The propagation characteristics of Lamb waves in a functionally graded material (FGM) plate with periodic gratings have been studied. The power series technique is employed to solve the governing differential equations with variable coefficients. In the propagation direction, the displacements of Lamb waves are expanded in the Fourier series due to the periodicity of the structure. The convergences of the power series and Fourier series are proved and the method presented in the article is verified by the finite element method (FEM). The band gaps are obtained by the couplings between the different modes of Lamb waves induced by FGM. The effects of the structural parameters (such as the periodicity, mass, and length of the gratings) and gradient coefficient on band gaps are investigated. Numerical results show that the band gaps shift up as the gradient coefficient increases and the second band gap (SBG) is closed when the gradient coefficient is large enough. The conclusions are of practical significance for designing elastic wave filters with high-performance.

The reflection of elastic waves in a piezoelectric semiconductor half-space under multiple physical fields has been investigated in the article. Four reflected waves, such as the quasi-pressure (QP) wave, quasi-shear vertical (QSV) wave, electron or hole carriers (CP) wave, and electric–acoustic (EA) wave, are generated when a QP wave is incident on the boundary of a piezoelectric semiconductor half-space. The energy reflection coefficients of the QP, QSV, CP, and EA waves are derived based on the governing equations and surface boundary conditions, and the energy-flux balance is used to verify the numerical results. Effects of the three different initial stresses, steady-state carrier density, and biasing electric field on attenuation characteristics, reflection angles, and energy reflection coefficients of the QP, QSV, CP, and EA waves are discussed in detail. Numerical results show that the initial stresses have limited but observable effects on the attenuation and reflection behavior of reflected waves. The energy distribution among reflected waves and interaction energy between different modes are also affected by initial stresses, while the overall energy-flux balance remains satisfied. The steady-state carrier density and biasing electric field change the energy carried by the CP and EA waves. The findings presented in this article are useful for the optimized design of piezoelectric semiconductor transducers and converters.