ANALYSIS OF THERMOELASTIC DAMPING FOR FUNCTIONALLY GRADED MATERIAL MICRO-BEAM

Based on Euler-Bernoulli beam theory and the one-way coupled heat conduction theory, thermoelastic damping (TED) of functionally graded material (FGM) micro-beams was studied. By assuming the material properties of the rectangular cross-section micro-beams to be varied continuously along the thickness direction as power law functions and ignoring the variation of the temperature gradient in the axial direction, one dimensional and one-way coupled heat conduction equation with variable coefficients was established. By using the layer wise homogenization approach, the heat conduction with variable coefficients was simplified as a series of differential equations defined in each layer. The equation governing flexural free vibration of the FGM micro beams subjected to time dependent non-uniform heating was developed on the basis of classical beam theory. By using the boundary conditions at the top and the bottom surfaces and the continuity conditions at the interfaces, analytical solution of the temperature field in the FGM micro-beams given layer wisely was obtained. Substituting the temperature field into equation of motion of the micro-beams, the complex frequency including TED was achieved, and finally, values of the TED was extracted. Numerical results of the TED were calculated for the given values of physical and geometrical parameters of a metal-ceramic FGM beam. Effects of the material gradient, the geometry, frequency orders and the boundary conditions on TED were analyzed in detail. The results showed that:(1) if the beam length is fixed, one can arrive at the minimum of the TED by changing the volume fraction of the ceramic when the beam thickness is less than a certain value; (2) the orders of the frequency have no influence on the maximum of TED, however, the larger frequency corresponds to the smaller critical thickness (at which the TED reaches the maximum); (3) for different boundary conditions the maximums of TED are same, but the critical thickness is smaller for the stronger end constraints; (4) both the maximum of TED and the critical increase of the FGM micro beams increase along with the increment in the values of the volume fraction of the metal.