Temperature-dependent free vibration analysis of functionally graded micro-beams based on the modified couple stress theory

In this paper free vibration analysis of functionally graded micro-beam is investigated based on the modified couple stress theory. The model is established using the Euler-Bernoulli beam theory. The thermal and mechanical properties of the micro-beam are assumed to be temperature-dependent and vary smoothly through the thickness direction. The power law distribution is used for exerting the material gradation. The micro-beam is initially stressed by temperature change thorough the thickness. The temperature field is supposed to be constant in the cross section plane. The induced thermal stress, and the power index affect dynamic responses of the micro-beam. The Hamilton's principle is utilized to derive the governing equation of motion, and Galerkin's method is used in the solution procedure. Upon using the modified couple stress theory, non-classical results are obtained, moreover by neglecting the non-classical parameter, classical results are reported. For verification, the numerical results are compared with those of benchmark. Present results denote the vitality of temperature and material gradation upon dynamic responses of micro-systems.