Chapter 1
Introduction to Nonlinear Acoustics
1.1 Introduction
Nonlinear acoustics is a branch of acoustics dealing with sound waves of sufficiently large amplitudes. This study will require the full form of the governing equations of fluid dynamics for sound wave propagation in liquids and gases and elasticity for sound wave propagation in solids. These equations are generally nonlinear and linearization is no longer possible for dealing with large amplitude sound waves. The solutions of these equations also show that sound waves are being distorted as they propagate due to the effect of nonlinearity.
In general, the world is of nonlinear in nature. For sound propagation in fluids (liquids and gases), the full nonlinear equation of fluid mechanics will be involved. For propagation in solids, the full equation of elasticity will be used. Practical examples of nonlinear acoustics are shock wave, cavitation, high intensity focused ultrasound (HIFU) and music. Ultrasonic waves commonly display nonlinear propagation behaviour due to their relatively high amplitude to wavelength ratio.
The nonlinear behaviour of sound wave is due to both the nonlinear nature of the propagating sound wave and also the nonlinear nature of the medium of propagation. The nonlinear nature of sound wave means that the propagating sound wave must have large amplitude and the nonlinearity of the medium of propagation means medium also to generate harmonics such as in medical ultrasound imaging [1] due to the nonlinear nature of the human tissue. This means nonlinearity will be generated even with an ordinary intensity sound and without the necessity of a high intensity sound wave. It has also been known that cracks in metals also generate harmonics with ordinary intensity sound wave [2]. The nonlinear nature of sound wave itself and the nonlinear nature of the propagating medium situation is analogous to that of symmetry can be due to the symmetry property of the sound wave and can also be due to the symmetry nature of the medium of propagation for instance crystals.
The nonlinear nature of the medium can be described by designating a nonlinear parameter to describe the medium such as the B/A nonlinear parameter. Sofar B/A
© Springer Nature Singapore Pte Ltd. 2021 |
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W. S. Gan, Nonlinear Acoustical Imaging, https://doi.org/10.1007/978-981-16-7015-2_1
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1 Introduction to Nonlinear Acoustics |
nonlinear parameter has been used mostly for human tissues. In this chapter we extend its use to metals.
1.2 Constitutive Equations
The constitutive equations of nonlinear acoustics can be divided into two categories: one is for sound propagation in fluids (liquids and gases) and the other is for sound propagation in solids. For sound propagation in fluids, the constitutive equation is based on the Navier Stokes equations. The popular equations of nonlinear acoustics in fluids are the Westervelt equation, the Burgers’ equation, and the KZK equation. They can be derived from the basic equations of fluid mechanics. For sound propagation in solids, the nonlinear elasticity equation has to be used. All these equations are analysed in more details in the subsequent chapters of this book.
Harmonics generation is also an important phenomenon in nonlinear acoustics. This is due to the nonlinear nature of the sound propagating medium such as the human tissues and the cracks in metals. They are especially useful in medical ultrasound imaging as it gives higher sensitivity and enables the detection of phenomena not seen in linear ultrasound imaging.
1.3 Phenomena in Nonlinear Acoustics
The following are common phenomena in nonlinear acoustics: sonic boom, acoustic levitation, musical acoustics and parametric arrays.
References
1.Tranquart, F., N. Grenier, V. Eder, and L. Pourcelot. 1999. Clinical use of ultrasound tissue harmonic imaging. Ultrasound in Medicine and Biology 25: 889–894.
2.Kristian, Haller. 2007. Nonlinear Acoustics Applied to Nonodestructive Testing, PhD. Thesis. Sweden: Blekinge Institute of Technology.