Thermomechanically coupled non-linear vibration of plates

An analytical method is presented for the analysis of large amplitude thermomechanically coupled vibrations of rectangular elastic thin plates with various boundary conditions. The field of temperature and deformation are assumed to be coupled, and the transverse and longitudinal deformations are mutually dependent. The fundamental equations of non-linear flexural vibration of a plate stemming from Berger's analysis are coupled with the energy equation. Based on one-term approximate solution technique, the system of non-linear equations is solved by employing the methods of Galerkin and successive approximations. The analytical solutions are compared with those for the linear case and from the numerical analysis to investigate the influence of thermomechanical coupling and large amplitude on the period of plate lateral vibration.