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

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.

Vibrations Analysis of Rectangular Plates with Clamped Corners

“…(17) and Eq. (18), respectively. As this eigenvalue is a function of β and β , then it is a function of plate aspect ratio b/a and Poisson's ratio ν only.…”

“…Raju et al [16] and Rao et al [17] studied the natural frequencies of point-supported elastic plates using nite element method. Pitarresi and Kunz [18,19] developed a simple technique using two-dimensional nonlinear least-squares t, and nite element simulations, to study the natural frequency of plates having point supports. Recently, Gharaibeh et al [20,21] employed the assumed mode method to evaluate the fundamental natural frequency of corner-supported plates using an electronic package.…”

Optimal Pick-up Locations for Transport and Handling of Limp Materials

“…In all the above vibration problems, the objective function was computed using the Rayleigh-Ritz method. Pitarresi et al [22] presented a simple technique that uses a two-dimensional nonlinear least-squares fit of natural frequency versus support location data for rapid estimation of optimal support locations for vibrating plates. Roschke [23] used an iterative method based on Powell's conjugate directions to find optimal pick-up locations that minimize the absolute value of principle stresses in beams and plates.…”

Optimal Pick-up Locations for Transport and Handling of Limp Materials

“…In all these vibration problems, the objective function was computed using the Rayleigh-Ritz method. Pitarresi et al [15] presented a simple technique that uses a two-dimensional nonlinear leastsquares fit of natural frequency versus support location data for rapid estimation of optimal support locations for vibrating plates. Roschke [ 17] used an iterative method based on Powell's conjugate directions to find optimal pick-up locations that minimize the absolute value of principle stresses in beams and plates.…”