Vibration analysis of rectangular plates resting on four rigid supports

Abstract

Purpose This paper aims to thoroughly investigate the free vibration characteristics of rectangular plates resting on symmetrically distributed four rigid supports by using a finite element (FE) method. Design/methodology/approach ANSYS parametric design language was used to generate the FE models and to run the analysis. The FE models were initially validated and were then used to solve for the plate first natural frequency and mode shape. The effect of the plate aspect ratio and support location on the free vibration properties of the plate was thoroughly studied by conducting several FE runs. Finally, simple empirical formulas were developed to conveniently calculate the plate first natural frequency based on the geometric parameters and support type, as well as support locations. Those well-formulated equations were in a great match with the FE data. Findings The results showed that the plate first natural frequency and mode shape are highly affected by the plate size and support locations. Specifically, the natural frequency deceases as the plates becomes larger. Also, the bending behavior of the first mode is highly affected by the support location, which results in a significant change in the natural frequency of the plate structure. In addition, the presently formulated empirical formulas are faithfully able to predict the natural frequency of the plate based on the geometric parameters and support location. Originality/value This paper provides numerous new data on the vibration properties of the rectangular plate resting on rigid supports. Also, it provides a simple way to easily calculate the natural frequency of this plate problem, unlike the very limited and complicated analytical solutions available in literature.