Transient ultrasonic guided waves in layered plates with rectangular cross section

Abstract

Transient ultrasonic guided waves in anisotropic layered plates with finite and infinite width are presented in this article. A semianalytical finite-element method is adopted to study the guided waves in both infinite- and finite-width elastic plates. Three-noded beam elements in the thickness direction are used in infinite plate model, whereas the cross section of the finite-width plate is represented by nine-noded quadrilateral elements. Propagation in the axial direction is modeled by analytical wave functions. Elastodynamic Green’s functions are derived using modal summation in the frequency–wave number and time–space domains. Results for dispersion and transient analysis of guided waves in infinite nickel plates are presented and compared with those of finite-width plates. Group velocities are calculated and wave arrival times are computed for different plate cross sections. Numerical results show a significant influence of the plate aspect ratio on the dispersion and transient wave response. The complex natures of mode dispersion and propagation due to several mode excitation in finite-width plates require such quantitative analysis to afford easy interpretation. These results play a role of guidance for nondestructive material evaluation.

Time–transient response for ultrasonic guided waves propagating in damped cylinders

“…To overcome these difficulties, for example, Mukdadi and Datta (2003) introduced an artificial small imaginary part ''ig" to the input frequency x in the calculation of the frequency response. A different approach would consist in filtering out the contribution of the modes in proximity of their cut-off frequency by using a phase or group velocity threshold.…”

“…The idea behind this work is to exploit the approach for viscoelastic material description of Bartoli et al (2006) and a procedure similar to that of Mukdadi and Datta (2003) in order to build a SFE-based time-transient response in which the effect of material damping is included. The formulation will allow for a more real simulation of GWs propagating in structures where non-perfect elasticity and/or homogeneity, transforming part of the mechanical energy into heat (material absorption) and/or scattering, originate wave attenuation reducing therefore the propagation distance of the waves.…”

“…In brief, the SFE formulated time-transient response at a point can be obtained by means of the inverse Fourier transform, that turns into the time domain the waveguide frequency response calculated as a summation of the modal data contribution at that point weighted with the spectrum of applied load (see e.g. Mukdadi and Datta, 2003).…”

Computation of dispersion relations of functionally graded rectangular bars

“…The SAFE theory, as a prevalent method, was exploited to study uniform straight waveguide of arbitrary cross section [7]. Datta [8,9] applied the SAFE method for analyzing characteristics of waves and transient responses of layered plates with rectangular cross section. But, the cross section is divided into layered cylindrical elements and materials in each layered element are assumed to vary linearly along the thickness direction in this method.…”

Elastodynamic Green’s function for reinforced concrete beams

“…One is based on integral transform and the other on forced vibration. Recently, Mukdadi and Datta (2003) constructed the GreenÕs function based on integral transform. Other approach of forced vibration has been pursued in the present work by making use of the spectral data obtained using three dimensional wave propagation analysis (Taweel et al, 2000).…”