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The Lamb waves in nematic elastomer plates are investigated by adopting the viscoelasticity theory in the hydro-dynamic (low frequency) limit. The Legendre polynomial series approach is employed to obtain the complex wave number solutions to characterize the wave propagation and attenuation. Some unique Lamb wave characteristics are revealed. Results show that the cutoff frequencies of all Lamb modes vanish due to the high viscoelasticity. Except for A0 mode, each mode has a minimal attenuation frequency. Besides, the attenuation of nematic phase is thousands of times greater than the isotropic phase, which would be significant in designing damping applications. [ABSTRACT FROM AUTHOR]

A double Legendre polynomial quadrature-free method was presented to analyze axisymmetric free vibration problem for axially polarized Functionally Graded Piezoelectric circular plates. The present analytical method directly incorporated the boundary conditions into the vibration control equation. At the same time, the mechanical displacements and the electrical potential were defined as the form of double Legendre polynomials series. Then, the solution of eigenvalue was used to obtain the resonant/anti-resonant frequencies. In view of including lots of time-consuming integration calculations, the quadrature-free process was deduced to improve the computational efficiency. The valid of the presented method was verified by the comparison with the existing literature and the commercial software COMSOL. Furthermore, the effects of the material gradient index, radius-thickness ratio on the frequencies, and electro-mechanical coupling efficient were studied. The results showed that the frequency-radius product tends to be stable with the increase of the radius-thickness ratio, and the increase of gradient index led to the increase of the frequency-radius product. [ABSTRACT FROM AUTHOR]

In recent years, guided wave propagation in piezoelectric-piezomagnetic composite (PPC) structures are paid much attention for the design and optimization of PPC transducers. Previous investigations are mainly limited in horizontally infinite flat plates, axially infinite hollow cylinders, and so on. They are all one-dimensional model structures, i.e. structures having variable displacement field in only one direction, and the other two displacement fields are both constant. In this paper, a double orthogonal polynomial series approach is proposed to solve the guided wave in two-dimensional model structures, namely, a functionally graded piezoelectric-piezomagnetic (FGPP) bar with a rectangular cross section. The validity of the double polynomial approach is illustrated by the comparison with the available reference results for a pure elastic homogeneous rectangular bar. The guided wave characteristics, including dispersion curves and mechanical displacement distributions, are discussed by calculating various FGPP rectangular bars.

An analytical integration Legendre polynomial series approach (AILPSA) is proposed to study guided waves in a resin bolt, which is a typical layered cylindrical structure. Compared with the conventional Legendre polynomial series approach, the AILPSA can save the abundant numerical integration calculation time and dramatically improve the computational efficiency. The attenuation and group velocity curves of the resin bolts are calculated. The errors of group velocity between the theoretical and the experimental are analyzed, and the contrast diagrams between amplitude curves of end reflection and attenuation curves are given to illustrate the law between these curves. [ABSTRACT FROM AUTHOR]