Research On Lamb Wave Propagation In Elastic Plates And The Resonance Mode For Edges

Elastic waves are widely used in the acoustic scattering of underwater elastic targets,the identification of elastic target signals in underwater target detection and positioning,and the acoustic propagation characteristics in seabed or ice.The modal characteristics of acoustic waves in elastic waveguides are the theoretical basis for the study of acoustic field changes under active excitation.Utilizing local resonance modes to achieve high-efficiency sound absorption is one of the important sound-absorbing mechanisms for designing small-sized sound-absorbing metamaterials.In this paper,the following basic research is carried out around the Lamb wave and edge resonance mode characteristics in the elastic plate:First,starting from the one-dimensional planar layer waveguide,based on the numerical solution idea of the spectral method,the problem of solving the eigenvalues of the Helmholtz equation is studied.Using the finite difference method of uniform and equally spaced points and the non-uniform Chebyshev spectrum method of "sparse in the middle and dense at both ends",the numerical approximate solution of the mode is obtained respectively,and compared with the strict analytical solution,the accuracy of the numerical method is discussed and calculation errors.The Chebyshev spectral method is significantly better than the finite difference method.Then,it is upgraded to the study of Lamb wave modes in a two-dimensional planar elastic plate.Based on the sound propagation equation in an infinite elastic medium,the free boundary conditions and the two-dimensional plane strain assumption are introduced,and the dispersion equations of symmetric and antisymmetric modes in a free elastic plate are obtained.Using the Chebyshev spectrum method and introducing boundary condition correction to the differential operator matrix,the eigenvalues and eigenfunctions of each mode of the Lamb wave in the free elastic plate are obtained.Combined with symmetry,wave number properties and propagation direction,the numerically obtained eigenvalues are classified,screened and modal matched,and three different dispersion characteristic curves are obtained,which fully display the various modes of Lamb waves in the free elastic plate.State changes with frequency.Finally,the study of the characteristics of the edge resonance modes excited when a plane wave is incident on the end face of a semi-infinite free elastic plate is considered.Using mode superposition method,the stress and displacement field in the elastic plate are expressed as the superposition of modes of each order,and the matrix operator is corrected for boundary conditions to obtain the functional form of reflection coefficient with respect to frequency and Poisson’s ratio.Based on the resonant scattering theory,the Newton-Raphson algorithm in the complex number field is used to obtain the zero and pole points of the reflection coefficient in the complex frequency plane,and to calculate the displacement field and stress field of the end face of the elastic plate at the edge resonance,and to study the edge resonance mode.frequency characteristics.The edge resonance shows that the amplitude of the evanescent wave mode has a maximum value near the frequency point.Considering the plane stress assumption and modifying the large-size thin plate,the edge resonance frequency can be adjusted,and it is found that the complex resonance frequency moves to a lower frequency.