Limit Imposed Loads on SSSS Rectangular Panels Forced to Vibrate Under a Uniformly Distributed Load

Résumé

Abstract This paper presents the determination of limit imposed loads on ssss rectangular panel that is forced to vibrate under uniformly distributed load. By employing the principles of elasticity, the total potential energy functional of a rectangular plate under forced vibration is obtained. This functional is minimized with respect to the deflection function. The minimization gives the governing equation of the plate. A general deflection function that satisfies the governing equation is obtained after integrating the governing equation. With the general deflection, the boundary conditions of ssss plate are satisfied and a peculiar deflection function for ssss plate is obtained. This deflection function is substituted into the total potential energy functional earlier obtained and the outcome minimized with respect to the coefficient of the deflection to get the formula for the deflection coefficient. The obtained deflection coefficient is substituted into stress formulas and the outcomes rearranged to get formulas for limit imposed loads that satisfied the requirements of allowable deflection and yield stress. Using these formulas limit imposed loads for various aspect ratios, forcing frequency ratio and thicknesses are calculated and presented in tables. From the obtained results it is obvious that square panels are stronger than rectangular panels. It is also obvious that strength of panels reduces as the forced frequency ratio increase from zero to 1. It is also seen that panels whose spans are up to 1m should be designed with thickness less than 8mm.

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