Vibration analysis of rotating functionally graded Timoshenko microbeam based on modified couple stress theory under different temperature distributions

In this study, thermal vibration of rotary functionally graded Timoshenko microbeam has been analyzed based on modified couple stress theory considering temperature change in four types of temperature distribution on thermal environment. Material properties of FG microbeam are supposed to be temperature dependent and vary continuously along the thickness according to the power-law form. The axial forces are also included in the model as the thermal and true spatial variation due to the rotation. Governing equations and boundary conditions have been derived by employing Hamiltonian's principle. The differential quadrature method is employed to solve the governing equations for cantilever and propped cantilever boundary conditions. Validations are done by comparing available literatures and obtained results which indicate accuracy of applied method. Results represent effects of temperature changes, different boundary conditions, nondimensional angular velocity, length scale parameter, different boundary conditions, FG index and beam thickness on fundamental, second and third nondimensional frequencies. Results determine critical values of temperature changes and other essential parameters which can be applicable to design micromachines like micromotor and microturbine.