Transient Elastic Waves in a Transversely Isotropic Plate

Abstract

The elastodynamic response of a thick plate, with the axis of transverse isotropy normal to the plate surface, is calculated by double numerical inverse transforms, a method particularly well-suited for calculations of responses in the near field of layered structures. Applications of these calculations include point-source/point-receiver ultrasonics, quantitative acoustic emission measurements, and seismology. The singularities of the integrand are eliminated by the introduction of a small, but nonzero, imaginary part to the frequency. We discuss issues of numerical efficiency and accuracy in the evaluation of the resulting integrals. The method can be generalized to calculate the responses in materials of more general symmetry, in viscoelastic materials and to include the effects of finite aperture sources and receivers. The calculated responses are compared to those measured in a single crystal specimen of zinc.

Time-domain computation of the response of composite layered anisotropic plates to a localized source

“…(3)-(5) is to apply a 3D Fourier transformation to them, with respect to x, y and t (e.g., [5,16,6]). The three space and time frequencies, denoted by k x , k y and ω, are independent variables.…”

Acoustic waves generated by a line source in a viscoelastic anisotropic medium

“…The method implemented has first been used to calculate the response of an elastic material with restricted symmetry. 6,7 A similar modeling has been introduced to represent the wave forms generated in isotropic viscoelastic materials. 8 Due to the frequency dependence attendant on the viscoelastic rheology, the method is especially appealing to describe the propagation in such materials.…”

“…The use of even and odd solutions uncouples this system to give two distinct systems of three equations. 6 Notice that the finally considered solutions can be either the displacement at the interface x 1 ϭh, if the transmission response is sought, or the displacement at the interface x 1 ϭϪh, if the interface waves are inspected. Now, let us focus on the calculation of the integral ͑2͒.…”

Measurement by Laser Generated Ultrasound of Both Stiffness Coefficients and Viscosities of an Isotropic Polymer Material

“…However, for each value of the angular frequency ro, inversion of the X3 Fourier transfonn is perfonned by a numerical integration over variable k3' according to the method described by Weaver [6].The method uses generalized Fourier transfonn in which the frequency becomes complex, 0) -j5, with a small constant imaginary part 5. The general solution of the displacement field expresses itself in tenn of a linear combination of symmetric and anti-symmetric solutions with respect to the variable XI'…”