Mode Control And Separation Of Lamb Wave In Hamiltonian System

The damage diagnosis technology based on Lamb wave plays an important role in structural health monitoring.For the advantages of long propagation distance and sensitivity to small damage,Lamb wave can be used for damage diagnosis of large-area structures.However,the main challenge lies in the fact that Lamb wave has the property of multi-mode.There are at least two propagation modes at any frequency,and Lamb wave scatters at the discontinuous such as the structure boundaries,which makes the diagnosis signal very complicated.As a consequence,it is difficult to extract the damage information of the structure,which provides challenges for damage diagnosis.To solve this problem,this paper investigates the methods which can simplify the Lamb wave diagnosis signals from two aspects,i.e.,mode control and mode separation.The contents mainly include the following aspects:To solve Lamb wave propagation problem,the Hamiltonian system method is established.Based on the strain energy and kinetic energy,the Lagrange function is derived,and the Hamiltonian canonical equation is established by using the variation operation.The derived Hamiltonian canonical equation is solved by separation variable method.Then the problem of Lamb wave propagation is transformed into the eigenvalue and eigensolution problem.The eigenvalue describes the wave number,and the eigensolution represents the corresponding displacement field and stress field.Considering the two assumptions of plane Lamb wave and cylindrical Lamb wave,the frequency equations and displacement expressions are derived respectively,and the adjoint orthogonal relation between Lamb modes is proposed.The general and specific propagation characteristics of plane and cylindrical Lamb wave are analyzed discussed.The reason and performances of the multi-mode and dispersion properties of Lamb wave are explained through the frequency equations.Finally,the propagation characteristics of plane Lamb wave and cylindrical Lamb wave are verified by numerical simulations and experiments.The excitation problem of Lamb wave under applied surface loading is solved using the Hamiltonian system method,and the analytical expressions of the amplitude of Lamb modes are obtained.The Lamb wave propagation problem with nonhomogeneous term is firstly investigated using eigensolution expansion method,and the nonhomogeneous Lamb wave solutions are obtained.Considered as the boundary condition of the structure,the applied surface loading is introduced into the Hamiltonian system.The nonhomogeneous boundary condition is then transformed into the nonhomogeneous term of the equation,and a special solution satisfying the nonhomogeneous boundary condition is obtained.The special solution is expanded by the basic solutions of Lamb wave,and the expansion coefficients are the coefficients of corresponding Lamb modes excited by the applied loading.Based on the plane Lamb wave and cylindrical Lamb wave models,the effects of loading direction and loading distribution on the amplitudes of the excited Lamb modes are discussed.The results show that the loading direction affects the overall amplitude of each Lamb mode,the radial length of the loading affects the frequency responses and circumferential distributions of amplitudes of the excited Lamb modes,and the circumferential distribution of the loading mainly affects the circumferential distributions of the amplitudes of the excited Lamb modes.These excitation models,namely plane Lamb wave model and cylindrical Lamb wave model,are verified through numerical simulations.Numerical simulation results demonstrate the validity of the theoretical predictions.The mode control method of Lamb wave based on piezoelectric transducer is proposed,including mode selection and circumferential control method.An appropriate type piezoelectric transducer is firstly selected,and the transducer is equivalent to the loading applied on the structure surface.Considering that the Lamb wave excited by the finite dimension transducer is cylindrical Lamb wave,while the plane Lamb wave model is simple and straightforward,the effect of the transducer on amplitudes of the excitation Lamb modes is divided into the effect of the transducer size and the effect of the transducer circumferential configuration.Appropriate excitation models are adopted to demonstrate the principle of mode selection based on double side excitation method as well as frequency selection method.The circumferential distributions of Lamb wave field excited by circular transducer and rectangular transducer are investigated,and a method for mode control of Lamb wave in circumferential direction based on the selection of transducer and excitation frequency is proposed.The mode selection and circumferential control methods are used to detect the aluminum plate damage without baseline.Numerical simulation and experimental results show that the diagnosis signal can be simplified by using the mode control method,which contributes to the accurate identification of the damage signal.This mode control method provides a potential baseline free alternative for damage diagnosis in structures.Mode separation methods for Lamb wave are proposed.Considering the dispersion of Lamb wave,the mode signal of Lamb wave propagating for a certain distance is firstly calculated based on the phase velocity and group velocity,and the displacement field is obtained.A method of mode separation of Lamb wave is proposed based on the adjoint orthogonal relation,which can be used to extract the amplitudes of different modes from multi-mode signals.This mode separation method is then used in numerical simulation,and simultaneously the limitations of this method are pointed out.Based on the signal correlation analysis,another mode separation method for Lamb wave based on signal reconstruction is proposed.Multi-mode numerical simulation or experimental signals can be separated through reconstruction using calculation signals.The signals of arrival waves and boundary reflection waves can be removed by mode separation methods.As a consequence,the hidden damage signals can be extracted.The mode separation method provides a possible selection for baseline free damage diagnosis in structures.