Non-classical thermoelastic wave dispersion in microstructured plates: A structural dynamics approach based on couple-stress theory

In this study, non-classical wave dispersion for the thermoelastic waves propagating in a microstructured plate with a central rectangular hole is examined. A size-dependent theory of couple-stress thermoelasticity is used, where an intrinsic length scale parameter is introduced. Based on the governing equations of consistent couple stress thermoelasticity, the problem domain is assumed to consist of three sub-domains: above, besides, and below the hole. Fourier series expansion in the region where the hole is located is matched with exponential functions in other regions so that traction-free and thermal boundary conditions are satisfied. For the symmetric and antisymmetric Rayleigh–Lamb waves, secular equations are derived by considering both insulated and isothermal boundary conditions. Numerical calculations indicate that increasing the width and height of the hole decreases the phase velocity of both symmetric and antisymmetric waves. The phase velocity increases due to the influence of the characteristic length ratio and decreases for the antisymmetric modes due to thermal coupling. Higher velocities will be observed with insulated boundaries when compared with isothermal boundaries because of the existence of thermal gradients. Sensitivity studies show the effects of thermal expansion, conductivity, reference temperature, and specific heat, indicating that the shape and elastic properties of the voids play a critical role in the dispersion characteristics. The agreement between the real and imaginary parts of the secular determinant confirms the correctness of the theoretical framework. Group velocities for both fundamental and higher-order modes have been calculated, and limiting cases lead to classical and pristine plate solutions.