Meshless stochastic vibration for laminated quadrilateral plates considering thermal factor

Abstract

This paper presents a node-based meshless model for investigating the stationary/non-stationary stochastic thermal response characteristics of laminated arbitrary quadrilateral plates excited by various random loads. The thermo-elastic theory is incorporated into Hamilton's principle for deriving the dynamic governing formulas of the arbitrary quadrilateral plate. The displacement variables of plate structure are approximated by two-dimensional Chebyshev meshless shape functions, which is combined with multipoint mapping theory to discretize the system equations. After that, the stochastic dynamic response solutions of quadrilateral plates considering different boundary cases are generated by introducing a pseudo excitation methodology (PEM). The applicability and predictive accuracy of the present formulation to thermal vibration behaviors of quadrilateral plates are elucidated by means of carrying out convergence clarification and sufficient comparative studies between the calculated results as well as reference solutions from available literature. Also, the effects of several main factors including laminated parameters, thermal effects, excitation loads, etc. on free vibration and stationary/non-stationary response properties of laminated quadrilateral plates are revealed, which may serve as benchmark solutions for evaluating the correctness of other analytical or numerical methods.