The Terrace on the Park Building in New York was originally built for the 1964 World’s Fair. After the fair was over, the building was converted into halls for catered events. The halls on the building's cantilevered main floors had dining areas and dance floors. As soon as the halls were used, guests immediately started experiencing noticeable vibrations, including sloshing waves in drinks and bouncing chandeliers.
The building’s unique design features an elliptical promenade suspended six floors above the ground on four steel columns. The columns support a grid of floor girders and an elliptical ring girder. The girders in turn support radial cantilevered floor beams. Modifications had been made to divide the main ballroom into four dining and dancing halls. Individual halls were arranged with dining tables near the center of the hall. Bandstands and dance floors were located at the tip of the cantilevered floors. Initial analysis performed on each quadrant of the ballroom found the natural frequency to be 2.3 Hz, which corresponded to the beat of the music that was being played in the dance halls.
After considering various expensive and/or impractical solutions, this problem was eventually solved in 1988 by the use of tuned mass dampers (TMDs) to dampen the vibrations. A case study1 published in 1988 gave details of the problem and its solution. Staff at Maplesoft decided to see if MapleSim could be used to solve this problem, how long it would take, and if MapleSim could reach an even better solution.
The first step was to extract data from the report and use it to re-create the original model within MapleSim. The model developers used sliding mass and spring damper components to represent the floor of the ballroom and the tuned mass dampers. Using the spring and damping constants from the paper gave results similar to those reported by the authors.
The next step was to see if MapleSim could be used to find better values for the damping and spring constants that would reduce the vibration even further. To find their optimal values, these constants were made parameters of the model. The parametrized model, along with the corresponding equations that were generated automatically by MapleSim, was loaded into the MapleSim optimization template. An objective function was created to find the optimal values for both constants that would result in the least amount of vibration. The optimal values were found to be different than those used in the original solution. When compared to results using the original constants, the new spring and damping constants resulted in less vibration than those used in the original solution.
From start to finish, such problems typically take over a week to solve. The entire process took less than a day in MapleSim, and resulted in a better solution.
1Webster, A.C., and Vaicajtis, R. “Application of tuned mass dampers to control vibrations of composite-floor systems.” Engineering Journal of the American Institute of Steel Construction, vol. 29 (1992): 116–124.