| Guided wave-based method is a kind of structural health monitoring technology with development potential,which has the advantages of long-distance propagation and high damage sensitivity and concealed damage detection.However,the multimode and dispersion characteristics of guided waves have become the bottleneck of the application in engineering.At present,guided wave technology is still mainly used in plate,thin-walled tube and rod structures,where the multimode and dispersion phenomenon is relatively slight and easy to be controlled.However,civil engineering structures are more complex,which will lead to more serious multimode and dispersion phenomenon.To develop the guided wave technology for civil engineering health monitoring,the numerical simulation and damage monitoring of multimodal and dispersive guided waves were studied from two aspects of forward and inversion analysis.On the one hand,the short wave problem,numerical dispersion problem and geometric dispersion problem in numerical simulation of guided waves have been discussed,where the wavelet finite element was selected to develop an accurate and efficient numerical simulation method for guided waves.On the other hand,the wavelet finite element method was applied to reinforced concrete structures to study the effect of multimode and dispersion phenomenon on the interaction mechanism between guided waves and interface damage in reinforced concrete structures,and then a more effective interface damage monitoring technology was proposed based on guided waves time reversal method.The main research contents and achievements are as follows:(1)The requirements of element size and time step for wavelet finite element in guided wave modeling were discussed,and then a hybrid method that combines the wavelet finite element and spectral analysis based on Fast Fourier Transform was proposed.B-spline wavelet on interval(BSWI)with compact-support,multiscale and multiresolution characteristics was used to construct wavelet-based element.The BSWI element have higher spatial approximation ability than the conventional low-order element,so that the length of BSWI element can be 40 to 60 times larger than that of conventional low-order element;however,the time-domain wavelet finite element still needs to meet the strict time step requirements.Therefore,the BSWI scaling functions were utilized to approximate theoretical wave solution in spatial domain and construct a high-accuracy dynamic stiffness matrix.Dynamic reduction on element level was applied to substantially reduce the size of the system matrix,and then the dynamic equations of the system were transformed and solved in the frequency-domain through FFT-based spectral analysis which can greatly reduce the number of times to solve the system equation in narrow-band guided wave problem.Numerical results showed that the proposed method can significantly improve the efficiency for solving narrow-band guided wave problems,and can extend the frequency-domain spectral analysis to complex structures.(2)The numerical dispersion characteristics of BSWI elements in guided wave propagation were studied in theory,and the suppression conditions of numerical dispersion and numerical anisotropy were given.Some difficulties caused by the wavelet element with large internal nodes in solving generalized eigenvalue problem were solved.For one-dimensional numerical dispersion analysis.the BSWI element was transformed into"two-node" elements to solve the complex-wavenumber dispersion relations of reduced wave equation,where the numerical dispersion characteristics of BSWI elements with different orders and scales were studied.For two-dimensional numerical dispersion analysis,the Rayleigh quotient technique was introduced to obtain the approximate solution of the two-dimensional dispersion equation.The numerical anisotropy phenomenon for different BSWI elements was highlighted,and the effects of material parameters and element distortions on the numerical dispersion were elucidated.Studies showed that the numerical dispersion and numrical anisotropy of the higher-order BSWI element can be almost completely suppressed when the node space is less than a critical value,and the numerical dispersion suppression ability of the BSWI element can be significantly improved by local lifting scale scheme.(3)Five kinds of BSWI rod elements were developed for modeling dispersive waves in a rod,and the corresponding simplified crack models of the interaction process between dispersive guided waves and crack damage were proposed.In view that the classical rod element cannot consider the geometric dispersion phenomenon of guided waves,the additional displacement modes based on higher-order rod theories were introduced to approximate the complex displacement distribution in cross-section.The stiffness matrix,mass matrix and generalized force vector of BSWI higher-order rod elements were derived by means of Hamilton's variational principle.Simplified crack models of the higher-order rod theories were proposed to consider the reduction of structural stiffness caused by a crack.,where the transverse shear and generalized degrees of freedom mactching problems in higher-order rod theories were considered.The flexibility of cracked higher-order rods was formulated in closed form based on Castigliano theorem and fracture mechanics.In addition,the applicability range and selection principle of the proposed element and model are discussed.Numerical results showed that the BSWI higher-order rod element and crack model proposed in this paper can quickly and accurately simulate the geometric dispersion of guided waves and the interaction process between the dispersive guided waves and the crack.(4)The interaction mechanism between guided wave and interface damage in reinforced concrete structure was studied,and the reason of interface damage indexes failure caused by multimode phenomenon was revealed.The wavelet finite element model was established to analyze the multimode and dispesion phenomena of guided waves in reinforced concrete structures.The influence mechanism of multimode and dispesion phenomena in the interaction process between guided waves and interface damage was studied.The effectiveness of existing interface damage indexes based on amplitude and wave velocity was discussed,and the failure reason was explained by multimode guided wave mathematical model.Studies showed that the interaction mechanism between guided waves and interface damage is mainly affected by energy leakage,mode transformation and multimode phenomena,among which multimode and dispersion phenomenon will be more serious with the increase of concrete transverse size.Because of the difference of wave velocity,attenuation coefficient and damage sensitivity between multimodal guided waves,the mode composition and superposition form of reference wave packet may change with the change of interface damage degree.As a result,the damage indexes constructed by the first wave,main wave packet or frequency spectrum can not be used to evaluate the interface damage degree of large-scale reinforced concrete structures.(5)The interface damage monitoring based on time reversal method was proposed for RC structure,and some damage indexes suitable for interface damage evaluation of large-scale reinforced concrete structures were constructed.To overcome the difficulty from the multimode and dispersion phenomenon of guided waves,the time reversal technology was used to realize automatic dispersion compensation and automatic focusing of multimode signals.The linear damage hypothesis with frequency-dependent damping for reinforced concrete structures was proposed for analyzing the influence of interface damage on time-reversal-reconstruction signal,and then the amplitude,similarity and wavelet packet energy damage indexes based on the reconstruction signal were proposed.In addition,the interface damage monitoring testing of reinforced concrete beam was designed and carried out,where the automatic processing algorithm of guided wave time reversal online monitoring was also developed.The experimental results showed that the damage indexes based on the time-domain amplitude and wavelet packet energy of the reconstructed signal can effectively eliminate the influence of multimode and dispersion phenomenon,and thus can better evaluate the interface damage degree of reinforced concrete beams compared with the existing damage indexes based on direct response. |
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