THERMALLY INDUCED VIBRATION OF A FUNCTIONALLY GRADED MICRO-BEAM SUBJECTED TO A MOVING LASER BEAM

In this paper, the thermally induced vibration of a functionally graded (FG) cantilever micro-beam subjected to a moving laser beam is investigated via simulating the equivalent third-order dynamic system. The material properties of the FG micro-beam are defined by an exponential function through the thickness. The coupled thermo-elastic equations are obtained utilizing the first law of thermodynamics under the assumption of the classical Fourier heat conduction model and Euler-Bernoulli beam theory. To evaluate the dynamic response of the micro-beam, the coupled equations are first discretized by employing a Galerkin based reduced-order model and then decoupled by applying the Cramer's rule. Solving the decoupled equations analytically, effects of key parameters are illustrated by means of time histories and phase portraits. Furthermore, by investigating the case of resonant excitation, the critical velocity corresponding to mobile heat source is obtained.