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Amplitude-dependent Lamb wave dispersion in nonlinear plates
Pawel Packo1, Tadeusz Uhl1, Wieslaw J Staszewski1
1Department of Robotics and Mechatronics, AGH - University of Science and Technology, Al. A. Mickiewicza 30, 30-059 Krakow, Poland.
The Journal of the Acoustical Society of America
|September 3, 2016
Summary
This study introduces a perturbation method to calculate how Lamb wave dispersion in nonlinear plates changes with amplitude. The findings provide crucial, amplitude-dependent dispersion relationships for nonlinear wave phenomena.
Area of Science:
- Solid Mechanics
- Acoustics
- Nonlinear Dynamics
Background:
- Lamb waves are critical for structural health monitoring.
- Nonlinear effects in materials can alter wave propagation.
- Accurate dispersion relations are needed for advanced wave analysis.
Purpose of the Study:
- To develop a closed-form analytical method for amplitude-dependent Lamb wave dispersion.
- To investigate nonlinear dispersion in hyperelastic plates.
- To provide precise dispersion data for nonlinear wave phenomena.
Main Methods:
- Utilized a Lindstedt-Poincaré perturbation approach with partial wave techniques.
- Employed hyperelastic constitutive relations and Green-Lagrange strain.
- Derived solvability conditions using operator formalism and adjoint problems.
Main Results:
- Obtained closed-form, amplitude-dependent nonlinear dispersion relationships.
- Quantified frequency shifts as a function of wavenumber.
- Verified predictions through numerical simulations on a nonlinear plate model.
Conclusions:
- The perturbation method accurately captures nonlinear Lamb wave dispersion.
- Results are essential for understanding higher harmonic generation and internal resonance.
- This work enhances the predictive capability for wave propagation in nonlinear structures.
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