By Don Dissanayake
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Additional info for Acoustic Waves
Substitution of Eq. (42) into Eq. (35) gives the system equation (APU + D)d = Rd = s0 (46) where R = APU + D is the system matrix. e. s0 = 0 and the free wave propagation problem is considered, the vanishing of the system matrix determinant yields the following dispersion equation R( k x ; k y ; ω ) = 0 (47) which may be solved numerically by a proper root searching technique (Guo, 2008). Thus, the complete dispersion curves of various waves can be obtained, as illustrated in Section 4 for multilayered anisotropic elastic structures.
To reduce the dimension, we substitute the phase relation into the scattering relation to obtain a system equation, from which the dispersion relation for free wave propagation is obtained by letting the determinant of coefficient matrix vanish, and the steady-state and transient wave propagation due to the external force excitations can be obtained by inverse Fourier transforms. Section 4 gives numerical examples of guided wave propagation in cross-ply elastic composite structures. Dispersion curves for different configurations, various boundary conditions and in particular at the high frequency range are illustrated to show the versatility and numerical stability of the proposed formulation of MRRM.
There exist two electromagnetic waves, respectively, but the two waves were all affected by the piezoelectric coefficients. The fully dynamic theory of Maxwell’s equations, coupled to the mechanical equations of motion, are studied here. The complete set of uncoupled dynamic equations for piezoelectromagnetic waves in anisotropic media are deduced. For the piezoelectric material of class 6mm, it will be seen that there exist eight electromagnetic waves and also eight elastic waves, respectively.