Free vibrational analysis of square plate under different boundary conditions using ANSYS and MATLAB

Abstract

Vibration is a mechanical phenomenon where a body/member oscillates about an equilibrium point. Vibration of plates is a special case problem in mechanical field. Plate is a very basic and simple structure to study the structural behaviour, mechanical properties, etc. A surface of any plane undergoes huge amount of vibration which might cause instability to the structure and may result in a failure. This surface is divided into square plates and analysis of such square plate is studied in this paper. This square plate needs to be constrained in such a way that the whole structure will not only be stable but also eliminates the unwanted resonant frequency. To eliminate the state of resonance, it is very important to identify the natural frequency of a plate under different boundary conditions. This paper mainly focuses on identifying natural frequency of a plate constrained in various manners. This paper also compares ANSYS results with the theoretical results using MATLAB. As a result of this comparison, a slight variation in values are obtained but no significant trend is observed. The results obtained by MATLAB are obtained from theoretical formulations. For this study, Modal analysis is considered to find the natural frequencies of an aluminum isotropic square plate. For MATLAB calculations, Navier solution is used to determine the natural frequency for different modes (m, n). The effect of different boundary conditions on the natural frequencies and mode shapes are also investigated.