Investigation of Wave Characteristics in Magneto-electro-elastic Plates Using the Spectral Element Method
Author:Xiao Dong Liang
The piezoelectric magnetic smart material is widely used due to its electromagnetic coupling effect and fast response.It is important to detect the structure of the material due to the complex working environment.As an efficient non-destructive testing technology,guided wave technology has broad application prospects in piezoelectric/magnetic materials.For piezoelectric/magnetic composite materials,the complex electromagnetic coupling characteristics and the anisotropy of the medium bring great difficulties to the wave problem.The spectral element method proposed in this paper has the advantages of the finite element method and the spectral method.The spectral element method proposed in this paper is based on the Fourier series expansion displacement field hypothesis,which can reduce the dimension of the solution and save computational resources.At the same time,the Chebyshev orthogonal polynomial can be used to spectral element interpolation,which improves the computational efficiency of eigenvalues.The spectral element method is an effective calculation method for solving the wave propagation characteristics of piezoelectric in piezoelectric materials.Based on this method,the main research work of the thesis is as follows:(1)The high-order spectral element interpolation program was independently written and combined with the general finite element software Abaqus to generate a grid of arbitrary crosssection spectral elements.Based on fundamental equations of magneto-electro-elastic medium in the Cartesian coordinate system,the dispersion equation of the spectral element method in arbitrary cross section is derived.The accuracy and convergence of the spectral element method are verified by comparison with the periodic finite element method.The elastic wave propagation problem of functionally graded rectangular plates is studied by this method.The effects of functional gradient volume index and section aspect ratio are discussed.(2)The characteristics of elastic guided waves in an infinite functionally graded magnetoelectro-elastic plate is investigated.For the infinite functionally graded plate composed of piezoelectric and magnetostrictive,some numerical examples about dispersion curves and wave structures are given,and the influence of the change of the volume fraction index on dispersive behavior are analyzed.In addition,a new phenomenon is observed in the dispersion curve: the mode deletion.The mode deletion is a physical phenomenon,which is closely related to the negative permeability of piezomagnetic materials,which has not been mentioned in previous studies of the infinite functionally graded magneto-electro-elastic plate,is found with the dispersion curves.(3)Based on the Hamilton principle,the Chebyshev spectral element method is applied along the radial and circumferential directions to obtain the dispersion equation of the waves.The equation has wide applicability and can solve the dispersion curve of curved plates with arbitrary curvature including hollow cylinders.The influences on the dispersion characteristics is analyzed in terms of four factors: structural radian,magneto-electro effect,thicknessdiameter ratio,and stacking sequence.(4)The purpose of this study is to investigate the propagation characteristics of guided waves in functionally graded piezoelectric annular plates.By introducing an orthogonal circular curvilinear coordinate system,the elastic mechanics equation of annular plates in the curvilinear coordinate system is derived.The Chebyshev spectral element method is presented for an annular waveguide,and the dispersion equation of elastic waves in functionally graded piezoelectric annular plates is obtained.The convergence and accuracy of this method are evaluated by comparison with the literature.Through numerical examples,the dispersion characteristics of annular plates with different volume fraction index,curvature,and section size are compared,and the phenomena of mode separation,mode conversion,and cut-off frequency are revealed.(5)Combining the spectral element method(SEM)with the perfectly matched layer(PML),a method(SEM-PML)for solving the surface wave characteristics in a half-space laminated structure is proposed.PML has excellent absorption performance and prevents the calculation of reflection interference dispersion characteristics of leakage waves.Based on the screening modal criteria,the propagation modes and leakage modes are screened.The influence of material properties and coating thickness on the propagation characteristics of Rayleigh surface waves is studied.(6)Based on the advantage of periodic finite element method in solving periodic structures,spectral elements are introduced into wave finite element method to analyze the band gap characteristics of periodic piezoelectric corrugated plates.The symmetry and band structure of the corrugated plate are controlled and adjusted by using the thickness,the amplitude and the phase difference between the upper and lower corrugated plates.