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

In this paper, the nonlinear size-dependent dynamics of aclamped-clamped functionally graded microbeam subjectedto thermal environment and external excitation, has beenstudied. The thermo-mechanical material properties areassumed to follow the power law and are considered to betemperature-dependent. The nonlinear governing equationof motion is derived using Hamilton’s principle based onEuler-Bernoulli beam model and Von-Karman nonlinearityand the modified couple stress theory is employed tocapture the size effect. The static response of the microbeamis obtained and the buckling amplitude is determined. Inorder to study the dynamic response of the system, thegoverning nonlinear partial differential equation isdiscretized using Galerkin technique and is solved usingmultiple scales method. The frequency response of themicrobeam is obtained in pre-buckling and post-bucklingdomains. It is found that in pre-buckling domain, themicrobeam shows a hardening behavior, while a softeningbehavior is observed in post-buckled state.