Researchers are investigating nonlinear acoustics as a tool for identifying material microstructure. Currently, their work involves reducing sensitivity to background nonlinearity by nonlinear mixing of surface acoustic waves.
Euler (1759) who helped lay the foundations of acoustics, established linear acoustic as a subset of nonlinear acoustics. This means that all wave phenomenon is nonlinear in nature. Mathematically speaking, the degree to which a system must be considered nonlinear is dictated by both the wave amplitude and the constitutive equation. Physically speaking, the mechanism for nonlinear acoustics depends strongly on the source of the nonlinearity. For instance, what is commonly referred to as crystal nonlinearity (discussed below) depends on atomic bonding while nonlinearity stemming from material microstructure such as micro cracks (discussed below) depends on microstructure geometry and orientation.
Crystal Nonlinearity
The physical basis of acoustic nonlinearity in a perfect crystal can be understood by considering the binding energy vs. atomic separation curve. For small longitudinal atomic displacements from equilibrium, the binding energy curve looks parabolic (i.e. F=kx or E=1/2kx2) and linear behavior can be assumed. As the atomic displacement becomes larger, the asymmetry of the binding curve must be considered giving rise to the second term in the strain energy equation. The above argument applies to longitudinal motion only. For shear distortion, the binding energy vs. atomic separation curve is symmetric and as a result, nonlinear shear wave distortion is a third order effect, proportional to strain to the forth power. Thus, the shear contribution to the nonlinear signature is exceedingly small and is usually neglected.
Cracks acting as Mechanical Rectifier
Micro cracks in a material serve as an intuitive example of how material microstructure can give rise to nonlinear behavior. Consider an initially sinusoidal wave, frequency=w1, propagating in a material. Since the micro crack or material discontinuity can only transmit compression, the wave is rectified as it passes through the micro crack. Mathematically speaking, the rectified wave can be represented as a Fourier series expanded about w1. Harmonic generation is a telltale sign of nonlinear behavior. From a bulk wave analysis, the ratio of the amplitude of the second harmonic component to the fundamental component serves as a convenient parameter for measuring the strength of harmonic generation. Identifying a nonlinearity parameter applicable for guided surface acoustic waves is of current interest to our group.
Additional Reading
Probing Acoustic Nonlinearity by Mixing Surface Acoustic Waves, David H. Hurley, Ken L. Telschow — 36kB PDF
- Contacts:
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Ken Telschow, Ph.D., (208) 526-1264, Send E-mail
David Hurley, (208) 526-3665, Send E-mail