A Simple Technique for the Rapid Estimation of the Optimal Support Locations for a Vibrating Plate

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Abstract
This paper is aimed at presenting a simple technique for the rapid estimation of the optimal point support locations of vibrating plates. Using a two-dimensional nonlinear least-squares fit of natural frequency versus support location data, along with the concept of response surfaces, a difficult design optimization problem involving changing boundary conditions is transformed to a much simpler, approximate form. By using classical optimization theory, the estimated optimal location of the support can then be readily found. The computations for the formation of the response function and its optimum can be readily carried out on a personal computer using a spreadsheet program. The validity of this approach is demonstrated through a number of examples using analytical, computational, and experimental data. The technique is well suited to preliminary design investigations where a rapid but accurate estimation of the support location is required. Finally, a key advantage of the proposed method is that it can be used with data from any analytical, computational, or experimental effort, including any combination of the above.

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