Perturbation approach to dispersion curves calculation for nonlinear Lamb waves

Pawel Packo; Wieslaw J. Staszewski; Tadeusz Uhl; Michael J. Leamy

doi:10.1117/12.2084300

7 May 2015 Perturbation approach to dispersion curves calculation for nonlinear Lamb waves

Pawel Packo, Wieslaw J. Staszewski, Tadeusz Uhl, Michael J. Leamy

Proceedings Volume 9438, Health Monitoring of Structural and Biological Systems 2015; 94381V (2015) https://doi.org/10.1117/12.2084300
Event: SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring, 2015, San Diego, California, United States

Abstract

Analysis of elastic wave propagation in nonlinear media has gained recent research attention due to the recognition of their amplitude-dependent behavior. This creates opportunities for increased accuracy of damage detection and localization, development of new structural monitoring strategies, and design of new structures with desirable acoustic behavior (e.g., amplitude-dependent frequency bandgaps, wave beaming, and filtering). This differs from more traditional nonlinear analysis approaches which target the prediction of higher harmonic growth. Of particular interest in this work is the analysis of amplitude-dependent shifts in Lamb wave dispersion curves. Typically, dispersion curves are calculated for nominally linear material parameters and geometrical features of a waveguide, even when the constitutive law is nonlinear. Instead, this work employs a Lindstedt - Poincare perturbation approach to calculate amplitude-dependent dispersion curves, and shifts thereof, for nonlinearly-elastic plates. As a result, a set of first order corrections to frequency (or equivalently wavenumber) are calculated. These corrections yield significant amplitude dependence in the spectral characteristics of the calculated waves, especially for high frequency waves, which differs fundamentally from linear analyses. Numerical simulations confirm the analytical shifts predicted. Recognition of this amplitude-dependence in Lamb wave dispersion may suggest, among other things, that the analysis of guided wave propagation phenomena within a fully nonlinear framework needs to revisit mode-mode energy flux and higher harmonics generation conditions.

Citation Download Citation

Pawel Packo, Wieslaw J. Staszewski, Tadeusz Uhl, and Michael J. Leamy "Perturbation approach to dispersion curves calculation for nonlinear Lamb waves", Proc. SPIE 9438, Health Monitoring of Structural and Biological Systems 2015, 94381V (7 May 2015); https://doi.org/10.1117/12.2084300

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