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Nonlinear Ultrasonic Techniques for Nondestructive Evaluation
Published in Kundu Tribikram, Mechanics of Elastic Waves and Ultrasonic Nondestructive Evaluation, 2019
As mentioned before, a stress–strain curve that looks linear to the naked eye may not be linear. A nonlinear curve that has a very large radius of curvature looks linear when a small part of the nonlinear curve is plotted. In such a material even a small amplitude wave can cause a very small nonlinear response of the material. The challenge is how to detect such a small nonlinear response in the material. Various nonlinear acoustic/ultrasonic techniques discussed in this chapter (higher harmonic generation, frequency modulation, sideband peak count and resonance acoustic spectroscopy, to name a few) can detect minute nonlinear responses in a material. The SPC technique is relatively new and simple to use.
The Linear Wave Equation and Fundamental Acoustical Quantities
Published in Lawrence J. Ziomek, Fundamentals of Acoustic Field Theory and Space-Time Signal Processing, 2020
In the absence of any applied forces, an infinitesimal volume element of fluid which is at rest at time t and position r = (x, y, z) has an equilibrium or ambient density of ρ0 kilograms per cubic meter, is under an ambient pressure of p0 pascals (newtons per square meter), and is at an ambient temperature of T0 degrees Celsius (°C). The presence of an acoustic (sound) wave produces changes in pressure, velocity, density, and temperature in the fluid, each change being proportional to the amplitude of the wave. The change in pressure from the equilibrium or ambient value p0 that is due to the presence of an acoustic wave is called the acoustic pressure p. If the amplitude of the acoustic wave is large, so that p is not small in comparison with the ambient pressure p0, then nonlinear effects become important. As a result, a nonlinear wave equation must be used to describe the propagation of large-amplitude acoustic waves. This type of wave propagation falls into the general area of acoustics known as nonlinear acoustics. However, if the amplitude of the acoustic wave is small, so that p/p0 ≪ 1, then nonlinear effects become negligible. As a result, a linear wave equation adequately describes the propagation of small-amplitude acoustic waves. This type of wave propagation falls into the general area of acoustics known as linear acoustics. In this chapter, we shall be concerned with the derivation of the linear wave equation. Indeed, this entire book is devoted to the study of fundamental problems in linear acoustics. In order to derive the wave equation, we need equations of motion, continuity, and state.
Exact sub and supersonic pressure wave-fronts in nonlinear thermofluid medium
Published in Waves in Random and Complex Media, 2021
Ramita Sarkar, Prabodh Kumar Pandey, Satyaki Kundu, Prasanta K. Panigrahi
Nonlinear acoustics plays an important role in describing the motion of high amplitude waves and also when the medium experiences high pressure. Generally, nonlinearity significantly affects large amplitude sound waves, propagating in gaseous or liquid media [1], as also biological tissue systems [2–4]. Higher order dispersion manifests in thermo-viscous media, altering the wave propagation. In 1963, Westervelt modified the linear wave equation, taking into account both these effects [5]. Depending on the general considerations, the Westervelt equation (WVE) may include loss and inertial terms [6–8] which finds applications in modeling physical phenomena, such as ultrasound propagation in tissue [8–12], underwater acoustics [13], acoustic cavitation [14], acoustic levitation [15], to name a few.