Investigation Of Semi-analytical Finite Element Method For Guided Wave Based Monitoring In Arbitrary Cross-section

Compared with the traditional ultrasonic wave,guided wave has many advantages,such as long propagation distance,high detection efficiency,high precision and low cost,which attracts more and more attention in the engineering field of structural health monitoring.However,the propagation of guided wave not only has multi-mode and dispersion characteristics in arbitrary cross-section,which leads to the complexity of guided wave signal and makes it difficult to extract structural state information;guided waves are also affected by external environment factors,such as load and temperature.Therefore,there have some theoretical and technical difficulties in the analysis of wave structure and guided wave propagation characteristics on arbitrary cross-section under complex stress and thermo-stress.It is necessary to carry out theoretical and technical research on acoustoelastic guided wave of pre-stress,temperature,signal-to-noise ratio and other influencing factors.This paper is devoted to perfect,improve and expand guided wave based monitoring techniques in arbitrary cross-section using semi-analytical finite element(SAFE)method.The research contents mainly include the following aspects:The key point of ultrasonic guided wave detection technology is to know the propagation characteristics of guided wave in structures.In order to obtain the propagation characteristics of ultrasonic guided waves in different waveguide structures,a semi-analytical finite element method is used.Based on Hamiltonian principle,the wave equation of a free waveguide structure is derived.By solving the wave equation,the wave velocities and mode-shape of different waveguide structure can be obtained,and the dispersion curves are drawn to analyze the guided wave dispersion characteristics.In cartesian coordinate and cylindrical coordinate system,the dispersion curves and mode-shape of plate and pipe structures are analyzed by SAFE method.Using the classical dispersion curve "Disperse",the semi-analytical finite element method is verified.Then,the guided wave propagation is analyzed in arbitrary cross-section,including the multi-mode,dispersion and wave structure characteristics,and the accuracy of semi-analytical finite element method is further verified by commercial finite element software ABAQUS and experiment method.For pre-stressed sturcutures,it is a necessary problem to understand the propagation state and change of guided wave for monitoring application.The wave velocity change caused by environment change is called acoustoelasticity,which is a nonlinear phenomenon related to third order elastic constants.This paper deals with an acoustoelastic theory combined with semi-analytical finite element(AE-SAFE)method for modeling stressed wave propagation.We compare numerical results in an aluminum plate with theoretical results.The results show both the veracity and validity of this AE-SAFE method.Then,the AE-SAFE method is applied to two arbitrary cross-sections,including load bearing stringer and rail track.The strategy of axial stress monitoring in an arbitrary cross section is also investigated.Results from acoustoelastic measurements on a T-type stringer are presented,showing the feasibility of this method for axial stress monitoring.Guided waves are sensitive to propagation environment variations,which will affect guided wave detection accuracy.Therefore,it is very important to obtain guided wave propagation information under different temperature environments.In this paper,acoustoelastic wave equation of thermal effect is formulated by Hamilton’s principle and computed by semi-analytical finite element(SAFE),the effective thermo-acoustoelastic constants which include the third order elastic constants are employed,method.A thermal acoustoelastic theory combined with semi-analytical finite element(TAE-SAFE)method is proposed to investigate both the uniform and non-uniform thermal effect on acoustoelastic guided wave propagation.To validate this method,numerical results of Lamb waves in an aluminum plate subjected the uniform thermal effect are compared with the previous theoretical analysis results,the results show computational veracity and validity.Then the wave velocity and velocity thermal sensitivity of stringer and rail track subjected different temperature change are revealed,and the ultrasonic guided wave propagation of stringer and rail track under the influence of temperature is analyzed.For arbitrary cross-sections,the biggest challenge of ultrasonic guided wave detection is to improve signal-to-noise ratio.Owing to the complexity of arbitrary cross-sections,its multimodal and dispersion characteristics are more prominent,it is necessary to fully study the excitation and receiving sensor array.In this paper,a semi-analytical finite element(SAFE)method for the quick and reliable solution of guided wave excitation and sensing in irregular cross-section is proposed.The surface excitation loads are equivalent to inhomogeneous boundary conditions and converted into inhomogeneous terms.The modal expansion method is used to study the solution of ultrasonic guided wave propagation with inhomogeneous term.The excitation and sensing models are proposed to calculate the difference of guided wave signals under different excitation and sensing models in plate structure and arbitrary cross-sections.The results were verified by commercial finite element software ABAQUS.Finally,a practical and economical design method of excitation/sensing trasducer array is proposed based on the formation analysis and excitation/sensing mathematical model on arbitrary cross-sections.