Abstract
This paper presents an approach to calculate dispersion curves for homogeneous and isotropic plates subject to stress, via Semi-Analytical Finite Element and the Effective Elastic Constants, since stresses in the waveguide modify the phase and group velocities of the lamb waves. In the proposed methodology an isotropic specimen subjected to anisotropic loading is emulated by proposing an equivalent stress-free anisotropic specimen. This approximation facilitates determining the dispersion curves by using the well-studied numerical solution for the stress-free cases. The lamb wave in anisotropic materials can be studied by means of the Effective Elastic Constants, which reduces the complexity of the numerical implementation. Finally, numerical data available in literature were used to validate the proposed methodology, where it could be demonstrated its effectiveness as approximated method.
Highlights
In last years, application of lamb waves in non-destructive tests is of a growing interest [1][2][3][4][5][6]
In Semi-Analytical Finite Element (SAFE) methodology the waveguide is discretized over the cross section, while in an analytical solution is in the wave propagation direction
Analysis According to figure 3, the dispersion curves of S1 mode computed by means of EEC approach for a load of σ11 = 120 MPa are close to the analytical solution
Summary
Application of lamb waves in non-destructive tests is of a growing interest [1][2][3][4][5][6]. The Semi-Analytical Finite Element (SAFE) method has been proposed to compute rapidly and efficiently the dispersion curves for any constant cross section specimen. In SAFE methodology the waveguide is discretized over the cross section, while in an analytical solution is in the wave propagation direction. The dispersion curves in stress-free isotropic and anisotropic specimens have been widely studied and can be adequately described based on the theory of elasticity This formulation is insufficient to describe wave propagation in specimens under stress since small non-linearities in the stress-strain relationships become significant, which can be described by using the acoustoelasticity approach. This paper proposes the use of EEC to describe the anisotropy effect presents in the lamb wave dispersion curves when a load is applied along one direction in an isotropic plate, based on the SAFE scheme. Where ψLM and ψRMare the mth left and right eigenvectors of the eigenfunction, K,ξ is 2ξK3 + K2 and M is the mass matrix
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