Deterministic and stochastic thermomechanical nonlinear dynamic responses of functionally graded sandwich plates

Abstract

Abstract Functionally graded composites are commonly used under extreme mechanical and thermal loads wherein a minimal degree of uncertainty might significantly deviate the structural responses. Meanwhile, there is a lack of studies that consider the effects of inevitable source-uncertainty, especially in the stochastic dynamics of composites. This paper, for the first time, investigates both deterministic and stochastic dynamics of functionally graded sandwich plates with four different layering configurations under thermomechanical loads. Euler-Lagrange equations are derived based on the third-order shear deformation theory and Hamilton principle. Closed-form solutions for fundamental frequencies are obtained by introducing a stress function. Dynamic responses, phase-space plots, backbone curves, and forced response curves are numerically solved and graphically illustrated leading to notable insights into the stability and softening/hardening behaviors of the plate dynamics. A large number of random configurations are generated and analyzed resulting in stochastic dynamic bounds of dynamic responses, backbone curves, and forced response curves. The study shows that the plates have dynamic hardening behaviors, and the existence of thermal loads makes the plate random responses more diverse in stochastic environments. This work provides a good understanding of the deterministic and stochastic dynamics of the composites, which are crucially important for practical engineering applications.