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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.

The present paper deals with the study of nonlinear vibration of a functionally graded cantilever micro-beam imposed on a bias DC voltage and superimposed on a sinusoidal heat source. The governing equation of motion is derived extremizing the Lagrange’s equation and Hamilton’s principal under the assumption of Euler–Bernoulli beam theory. The thermo-elastic equation is obtained utilizing the first law of thermodynamics under the assumption of the classical Fourier heat conduction model. Due to the displacement dependency of the electrostatic force and time variability of the heat source, the governing differential equations of the system are nonlinear implicitly parametrically electro-thermo-elastic coupled equations. To evaluate the dynamic response of the micro-beam, the coupled equations are discretized applying a Galerkin-based reduced order model and then integrated numerically by the Runge–Kutta method. By solving the equations, the stable and unstable regions at different bias DC voltages are identified. By picking some special points from these regions and depicting the time history and phase portrait diagrams, their behaviors are investigated in detail. In addition to the classical dynamic pull-in, in which a homoclinic orbit separates stable periodic orbits from the unbounded solutions, a new kind of dynamic pull-in is presented, which separates unstable solutions, due to parametric resonance response, from unbounded rapidly growing solutions owing to the existence of saddle and singular fixed points in the system.

This paper studies the characteristics of a micro-beam interacting with an incompressible fluid in a fluid chamber with an opening in its bottom face for fluid flow. The Euler–Bernoulli equation for transverse deformation of an elastic beam is coupled with the fundamental hydrodynamic equation, which is solved by Galerkin and separation of variables method. The 2D fluid flow assumption in Cartesian coordinate has been used. Natural frequencies and mode shapes of wet beam are calculated and compared with the dry beam. The effects of geometrical parameter changes are also computed as a benchmark for the design of the micro-pump. It is observed that fluid coupling causes a decrease for beam’s natural frequencies, especially in higher modes. Furthermore, since the results of the dry and wet beam show a small discrepancy in lower modes, the mode related to the dry beam was employed as the trial function in the forced vibration analysis of the coupled system.