Study Of Lamb Wave Dispersion Characteristics Of Plate Structures Based On Bloch-Floquent Theory

Plate structures are widely used in the construction of industrial buildings and large transportation equipment,and the structural damage produced during long-term service can greatly affect the overall safety and stability of the system,so the damage detection and evaluation of plate structures has important scientific significance and engineering testing needs.This paper calculates the dispersion characteristics of guided waves of plate structures based on Bloch-Floquent period theory and finite element numerical method,which can simultaneously obtain the amplitude of the corresponding modal guided waves and specifically analyze the dispersion curves of single-layer plates and double-layer composite plates containing amplitude information.The main elements and innovations of the thesis research are as follows.1.A method for solving dispersion relations containing amplitude information in plate structures.First,based on the Rayleigh-Lamb dispersion equation in the plate structure,a method for obtaining the exact numerical solution of the Rayleigh-Lamb equation using the dichotomous method is given;on this basis by using the global matrix method,the characteristic equation of the dispersion relation of the double-layer composite plate is obtained;then,we propose a method to calculate the dispersion relations of guided waves of plate structures based on Bloch-Floquent period theory combined with the finite element eigenfrequency method.This calculation method has the advantages of being able to handle complex boundary conditions,fast calculation speed and high accuracy,and can effectively obtain the dispersion relations of the plate structure and the displacement distribution of each mode at propagation.2.A method for solving complex dispersion relations for single-layer plate structures containing relative off-surface amplitudes.First,the dispersion relations of the single-layer plate structure in the range of Irreducible Brillouin Zone are obtained by using the finite element eigenfrequency method and Bloch-Floquent theory calculations;secondly,by sampling and expanding the displacement field of each mode and obtaining the actual wave number and relative off-surface amplitude of each mode by Fast Fourier Transform,the dispersion relation of the singlelayer plate structure containing amplitude is calculated and verified and compared with the results of theoretical calculations;then,the Bloch wave vector is extended to the complex wave number domain,the evanescent guided wave oscillations with complex wave numbers are analyzed,and the complex dispersion curves of the single-layer plate structure are obtained;finally,the physical significance of the relative off-plane amplitudes of various modes is investigated using finite element time domain calculations,and it is pointed out that modes with larger relative off-plane amplitudes will be more easily excited by the normal excitation,which can provide guidance value for practical detection and application.3.A method for solving dispersion relations for double-layered composite plates containing amplitudes.Firstly,the dispersion relations of the double-layered composite plate structure in the range of Irreducible Brillouin Zone were obtained by using the finite element eigenfrequency method and Bloch-Floquent theory to calculate the dispersion relations;Second,the displacement fields of various modes of the composite plate structure were analyzed,and the off-plane displacements on both sides of the structure were sampled and subjected to Bloch-Floquent expansion and Fast Fourier Transform respectively,and the dispersion curves calculated after extracting the displacements on the rubber side and on the steel side were obtained,and the curves matched well with the results obtained by the global matrix method,and the relative off-plane amplitudes of these characteristic modes on both sides of the composite plate were marked,leading to the conclusion that in this double-layered composite plate,the dispersion relations detected on both sides when the guided waves pass through the structure are the same;then,the finite element method was used to perform time domain excitation on a large composite plate to verify the offplane amplitude relations calculated by the proposed method as follows: the larger the relative offsurface amplitude of the mode,the more it will be generated and more easily detected by the normal excitation;finally,the change law of the dispersion relation of the overall structure when the thickness of the steel plate in the rubber-steel composite plate is changed is studied,and it is found that the dispersion law of the modes in the rubber-steel structure,which can produce large offsurface displacement on the steel side,is mainly influenced by the thickness of the steel plate layer,and the change of the dispersion relation of these modes is consistent with the change of the dispersion relation of the single-layer steel plate with the thickness,which has a guiding role in regulating the dispersion relation of the overall rubber-steel structure.The Lamb wave dispersion curve calculation method with relative off-surface amplitude proposed in this paper can quickly and accurately obtain the dispersion relationship between singlelayer plate structure and composite plate structure,and can indicate the displacement distribution information of Lamb wave during propagation,which provides theoretical guidance for the selection of key parameters such as excitation frequency,reception conditions and working mode of Lamb wave ultrasonic nondestructive testing technology,and has high application prospects and research value.