Large Amplitude Free Vibration Study of Square Plates under Different Boundary Conditions Through a Static Analysis

Abstract

The free v ibration problem of thin isotropic plates incorporating the effect. of geometric non-linearity is studied by developing a specific numerical methodology. The problem is formulated by using a variational method. The large amplitude vibration problem is addressed by solving the corresponding static problem first through an iterative schemne using a relaxation parameter. Subsequently. with the resulting displacement field, the dynamic problem is solved as a standard eigenvalue problem. The assumed deflection field, required for the analysis, is constituted through linear combinations of beam vibration modes corresponding to the specific boundary conditions of the plate. Typical results for the square plates, in the form of backbone curves, have been furnished in the dimensionless amplitude-frequency plane. Two different combinations of the boundary conditions for the purpose are chosen following an earlier benchmark work. Much insight on large amplitude dynamic behavior of the plate is obtained through the vibration mode shapes. presented for each case. A comparison of the results of the reduced problem with those of earlier studies indicates excellent agreement.