Propagation Of Elastic Waves In Multilayer Piezoelectric And Piezomagnetic Structures

Magneto-electro-elastic materials have broad application prospects in the sensor, smart material and structure engineering due to the conversional function among the magnetic energy, electric energy and mechanical energy. The layered periodical structures made by piezoelectric and piezomagnetic materials, which are usually called phononic crystals, exhibit also band gaps characteristics of elastic waves. The characteristics of band gaps of phononic crystals provide a totally new solution for noise and vibration isolation and for designing acoustic function devices. It is systematically investigated the influences of initial stresses, mechanically and dielectrically imperfect interfaces and functionally graded interlayers on the propagation of elastic waves in layered piezoelectric and piezomagnetic structures in this doctoral dissertation. The following contents are included:(1). Based on the increment stress theory, it is discussed that the reflection and transmission of elastic waves at the interface between two piezoelectric half-spaces with initial stresses. Furthermore, the one-dimensional pre-stressed phononic crystals of piezoelectric/piezoelectric type and piezoelectric/piezomagnetic type are investigated. The dispersion equations of elastic waves are established according to the transfer matrix and Bloch theorem. Numerical simulations are performed, and the effects of initial stresses on the propagation and dispersion characteristics of elastic waves are studied. The numerical results obtained are validated by the energy conversation law. The investigation shows that the initial stresses affect the propagation and dispersion characteristics of elastic waves though modifying the constitutive equations, the governing equations and the boundary conditions.(2). By considering mechanically and dielectrically imperfect interfaces resulted from the interface defects and damage accumulations, it is investigated that the reflection and transmission of elastic waves at various mechanically and dielectrically imperfect interfaces between two piezoelectric half-spaces. The energy fluxes carried by reflection and transmission waves are calculated and the numerical results are verified by the energy conservation law. The influences of mechanically and dielectrically imperfect interfaces on the reflection and transmission characteristics of elastic waves are discussed and analyzed. Furthermore, the one-dimensional piezoelectric/piezoelectric phononic crystals with mechanically and dielectrically imperfect interfaces are investigated based on the method of transfer matrix and Bloch theorem. The influences of mechanically and dielectrically imperfect interfaces on the propagation and dispersion characteristics of elastic waves are studied. It is shown that the mechanically and dielectrically imperfect interfaces can enhance the model conversion and change the energy partition between reflection and transmission waves, and thus have evident influences on the propagation and dispersion characteristics of elastic waves.(3). For functionally graded interlayers of the continuously change of material parameters, the state transfer differential equations are established. The state transfer differential equations are solved by using the Magnus series expansion, and the transfer matrix of the functionally graded interlayer is obtained. Then, the dispersion equations of one-dimensional piezoelectric/piezomagnetic phononic crystal are derived by using the Bloch theorem. The influences of functionally graded interlayers on the dispersion relations of Bloch waves are analyzed. Furthermore, the multilayer piezoelectric/piezomagnetic cylindrical shell structures with functionally graded interlayers are also investigated. It is discussed that the influences of functionally graded interlayers on the dispersive relations of shear horizontal waves which propagates along the circumferential direction. It is shown that the functionally graded interlayer has evident influences on the propagation and dispersion characteristics of elastic waves. The propagation and dispersion characteristics of elastic waves can be adjusted artificially by designing elaborately the gradient profiles of graded interlayers.The initial stresses, the mechanically and dielectrically imperfect interfaces and the functionally graded interlayers have different influences on the propagation and dispersion characteristics of elastic waves. In general, the propagation and dispersion characteristics of high frequency elastic waves are more sensitive to these factors. Through investigating the influences of initial stresses, mechanically and dielectrically imperfect interfaces and functionally graded interlayers on the propagation and dispersion characteristics of elastic waves, the physical mechanisms and the law of these influences are revealed. These investigations will provide some theoretical guidance for the design of acoustic functional device and band gaps of phononic crystal.