Modal displacement analyses of Lamb waves in micro/nano-plates based on the consistent couple stress theory

Abstract

In micro-scale structures, the influence of scale effects on the mechanical properties cannot be ignored, and the continuum mechanics theory cannot effectively describe guided wave propagation. This paper studies modal displacements in an isotropic micro/nano-scale plate — an essential factor for the mode selection of Lamb waves in non-destructive testing technology. To achieve this, the consistent couple stress theory, which additionally accounts for the impact of scale effects on wave propagation, has to be employed. A mathematical derivation method with singular value decomposition is proposed, and the excitation amplitude is computed by applying a normal stress source to evaluate the in-plane and out-of-plane displacements. The results indicate that the in-plane displacement vanishes on the plate surface for anti-symmetric modes when the phase velocity equals the velocity of shear waves. Moreover, the intersections of symmetric and anti-symmetric dispersion curves identify specific frequencies at which the out-of-plane displacement vanishes on the free surface. These findings highlight the difference in modal displacement characteristics between micro-scale and macro-scale structures. The results from this study may furnish theoretical guidance for ultrasonic non-destructive testing of microstructures.