Large Amplitude Vibration Analysis of Circular and Annular Plates by Meshless Local Petrov-Galerkin (MLPG) Method

In this paper, Meshless Local Petrov-Galerkin method (MLPG) is extended for large-amplitude (geometrically nonlinear) vibration analysis of circular and annular plates. Plates with thin and constant thickness are considered. Due to thin thickness of the plate, dynamic nonlinear formulations are based on Kirchhoff plate theory and von Kármán strains. In-plane displacement and inertia are both considered in the formulation. The coupled nonlinear equilibrium equations, corresponding to in-plane and transverse variables are derived by virtual work principle. A nonlinear local weak form is derived from Petrov-Galerkin weighted residuals. MLS approximation is used for shape function construction and approximation of the displacement. The bending and membrane stiffness matrices of the plate are evaluated using a Gauss integration method. This nonlinear vibration problem is solved as a nonlinear eigenvalue problem. Numerical results of circular and annular plates for two different radius ratios are presented to demonstrate efficiency and accuracy of the proposed method. To our knowledge this is the first time that MLPG method is extended for large-amplitude vibration analysis of plates.

کلیدواژه ها:

meshless ، MLPG ، large amplitude ، vibration ، plate