High-Intensity Ultrasonics

Theory and Industrial Applications

O V Abramov

• Publisher: CRC Press
• Year: 2019
• ISBN:
  9781351440776
• Edition: 1
• Topic: Technologie et ingénierie
• Subtopic: Ingénierie civile

Presenting a comprehensive description of the theory and physics of high-intensity ultrasound, this book also deals with a wide range of problems associated with the industrial applications of ultrasound, mainly in the areas of metallurgy and mineral processing.
The book is divided into three sections, and Part I introduces the reader to the theory and physics of high-intensity ultrasound. Part II considers the design of ultrasonic generators, mechanoacoustic radiators and other vibrational systems, as well as the control of acoustic parameters when vibrations are passed into a processed medium. Finally, Part III describes problems associated with various uses of high-intensity ultrasound in metallurgy. The applications of high-intensity ultrasound for metal shaping, thermal and thermochemical treatment, welding, cutting, refining, and surface hardening are also discussed here.
This comprehensive monograph will provide an invaluable source of information, which has been largely unavailable in the West until now.

Part I

Physical Aspects of Ultrasonics

An understanding of the specificities of high-power ultrasonic effects on technological processes is possible if the reader has a certain knowledge of engineering sciences and ultrasonics. As the book is primarily for those who are concerned, in one way or another, with material sciences and engineering, it seems reasonable in the first part of the book to introduce the reader to the physical and technical aspects of ultrasonics which is a branch of the wave motion science covering a diversity of phenomena, such as the propagation of elastic waves in water, earth crust, air, electromagnetic waves of a radio-frequency range, light waves, etc.

The first part of the book deals with the problems that will be considered to some extent in its subsequent parts. These involve the basic principles of ultrasonics: the regularities of vibrational motion and propagation of low- and finite-amplitude waves in fluids and solids, as well as nonlinear effects at interfaces.

Chapter 1

Low-Amplitude Vibrations and Waves

This chapter gives a brief description of the regularities of oscillatory and wave motion as well as the principles of the propagation of low-amplitude waves in fluids and solids.

The fundamentals of classical acoustics were formulated in the works of G. Galilei, M. Mersenne, L. Euler, V. Weber, and G. Helmholtz. The book by J. Rayleigh “Theory of sound” [1] completes the main stage of development of classical acoustics. For a more detailed information on acoustic fundamentals, the reader is referred to [2–10].

1.1 Harmonic Oscillator

Vibrations, or periodical reciprocating motion, is a widespread form of motion. Mechanical oscillations (e.g. of a pendulum, tuning fork, etc.) can be considered as repetitive alterations of position and velocity of a body or its parts. A change in the current and voltage in a circuit or movement of electrons in atoms, as well as other relevant processes, may give rise to electrical oscillations. Although different, various oscillations obey the same laws and can be described by the same equations.

Among a diversity of oscillations, those of a linear harmonic oscillator are considered to be simplest (Figure 1.1).

If mass m is disturbed from equilibrium by stretching or compressing a spring and then letting it free, the mass begins to oscillate around its equilibrium position*. Such oscillations are known as free or natural, as opposed to forced oscillations, when the system is subject to external force. Oscillations would not be damped if energy loss is absent, i.e. if the system is conservative. Let us consider the simplest case of undamped natural oscillations, which makes it possible to elucidate on the contribution from various parameters of real systems to the oscillatory process.

Figure 1.1. Vibrations in the simplest mechanical system.

The system under study is acted upon by two forces, inertial F_i and elastic F_e. The law of motion can be written as

Fi+Fe=0.(1.1)

According to the force law

Fi=md2ξdt2,(1.2a)

where ξ is the displacement, d²ξ/dt² is the acceleration equal to the second derivative of displacement with respect to time t.

For an ideal spring, the elastic force F_e counteracting the extension is given by

Fe=χξ,(1.2b)

where χ the coefficient of elasticity which is equal to the ratio of the acting force to the mass displacement (i.e. to the extension or compression of the spring).

In view of (1.2a) and (1.2b), the equation of motion (1.1) can be rewritten as

md2ξdt2+χξ=0.(1.3a)

For integration, this equation can be conveniently written in the so-called canonical form

d2ξdt2+ω02ξ=0,(1.3b)

where ω0=χ/m is the angular (circular) frequency of natural oscillations of the system.

In practice, the frequency f₀ is also used, which equals the number of oscillations per unit time and is related to the angular frequency and oscillation period T₀ as

f0=12πω0=1T0.(1.4)

The general solution to equation (1.3b) has the form

ξ=Acos⁡ω0t+Bsin⁡ω0t=ξmcos⁡(ω0t+θ),(1.5a)

where A = ξ_m cos θ; B = −ξ_m sin θ; ξ_m is the amplitude of oscillations (i.e. the maximum displacement of the mass from its eq...