Forced vibration of rectangular plates in thermal environments: Novel analytical solutions

Abstract This study addresses the challenging issue of analytical modelling of forced vibration of rectangular plates in thermal environments, which involves mathematical difficulties on treating complex boundary value problems in higher-order partial differential equations. An effective symplectic superposition method is extended for the present issue, focusing on non-Lévy-type boundary conditions that were not accurately analyzed by conventional analytical methods. To be specific, an original problem is decomposed into three subproblems, which are solved rigorously through separation of variables followed by symplectic eigen expansion, and the original problem's solution is determined by superposing the subproblems' solutions. Various forced vibration results under different thermal environments and different harmonic load scenarios are presented, showing good agreement with finite element numerical simulation results. Furthermore, the effects of temperature variation, harmonic frequency, simple harmonic load amplitude, and boundary conditions, among others, on the thermal vibration characteristics are explored. The findings delve into the significant impact of thermal environments on the forced vibration performance of rectangular plates, offering a theoretical basis for related structural designs.