| Lamb wave is a kind of wave mainly propagating in thin plate,so studying the mechanism and technology of Lamb wave in plate structure damage diagnosis and health monitoring has important scientific significance and engineering application value.The Lamb wave excited in the local area of the plate structure has the characteristics of cylindrical wave propagation,and the wave will be attenuated to a certain extent during the propagation process.Therefore,it is necessary to study the propagation characteristics of Lamb waves and the evolution of waveforms.In this paper,the Hamiltonian system method is used to analyze the relationship between the Lamb wave waveform mode and the eigensolution of the system,and with the aid of the symplectic conjugate orthogonal relationship to decompose and superimpose the waveform function,the analytical solution of the Lamb wave represented by the waveform function is obtained.Provide basis and analysis methods for structural damage diagnosis and health monitoring.The main research work includes the following aspects:(1)The time coordinate is simulated by the radial r coordinate in cylindrical coordinates and the space displacement is used as the original variable function.The energy method is used to determine the dual variable of the original variable in the phase space.Through the Lagrangian function(strain energy and kinetic energy)variation of the original variable and the dual variable,the Hamiltonian system of the Lamb wave problem of the plate structure is introduced.Thus,the Hamilton canonical equations and the corresponding boundary conditions are obtained.In this way,the Lamb wave problem is reduced to the boundary value problem under the Hamiltonian system.(2)Under the Hamiltonian system,the generalized variable separation method is used to solve the Hamiltonian regular equations of the Lamb wave problem,and the analytic expressions of the symplectic eigenvalue and the symplectic eigensolution are obtained.Symplectic eigensolutions include zero eigenvalue eigensolutions of axisymmetric problems and non-zero eigenvalue eigensolutions of non-axisymmetric problems.The two types of eigensolutions are decomposed into symmetrical and antisymmetrical solutions along the thickness of the plate.Since there is a symplectic conjugate orthogonal relationship between the eigensolutions,the solution of the Lamb wave problem can be expressed as a series solution in the expansion form of the eigensolution.Through the numerical analysis of the eigensolution,the characteristics of the waveform modes of each order are displayed,and a theoretical basis is provided for the change and identification of the Lamb wave waveform caused by damage.(3)Taking the propagation of Lamb wave under the local excitation load on the surface of the plate structure as the research object,solve the specific form of the series solution.Aiming at the problem of the Lamb wave excited by the rectangular piezoelectric ceramic sensor on the surface of the plate,the Lamb wave waveform and propagation characteristics under different excitation methods are analyzed,including excitation at different frequencies and different directions.The comparison shows that the numerical results are consistent with the experimental results.The expression of simultaneous solution provides a reliable method and technique for Lamb wave excitation.(4)Aiming at the problem of the local excitation source in the plate structure,using the series solution represented by the eigen solution,it is attributed to the boundary condition problem of the cylindrical hole.With the help of symplectic conjugate orthogonal relations,the problem is further transformed into the problem of solving algebraic equations,and the solution of the problem is obtained.The solution includes compressional waves(expansion waves)and shear waves(shear waves)and their relationships.Numerical calculations reveal the propagation law of cylindrical Lamb waves and the coupling characteristics of longitudinal and transverse waves in this case. |
PDF Full Text Request