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Two-dimensional wave propagation in an elastic half-space with quadratic nonlinearity: a numerical study
Sebastian Küchler1, Thomas Meurer, Laurence J Jacobs
1Institute for System Dynamics, University of Stuttgart, Stuttgart, Germany. sebastian.kuechler@isys.uni-stuttgart.de
The Journal of the Acoustical Society of America
|March 12, 2009
Summary
This study introduces a new parameter to quantify acoustic nonlinearity in elastic materials, revealing that nonlinear effects depend on observation point and material properties. Third-order elastic constants linearly influence this acoustic nonlinearity.
Area of Science:
- Solid Mechanics
- Nonlinear Acoustics
- Wave Propagation
Background:
- Understanding nonlinear wave propagation in elastic media is crucial for material characterization.
- Quadratic nonlinearity in two-dimensional wave propagation presents complex harmonic generation phenomena.
- Existing methods for quantifying material nonlinearity are limited, especially in multi-dimensional scenarios.
Purpose of the Study:
- To investigate two-dimensional wave propagation in an elastic half-space with quadratic nonlinearity.
- To develop a new parameter for quantifying material acoustic nonlinearity in 2D.
- To analyze the influence of material properties and observation points on nonlinear wave effects.
Main Methods:
- Formulation of the problem as a hyperbolic system of conservation laws.
- Numerical solution using a semi-discrete central scheme.
- Frequency domain analysis of numerical results to identify higher-order harmonics.
Main Results:
- Numerical analysis revealed the excitation of higher-order harmonics due to quadratic nonlinearity.
- A novel parameter, analogous to the 1D acoustic nonlinearity parameter beta, was introduced.
- Material nonlinearity was found to be dependent on observation angle and distance from the source.
- Third-order elastic constants demonstrated a linear impact on the acoustic nonlinearity parameter.
Conclusions:
- The introduced parameter effectively quantifies 2D acoustic nonlinearity.
- Nonlinear wave propagation effects are sensitive to geometric and material factors.
- Third-order elastic constants play a significant linear role in material acoustic nonlinearity.
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