Research On Elastic Wave Propagation In Magneto-electro-elastic, Multilayered Structures

The magneto-electro-elastic (MEE) structure consisting of piezoelectric and piezomagneticmaterial has the ability of converting one type of energies into the other (among magnetic,electric, and mechanical fields). Due to the three-phase coupling, the mechanical behavior ofthe MEE structure is more complicated than that of a purely elastic, single-phase piezoelectric,or piezomagnetic ones and has attracted a great deal of attention in the past few years. Just themulti-phases effect, especially large product effect, leads to wide application of the structurein sensors, actuators and other sensitive components. This work studies the propagation ofultrasonic guided waves in MEE multilayered structures, including plate and cylinder. Theprincipal motivation of this work is to achieve the ultimate goal of using guided waves forperforming a non-destructive test of MEE structures.Firstly, the propagator matrix method based on state space theory is employed to ana-lyze guide waves propagation in the MEE multilayered plate and cylinder. The state spacemodel, a general model of dynamic system, has many advantages such as simple formulationand program realization, small scale of matrix for analyzing the MEE multilayered structures.In order to build the state space model of MEE structures, the general displacements(includingelastic displacements, electric and magnetic potentials) and stress(including elastic stress, elec-tric displacement and magnetic induction) are divided into two categories. One is variables outof plane(so-called state variables), and the other is in plane. Based on the general constitutiveequations, equilibrium equations and deformation compatibility conditions, the state equationscan be obtained, which will be used to construct the propagation relation of state variables ontwo surfaces of a sole layer. Then by means of continuous condition between two adjoininglayers, the global propagation relation of state variables of structure can be given, which willbe used to solve the dispersion equation and mode shapes under the given boundary conditions.According to the previous theory, the formulations for dispersion equations and modeshapes for wave propagation in MEE multilayered plate and cylinder are derived. Andsome numerical examples are used to verify and illustrate these formulations and discuss the influences of incident angle, stacking sequences and wave number on dispersion relation andmode shapes. For transverse isotropic MEE multilayered plate, it is observed that dispersioncurves are not related to incident wave; the pure elastic and magneto-electro-elastic couplingmode shapes are concurrent in structure; the changes of stacking sequences and wave numbercan effect dispersion relation and mode shapes. For MEE multilayered cylinder, the dispersionrelation are more sensitive to the ratio of inner and outer diameters than stacking sequences.Although the three-dimensional solution of wave propagation in MEE structures hastheoretic universality, the plane problems are more interesting for application. Thus the planeand anti-plane problems for wave propagation in MEE multilayered plates are investigated.Only two typical plane waves, including Love wave and Lamb wave, are discussed in thiswork. Especially for Lamb wave, the method presented in this dissertation is very efficient forthe calculation of its phase velocity, group velocity and wave mode shapes. These parametersare also very important for non-destructive test of the plate structures.Then a novel mixed method composed of partial wave method and propagator matrixmethod is proposed, which bonds the advantages of the previous two methods and can be usedto calculate the re?ection and transmission coefficients of plane waves in MEE multilayeredplate. During researching the mixed method, the Christoffel equation for pure elastic mediais extended to MEE media. By means of the novel method, the in?uences of types, incidentangle and frequency of incident wave on re?ection and transmission coefficients are discussed.Some conclusions are drawn in this dissertation. Diversity of stacking sequences and materialproperties in MEE multilayered structures makes the re?ection and transmission coefficientsmore complex. And the re?ection and transmission coefficients are not sensitive to themagnetic and electric boundary conditions.To solve Green function and transient response of MEE multilayered plate, a new methodbonding the propagator matrix method and the residual theory is presented. So the drawbacksof modal representation method and partial wave method can be avoided. It is well-knownthat the motion of media is associated with propagating, non-propagating or evanescent modecorresponding to real, imaginary or complex wave number. In order to obtain such wavenumbers, the strip element method is introduced, which also demonstrates that the magneticpermeability coefficient of CoFe2O4 is positive from the point of view of conversation ofenergy and corrects an error in some recent literatures.As an application of above theories, a test scheme is designed and completed to detectthe default in multilayered elastic structure with Lamb wave, which includes the selection ofwave modes, the preparation of testing workpieces, the configuration of instruments, and et al. It is very easy to extend the detected method to MEE multilayered structure, thus an initialscheme for detecting the default of MEE structures is given finally.