlot commands for visualizing the behavior of a system when a control parameter is varied. This worksheet shows how systems with multiple free parameters can be analyzed.</p>
<p>This application is part of the <A HREF="/contact/webforms/ControlTheory/">Classroom Content: Control Theory</A> collection.</p><img src="/view.aspx?si=87682/thumb.jpg" alt="Lead and Lag Root Locus Design" align="left"/><p>Root locus plots can provide a great deal of information about a system. Maple's DynamicSystems package provides the RootContourPlot and the RootLocusPlot commands for visualizing the behavior of a system when a control parameter is varied. This worksheet shows how systems with multiple free parameters can be analyzed.</p>
<p>This application is part of the <A HREF="/contact/webforms/ControlTheory/">Classroom Content: Control Theory</A> collection.</p>87682Sun, 14 Nov 2010 05:00:00 ZMaplesoftMaplesoftThe Relationship between Pole Locations and Time-Domain Performance for a Second Order System
http://www.maplesoft.com/applications/view.aspx?SID=87681&ref=Feed
<P>An interactive worksheet that goes through the effect of pole locations on a second order system. The worksheet visually shows how changing the poles in the S-plane effects the step response in the time domain.
<p>This application is part of the <A HREF="/contact/webforms/ControlTheory/">Classroom Content: Control Theory</A> collection.</p><img src="/view.aspx?si=87681/thumb.jpg" alt="The Relationship between Pole Locations and Time-Domain Performance for a Second Order System" align="left"/><P>An interactive worksheet that goes through the effect of pole locations on a second order system. The worksheet visually shows how changing the poles in the S-plane effects the step response in the time domain.
<p>This application is part of the <A HREF="/contact/webforms/ControlTheory/">Classroom Content: Control Theory</A> collection.</p>87681Fri, 21 May 2010 04:00:00 ZMaplesoftMaplesoftThe Effect of a Zero on a Second Order System's Performance
http://www.maplesoft.com/applications/view.aspx?SID=87680&ref=Feed
<p>An interactive worksheet that goes through the effect of a zero on a second order system. The worksheet visually shows how changing the poles or zero in the S-plane effects the step response in the time domain.</p>
<p>This application is part of the <A HREF="/contact/webforms/ControlTheory/">Classroom Content: Control Theory</A> collection.</p><img src="/view.aspx?si=87680/thumb4.jpg" alt="The Effect of a Zero on a Second Order System's Performance" align="left"/><p>An interactive worksheet that goes through the effect of a zero on a second order system. The worksheet visually shows how changing the poles or zero in the S-plane effects the step response in the time domain.</p>
<p>This application is part of the <A HREF="/contact/webforms/ControlTheory/">Classroom Content: Control Theory</A> collection.</p>87680Fri, 21 May 2010 04:00:00 ZMaplesoftMaplesoftThe “Gray Box” Approach
http://www.maplesoft.com/applications/view.aspx?SID=32963&ref=Feed
<p>The proverbial "black box" refers to computing tools where the user is shielded from the inner algorithms and interacts with the system from a purely and input and output point of view. Most modern engineering modeling and simulation software are based on this notion. The "gray box" is a term that describes the symbolic approach to engineering computation that offers distinct benefits in education and research. This paper offers an introduction to the tools and techniques of successfully deploying symbolic tools. The Maple system will be used as the software context.</p><img src="/view.aspx?si=32963/thumb.jpg" alt="The “Gray Box” Approach" align="left"/><p>The proverbial "black box" refers to computing tools where the user is shielded from the inner algorithms and interacts with the system from a purely and input and output point of view. Most modern engineering modeling and simulation software are based on this notion. The "gray box" is a term that describes the symbolic approach to engineering computation that offers distinct benefits in education and research. This paper offers an introduction to the tools and techniques of successfully deploying symbolic tools. The Maple system will be used as the software context.</p>32963Fri, 08 May 2009 04:00:00 ZMaplesoftMaplesoftResolucion de la ecuacion de placas planas de germain-lagrange
http://www.maplesoft.com/applications/view.aspx?SID=19182&ref=Feed
RESOLUCION EFECTUADA EN LA CATEDRA MECANICA APLICADA III DE INGENIERIA CIVIL DE LA UNF.<img src="/applications/images/app_image_blank_lg.jpg" alt="Resolucion de la ecuacion de placas planas de germain-lagrange" align="left"/>RESOLUCION EFECTUADA EN LA CATEDRA MECANICA APLICADA III DE INGENIERIA CIVIL DE LA UNF.19182Mon, 02 Mar 2009 00:00:00 ZProf. Ing.Oscar BarretoProf. Ing.Oscar BarretoResolucion de la ecuacion de navier
http://www.maplesoft.com/applications/view.aspx?SID=19181&ref=Feed
RESOLUCION DE LA ECUACION DE AIRY CON MAPLE<img src="/view.aspx?si=19181/1.jpg" alt="Resolucion de la ecuacion de navier" align="left"/>RESOLUCION DE LA ECUACION DE AIRY CON MAPLE19181Mon, 02 Mar 2009 00:00:00 ZProf. Ing.Oscar BarretoProf. Ing.Oscar BarretoOrthogonal Functions, Orthogonal Polynomials, and Orthogonal Wavelets series expansions of function
http://www.maplesoft.com/applications/view.aspx?SID=7256&ref=Feed
The worksheet includes all the best known continuous orthogonal series expansions in the closed form. It demonstrates the use of Maple to evaluate expansion of a function by Fourier, Hartley, Fourier-Bessel, Orthogonal Rational Tangent, Rectangular, Haar Wavelet, Walsh, Slant, Piece-Linear-Quadratic, Associated Legandre, Orthogonal Rational, Generalized sinc, Sinc, Sinc Wavelet, Jacobi, Chebyshev first kind, Chebyshev second kind, Gegenbauer, Generalized Laguerre, Laguerre, Hermite, and classical polynomials orthogonal series. Also the worksheet demonstrates how to create new orthonormal basis of functions by using the Gram-Schmidt orthogonalization process by the example of Slant, and Piece-Linear-Quadratic orthonormal functions creating.<img src="/view.aspx?si=7256/thumb.gif" alt="Orthogonal Functions, Orthogonal Polynomials, and Orthogonal Wavelets series expansions of function" align="left"/>The worksheet includes all the best known continuous orthogonal series expansions in the closed form. It demonstrates the use of Maple to evaluate expansion of a function by Fourier, Hartley, Fourier-Bessel, Orthogonal Rational Tangent, Rectangular, Haar Wavelet, Walsh, Slant, Piece-Linear-Quadratic, Associated Legandre, Orthogonal Rational, Generalized sinc, Sinc, Sinc Wavelet, Jacobi, Chebyshev first kind, Chebyshev second kind, Gegenbauer, Generalized Laguerre, Laguerre, Hermite, and classical polynomials orthogonal series. Also the worksheet demonstrates how to create new orthonormal basis of functions by using the Gram-Schmidt orthogonalization process by the example of Slant, and Piece-Linear-Quadratic orthonormal functions creating.7256Wed, 18 Feb 2009 00:00:00 ZDr. Sergey MoiseevDr. Sergey Moiseev