Large Amplitude Free Vibration Analysis of Thin Rectangular Plates: Simple Closed-form Solutions

[摘要] Large amplitude free vibration behavior of thin, isotropic rectangular plate configurations are expressed in the form of simple closed-form solutions by using an application of the Ritz method based on coupled displacement fields. Influence of plate aspect ratio (a/b) and Poisson ratio (v) on the behavior of back-bone curves is briefly discussed for various boundary configurations of the rectangular plate. Proposed closed-form solutions are corrected for the simple harmonic motion (SHM) assumption using the well established harmonic balance method which is applicable for the homogeneous form of cubic non-linear Duffing equation.

[关键词] Large amplitude free vibratio;Thin rectangular plates;Ritz method;Closed-form solutions;Coupled displacement fields;von-Kármán type of geometric nonlinearity;Non-linear frequency