Chapter 5

Acoustical Sources of One-sided Radiation

Vladimir V. Arabadzhi


In monochromatic description (sections 5.1, 5.2), the results of the studies of the physical characteristics of unidirectional acoustic sources used in active sound control systems are presented. A discrete unidirectional source in the form of two phased monopoles (section 5.1) and a planar array of such unidirectional sources is considered (section 5.2.1). One-dimensional boundary-value problems with two (the two-point problem) and three (the three-point problem) controlled parallel planar boundaries between homogeneous media with arbitrary impedances are studied (sections 5.2.2-5.2.6). The boundaries (two or three) are subjected to the action of external forces. The case of the zero sum of external forces applied to the controlled boundaries corresponds to a supportless unidirectional source (SUS). It is shown that a unidirectional source can be created within the twopoint boundary-value problem, whereas a supportless unidirectional source can be created within the three-point problem (sections 5.2.5, 5.2.6). Such parameters such as transparency, small size, absence of support, and broad frequency band can be achieved for a unidirectional source in the form of two piezoelectric layers with the same impedance and velocity of sound as those of the surrounding medium (5.2.7-5.2.9). The aspects of linearity of the transparent SUS and its application to active sound control problems are described (sections 5.2.10, 5.2.11). A spatially one-dimensional model of a plane active double layer between two homogeneous elastic half-spaces is studied analytically in temporal representation (section 5.3). The layer synthesizes a preset smooth trajectory of the controlled boundary between the media without any mechanical support. The outer layer of the coating is piezoelectric, and the inner layer is a polymer that is transparent for low-frequency sound and opaque for highfrequency sound because of dissipation. An algorithm for controlling the piezoelectric elements of the layer on the basis of signals from surface particle velocity sensors is proposed (section 5.3.6), and a method for measuring the particle velocity is developed simultaneously (section 5.3.9). Conditions of stability and efficiency of the synthesis are formulated (section 5.3.7). It is shown that the active layer thickness can be much smaller than the wavelength corresponding to the minimal time scale of the boundary trajectory to be formed. The accuracy of the trajectory synthesis depends on the accuracy of measuring, computing, and actuating elements of the system but does not depend on the vibroacoustic characteristics of the half-spaces separated by the active layer or on the presence of smooth waves in these half-spaces. For the synthesis to be efficient, the operating frequency band and the dynamic range of sensors and actuators should be many times greater than the frequency band and the dynamic range of the trajectory to be formed.

Total Pages: 139-165 (27)

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