Vibrating Systems and Their Equivalent Circuits

Many researchers have investigated methods for describing systems with an infinite number of degrees of freedom and for finding their appropriate equivalents. The present work gives a comprehensive review of the methods available for finding analogues of waveguides in solids and gases, and in diaphragms, plates and air-gaps. Solutions and descriptions are given for various structures such as electromechanical filters, delay lines and acoustic systems. The book focuses on structures such as waveguides in solids and gases and discusses their analysis and gradual synthesis. The equivalent circuits of waveguides are based on a one-dimensional model, and solutions suitable for further analytical and numerical processing are examined. An analogue is provided with a wide range of applications for such systems; it allows the analysis or gradual synthesis of a whole series of more complex systems with reasonable accuracy. The book also tackles the dispersion problem in solid-state waveguides, and discusses some types of phase velocity approximations. The work is intended for electroacoustic and acoustic engineers and scientists, especially those working in the transducer field.

Table of Contents:
1. Equivalent Electrical Circuits of Thin Diaphragms. Circular diaphragms. Equivalent circuit of a thin annular diaphragm. Thin rectangular diaphragms. A thin diaphragm as part of an electrostatic transducer. Quasistatic stability of a single-acting transducer. Stability of a push-pull transducer. Electrostatic transducer with a thin annular diaphragm. 2. Equivalent Circuits of Thin Plates and Bars. Circular plates. Equivalent circuit of a thin flexuarally vibrating circular plate clamped at the edge. Equivalent circuit of a circular plate supported at the edge. Transverse vibrations of bars and their equivalent circuits. A uniform bar of rectangular cross-section: clamped at both ends; supported at both ends; clamped at one end and free at the other. Longitudinal vibrations of thin rods. Longitudinal vibration of a free-free bar with structural damping. Longitudinal vibrations of a free-clamped bar with structural damping. 3. Solid-State Waveguides of Uniform and Non-Uniform Cross-Section. Hyperbolic waveguides. Wave equation of a hyperbolic waveguide. A hyperbolic divergent waveguide of finite length. Hyperbolic divergent waveguide of infinite length. Exponential waveguide of finite length. Input impedance of convergent and divergent exponential waveguides of infinite length. Conical waveguide of finite length. Wave equation of a conical waveguide. Convergent conical waveguide. Divergent conical waveguide. Analogue circuit of a solid-state waveguide. The effect of transverse displacements in a mechanical waveguide with a longitudinal wave. Wave equation of a waveguide with transverse contraction. The measurement of dispersion in a cylindrical waveguide. Waveguides of non-uniform cross-section. Bessel waveguides. A Bessel waveguide of: finite length; infinite length. Some applications of equivalent circuits of solid-state waveguides. Waveguides of constant cross-section. Waveguides of non-uniform cross-section. Piezoelectric transducer with waveguides. 4. Acoustic Systems with Distributed Elements. Acoustic waveguides. Equivalent circuits for air-gaps. Air-gap with a centric opening. Air-gap with an opening on the circumference. Air-gap at low frequencies. Air-gap with an annular opening. Air-gap under a rectangular diaphragm. Impedance of an air-gap between two parallel planes. Resistance of an air-gap under: a rectangular diaphragm; a circular diaphragm. Resistance of an air-gap between two parallel planes at low pressure. Applications of the theory of acoustic waveguides. Divergent conical horn of infinite length. Hyperbolic divergent waveguide of infinite length. Hyperbolic waveguide of finite length terminated by an infinitely long conical waveguide. Waveguide of finite length terminated by an infinite impedance. Bibliography. Index.