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

• Main Author: Gunda Jagadish Babu
• Format: Article
• Language: English
• Published: De Gruyter 2013-06-01
• Series: Nonlinear Engineering
• Subjects: large amplitude free vibratio; thin rectangular plates; ritz method; closed-form solutions; coupled displacement fields; von-kármán type of geometric nonlinearity; non-linear frequency
• Online Access: https://doi.org/10.1515/nleng-2012-0012

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.