Elastic Wave Propagation And Localization In Magnetoelectroelastic Band Gap Materials And Structures

In recent years, there is a lot of work on the elastic wave propagation in periodic structures which becomes a hot topic on band gap materials (phononic crystals) in mechanics, physics and material science. With the stop band characteristics, these structures can be extensively applied in vibration isolation technology, sound isolation, noise suppression, sound wave-guide and sound filter. Due to the wide use of piezoelectric materials and the random disorder in periodic structures which results in the wave localization, it is important to investigate the elastic wave propagation and localization in intelligent band gap materials. In this thesis, the elastic wave propagation in piezoelectric and magnetoelectroelastic band gap materials and localization in randomly disorder systems are studied systematically. The primary obtained results are as follows:The effects of scatterer shapes and lattice constant ratios for rectangular lattice on the band gap structures of the two-dimensional piezoelectric phononic crystals are studied. Based on the plane wave expansion method in solid physics, the band gap structures of elastic waves are derived. The limitation of the relation between the band gap widths and the filling fractions with different scatterer shapes are pointed out for piezoelectric scatterers, which is valid for the photonic crystals and pure elastic systems. The influences of the lattice constant ratio for rectangular lattices on the band gap characteristics in the pure phononic crystals are also exist in the piezoelectric periodic structures with rectangular lattices.The plane wave expansion method for the two-dimensional piezoelectric acoustic band gap materials is developed and used to investigate the wave propagation in three-dimensional piezoelectric periodic structures. The generalized eigenvalue equation is presented for this case with coupling modes and the band gap structures can be obtained in the first Brillouin zone. At the mean time, the stop band characteristics are studied systematically by considering three typical kinds of lattices (i.e. sc, bcc and fcc). The effects of the filling fraction and piezoelectricity on the band gap properties are analyzed.The piezoelectric/piezomagnetic and magnetoelectroelastic band gap materials are designed and studied and the analytical method for this problem is presented. Based on the periodicity and the Bloch theory, the generalized eigenvalue equation of elastic dynamics is provided by considering the mechanical-electro-magneto coupling into account. The stop band characteristics for different lattices are compared. Simultaneously, the band gap characteristics of magnetoelectroelastic band gap materials with Kagome lattices are investigated and the effects of the piezoelectricity and piezomagneticity on the band gap structures are analyzed.The propagation and localization characteristics of Rayleigh surface waves in randomly disordered piezoelectric band gap materials are studied. With the surface boundary condition of the mechanical and electrical fields, the decaying rate of Rayleigh surface waves along the depth direction can be iteratively obtained. The expressions of the transfer matrix and the localization factor are presented. The effects of the random disorder of the structural length and the material constant on the localization behaviors of Rayleigh surface waves are analyzed. Simultaneously, the propagation and localization of elastic waves in randomly disordered piezoelectric rod band gap materials with initial stress are studied. The expressions of the localization factor and the localization length are presented. The effects of the random disorder and initial stress on the wave propagation and localization characteristics are analyzed.The SH waves propagation and localization in randomly disordered layered three-component band gap materials with thermal effects are studied. According to the continuous condition between the consecutive unit cells, the transfer matrix is derived and the expression of the localization factor is presented. The influences of the elastic wave incident angel, thickness ratio, material constant and thermal effects on wave propagation and localization characeristics are analyzed. The stop band characteristics of band gap materials with rubber are discussed.The elastic wave propagation and localization behaviors in two-dimensional band gap materials with random disorder are studied. The studies on the two-dimensional band gap materials with defects are mainly focoused on the point and linear defects which can be considered as the determined ones. The stop band characteristics can be described by the band gap structures. However, this method will not be suitable when these defects become random. Based on the plane wave expansion, transfer matrix and matrix eigenvalue methods, the localization factor is presented for two-dimensional phononic crystals. The localization factor is also an effective way to describe the band gap structures of two-dimensional band gap materials. The randomness and filling fraction on the elastic wave localization behaviors are analyzed. Compared with the case of the acoustic wave localization in liquid media with random bubble, similar phenomena can also be observed for this system and the difference between them is illustrated.