By Don Dissanayake
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Additional resources for Acoustic Waves
And the second consists of the remaining components. The combination of the displacements vu = [u , v , w]T and the first group of stresses vσ = [τ zx ,τ zy ,σ z ]T gives the state vector v = [( vu )T ,( vσ )T ]T . For piezoelectric materials of the most general kind, in the catalogue of three-dimensional linear theory (Ding & Chen, 2001), we have the constitutive relations instead of Eq. (1) σ ij = cijklε kl − ekij Ek , Di = eiklε kl + β ik Ek (5) the strain-displacement relations of Eq. (3) are complemented with (in absence of free charges) Di , i = 0 (7) where Di , Ek and ϕ are respectively the electric displacement, field and potential tensors, and ekij and β ik are the piezoelectric and permittivity constants, respectively.
7 and compared with those for a laminate with free surfaces. It is seen from Fig. 7 that some parts of the dispersion curves of certain specified modes for the four-layered composite with different surface conditions may coincide, but they may be completely different at other parts or for other modes. Fig. 7 indicates that the boundary conditions have a complex effect on the dispersion characteristics of free waves in multilayered anisotropic structures. In-depth study is needed. 0 (c) Phase velocity-frequency spectra Fig.
Guided waves in plates and their use in materials characterization, Applied Mechanics Reviews, 50(5): 247-284. Collet, B. (2004). Recursive surface impedance matrix methods for ultrasonic wave propagation in piezoelectric multilayers, Ultrasonics, 42: 189-197. Datta, S. , Shah, A. , Bratton, R. L. & Chakraborty, T. (1988). Wave propagation in laminated composite plates, Journal of the Acoustical Society of America, 83(6): 2020-2026.