Transverse vibration of thin solid and annular circular plate with attached discrete masses

Abstract

Circular plates have many engineering applications. These are commonly found in spacecrafts, missiles, land based vehicles, underwater vessels and structures. In many situations, these plates carry loads at eccentric positions. Therefore, one must know the fundamental frequencies of the plates with different boundary conditions with point masses placed at any arbitrary position. Leissa [1] and Laura et al. [2] have reviewed analytically most of the early works in the area of free vibration of circular plate with concentrated mass attached at the centre of the plate. Bambill et al. [3] determined the fundamental frequency of vibration of circular plate carrying a concentrated mass at an arbitrary position with different boundary conditions using variational approach with Rayleigh Ritz formulation. The present study is concerned with the determination of the fundamental frequency of vibration of solid and annular circular plate with different boundary conditions and with point mass attached at an arbitrary position using finite element analysis (FEA). The fundamental frequency of vibration of clamped and simply supported solid circular plate with point mass attached at the centre determined by other researchers [1–3] are compared with the present study. A good agreement is obtained in the values of fundamental frequency. This methodology has been extended to determine the fundamental frequency of solid and annular plate with different boundary condition with varying point masses placed at an arbitrary position.