Vibration And Wave Propagation In The Multi-field Laminated Structures

In multiferroic (or magnetoelectric) materials, there exist at least two ferroic orders (e.g. ferroelectric, ferromagnetic, or ferroelastic) in one phase. Multiferroic composite materials have drawn increasing interests due to their prospects in applications such as filters, energy harvesters, transformers, oscillators, switchable phase shifters and other multifunctional devices. An accurate and reliable analysis can assure devices and structures stable and safe during their lifetime. Hence, the thesis is to analyze the dynamic problems of mulitferroic composites, particularly vibration and wave propagation.The semi-analytical method is adopted to obtain dynamic character analysis of multiferroic laminates. Based on the three-dimensional magneto-electro-elastic theory, we established the dynamic formulations with the state-space method for multiferroic infinite plates with an arbitrary number of layers. For complicated boundary conditions, the application of differential quadrature method to the state equation to approximate the derivatives with respect to the in-plane direction yields a state equation valid at discrete points along that direction, which can serve as a benchmark for other theoretical or numerical analyses.The method of reverberation-ray matrix (MRRM) is employed to analyze high-frequency vibrations of multiferroic laminates to avoid numerical instability associated with long-element and high-frequency as encountered in the conventional state-space method. This thesis provides a mathematically more rigorous derivation of MRRM based on the theory of the first-order linear differential equations. In particular, the case of repeated eigenvalues, which has not been considered before is discussed to complete the formulating of MRRM.The bulk wave propagation in multiferroic laminates with initial stresses and imperfect interfaces is also investigated with the state-space method. The dispersion curves and normal modes in thickness direction are presented, and the effect of initial stresses/imperfect interfaces on dispersion curves and phase velocities is discussed. Meanwhile, two errors made in references, the initial stresses were far beyond the strength of real materials and the self-consistent condition of initial biasing field was not considered, are corrected in this thesis.On the basis of wave potential method for accurate analysis of wave equation, the wave propagation in multiferroic cylinders with respectively circular, sectorial, and sector-ring cross-section are studied. The main endeavor is made on the determinative effect of different boundary conditions, characteristic angle and radius ratio on the frequency spectra, phase velocities and cutoff frequencies. The special geometry will differ a lot from traditional flat plate in dispersion characteristics, which provides the basis for the design of particular functional waveguides.In this thesis, the vibration and wave propagation in multi-field layered media are considered, and many methods are utilized to develop theoretical formulations for different shapes and boundary conditions. This broadens the research scope of the multiferroic material structure, and also lays a solid theoretical foundation for design and development of new multi-functional devices.