Nonlinear statics and dynamics of size-dependent functionally graded microbeams in thermal environment

In this paper, the nonlinear size-dependent dynamics of a clamped-clamped functionally graded microbeam subjected to thermal environment and external excitation, has been studied. The thermo-mechanical material properties are assumed to follow the power law and are considered to be temperature-dependent. The nonlinear governing equation of motion is derived using Hamilton’s principle based on Euler-Bernoulli beam model and Von-Karman nonlinearity and the modified couple stress theory is employed to capture the size effect. The static response of the microbeam is obtained and the buckling amplitude is determined. In order to study the dynamic response of the system, the governing nonlinear partial differential equation is discretized using Galerkin technique and is solved using multiple scales method. The frequency response of the microbeam is obtained in pre-buckling and post-buckling domains. It is found that in pre-buckling domain, the microbeam shows a hardening behavior, while a softening behavior is observed in post-buckled state.