Thermoelastic damping in strain gradient microplates according to a generalized theory of thermoelasticity

Abstract

This paper deals with the small-scale effects on the thermoelastic damping (TED) in microplates. The coupled equations of motion and heat conduction are provided utilizing the strain gradient theory (SGT) and the dual-phase-lag (DPL) heat conduction model. Solving these equations and adopting the Galerkin method, the real and imaginary parts of frequency are extracted. The complex frequency approach is then employed to present a size-dependent expression for evaluating TED in thin plates. An analytical expression for TED incorporating small-scale effects is also derived on the basis of the energy dissipation approach. To survey the effect of different continuum theories on TED, the results obtained by SGT are compared with those predicted by the modified couple stress theory (MCST) and the classical continuum theory. Furthermore, through a number of parametric studies, the effects of some variables on the amount of TED, such as microplate thickness, type of material and boundary conditions are discussed.