Studies On Coupled Elastic Waves In Piezoelectric Composites And Layered Structures

Piezoelectric composites and layered structures have been extensively applied in the fields of modern science and technology. With the development of material science and processing technology, they have become important new-type materials and structures. In this dissertation, piezoelectric composites with 2-2 connectivity and {1-3} connectivity family and piezoelectric layered structures are taken into account based on the practical engineering applications of transducers, sensors, surface acoustic wave (SAW) devices and so on, the following studies are carried out.Based on the Floquet theory, from the general equations of elasticity and by solving the coupled electromechanical field equations, dispersion equations, solutions of the mechanical displacements and the electrical potential functions are obtained for waves propagating perpendicular and parallel to layered interfaces in the piezoelectric composite with 2-2 connectivity, respectively. The propagation behavior of SH-waves in the 2-2 piezoelectric composite with initial stress is analyzed. It is shown from numerical results that initial stress has effect on the width of individual stop-band as well as on the number of stop-bands in certain frequency interval; on the other hand, initial stress has effect on the lowest mode only in the low frequency scale and the effect becomes more remarkable with the increase of polymer volume fraction.According to the analogy between Maxwell's equations and the equations of linear elasticity in conjunction with the Bloch theory and the method of'phononic crystal'with some reasonable assumptions, the three-dimensional problem of elastic waves propagating in the piezoelectric composite with {1-3} connectivity family can be reduced to a two-dimensional one. The pass-band and stop-band distributions of Z mode and XY mode are obtained for cylinders with two different cross sections: circular and square cross section, respectively; the effect of volume fraction of cylinders on these distributions is also considered. It is shown from numerical results that for the 1-3 connectivity periodic piezoelectric composite with circular cross section cylinders, the filter effects in the low frequency scale are dominated by Z mode and the filter effect in the high frequency scale are dominated by XY mode. Meanwhile, for the 3-1 connectivity periodic piezoelectric composite with cylinders of circular cross section, the whole filter effects are controlled by XY mode. On the other hand, for the 1-3 connectivity periodic piezoelectric composite with cylinders of square cross section, the complete stop-band only exists at some special filling fractions of the piezoelectric cylinders, while for the 3-1 connectivity periodic piezoelectric composite with cylinders of square cross section, there exist no stop-band effect. In conclusion, for the periodic piezoelectric composite with {1-3} connectivity family, the filter effects of 1-3 connectivity are much better than those of 3-1 connectivity and the filter effects of circular cross section are much better than those of square cross sections.By the method of wave function expansion and the mode match principle, the scattering of plane P-waves by a piezoelectric cylinder in the piezoelectric composite with 1-3 connectivity is investigated, and the influence of the perturbations of the piezoelectric cylinder material parameters on the near-field backscattered amplitude spectrum is analyzed. It is shown from the numerical results that c44 and e15 obviously affect both the positions and the magnitudes of resonance frequencies in the backscattered amplitude spectra, while c11, c12, c13 and e31, e33 mainly affect the magnitudes of resonance frequencies and have neglectable influence on the positions of resonance frequencies. Furthermore, their sensitivities to wave fields are inferior to those of c44 and e15. These analysis results from near-field backscattered amplitude spectra are meaningful for the nondestructive evaluation of the bonding condition between the cylinders and the matrix in piezoelectric cylindrical composites.For the situation of covering layer with inhomogeneous initial stress, the propagation behavior of Love waves in piezoelectric layered half-space is studied by Wentzel–Kramers–Brillouin (WKB) asymptotic technique, the approximate analytical solutions are obtained. It is shown from numerical results that the inhomogeneity of initial stress has remarkable influence on all the modes in the dispersion curves but has no influence on the cut-off frequencies of each mode; the more inhomogeneous initial stress is, the smaller the velocity of Love waves becomes, but the electromechanical coupling coefficient decreases too. It is known from the influence of inhomogeneous initial stress on the distributions of stress and mechanical displacement fields that both the small interface stresses and the large surface mechanical displacements can be obtained simultaneously by adjusting the gradient coefficient of initial stresses in the piezoelectric layer, which may result in the enhancement of the SAW devices performance.