The effect of applied stress on the phase and group velocity of guided waves in anisotropic plates

Inverse of initial stress in carbon fiber reinforced polymer laminates using lamb waves and deep neural network

The prediction of the initial stress in composites is essential for the non-destructive testing (NDT) and structural health monitoring (SHM) of carbon fibre reinforced polymer (CFRP). This paper examines the potential of Lamb waves in the inverse of initial stress by calculating the influence of initial stress on the dispersion characteristics of Lamb waves propagating in multilayered CFRP laminates. By introducing the mechanics of incremental deformation into the linear three-dimensional elasticity theory, the Legendre orthogonal polynomial expansion (LOPE) method is used to mathematically model the Lamb wave propagating in multilayered CFRP laminates subjected to horizontal and vertical homogeneous initial stresses. Then, a three-hidden-layers Feed Forward Deep Neural Network (DNN) with Back Propagation (BP) algorithm is constructed to invert the magnitude and direction of the initial stresses. The input features are the phase velocities of fundamental Lamb wave A₀ mode at five different frequencies. Both training and testing samples are obtained by LOPE forward calculation. An ablation experiment is presented to compare the two different activation functions. Finally, the accuracy of the inverse is verified by comparing with the available outcomes of LOPE forward calculation.

A novel linear-correction localization method of acoustic emission source for velocity-free system

To improve the noise immunity to time-difference-of-arrival (TDOA) measurements and reduce the influence of wave velocity measurement error on localization accuracy, a novel linear-correction localization method of acoustic emission (AE) source for velocity-free system based on the TDOA measurements is proposed in this paper. First, the linear equations with unknown wave velocity are constructed by introducing two intermediate variables, and they are solved for the unconstrained least square (LS) solution. Second, the weight matrix is obtained by estimating the equation residuals. Third, the weight matrix and quadratic constraint are imposed on LS estimate to construct the constrained weighted least square (CWLS) criterion. Finally, the linear correction technique is used to minimize the CWLS criterion and obtain the optimal estimate. The proposed method is verified by pencil-lead breaks experiment. The results show that the locating accuracy and stability of the proposed method are higher than those of the traditional methods. Furthermore, simulation tests prove that the proposed method holds the optimal positioning performance and can reach Cramér-Rao lower bound (CRLB) under different TDOA noise powers.

Investigation of thermo-acoustoelastic guided waves by semi-analytical finite element method

Guided waves are sensitive to variations in propagation environments. Many recent studies have focused on the uniform thermal effect on Lamb waves. However, there is little research on the thermal effect in a more complex situation, such as a nonuniform thermal effect and wave propagation in an arbitrary cross-section. In this study, a thermo-acoustoelastic theory combined with the semi-analytical finite element (TAE-SAFE) method is proposed to investigate both uniform and nonuniform thermal effects on acoustoelastic guided wave propagation. In the TAE-SAFE method, effective thermo-acoustoelastic constants including third-order elastic constants are employed. Then, an acoustoelastic wave equation of the thermal effect is formulated by Hamilton's principle and computed by the semi-analytical finite element (SAFE) method. The phase velocity, group velocity, velocity thermal sensitivity, and displacement mode shape shift can be extracted by the proposed method. To validate this method, numerical results of Lamb waves in an aluminum plate subjected to a uniform thermal effect are compared with the results of a previous theoretical analysis. The results show computational veracity and validity. Two typical cases are investigated: (1) an isotropic aluminum plate under a linear temperature gradient condition; (2) a uniform temperature case in a rail track with a constant irregular cross-section. This study provides an effective numerical method to analyze thermo-acoustoelastic guided wave propagation.

Large acoustoelastic effect for Lamb waves propagating in an incompressible elastic plate

In this paper, the effect of a large pre-stress on the propagation of small amplitude Lamb waves in an incompressible elastic plate is investigated. Using the theory of incremental elasticity, the dispersion equations, which give the phase velocity of the symmetric and anti-symmetric wave modes as a function of the wavenumber, plate thickness, and pre-stress state, are derived for a general strain energy function. By considering the fourth-order strain energy function of incompressible isotropic elasticity, the correction to the phase velocity due to the pre-stress is obtained implicitly to the second order in the pre-strain/stress, and depends on the second, third, and fourth-order elastic constants. Numerical results are presented to show the dependence of the phase velocity of the Lamb wave modes upon the applied stress. These are compared to the first-order correction, and agree well with the limiting and asymptotic values obtained previously. It is envisaged that the present results may well find important practical applications in various guided wave based ultrasonic techniques utilising gels and rubber-like materials.

Computation of propagating and non-propagating guided modes in nonuniformly stressed plates using spectral methods

This paper presents a numerical approach based on spectral methods for the computation of guided ultrasonic wave modes (i.e., Lamb and shear horizontal) in nonuniformly stressed plates. In particular, anisotropic elastic plates subjected to a normal stress profile, which varies nonuniformly over their thickness, are considered. The proposed approach computes the modeshapes and the full three-dimensional dispersion spectrum (i.e., real frequency, complex wavenumber). It therefore includes both propagating (real wavenumber) and non-propagating (complex wavenumber) modes. Furthermore, an approach for robustly post-processing the dispersion spectra in order to compute the group velocity of propagating modes is presented, which is based on a spectral quadrature method. Numerical results are presented for two case studies: (1) a bending profile in a fiber-reinforced graphite/epoxy plate, and (2) an exponential profile in a silver plate. The results show the computational efficiency (i.e., spectral convergence) of the proposed method compared to other existing approaches such as the sublayering and finite element methods.