Absorption of long waves by linear structures

Abstract

The phenomenon of resonance absorption of long waves by small-size oscillators is studied both analytically and numerically. The phenomenon consists in that the scattering cross section of an oscillator (a monopole, a dipole, etc.) is determined by the wavelength of the absorbed wave and does not depend on the wave size of the oscillator when this size tends to zero. The expression for the optimal excitation amplitude is derived for a group of oscillators of arbitrary wave size in the framework of the boundary-value problem formulated in the general form in terms of the generalized velocities and generalized forces. Using examples of linear structures (consisting of monopoles equidistantly positioned on the axis), the possibility of obtaining the maximal absorption cross section for sound absorption by such structures with a small wave size is investigated. Examples of linear structures providing unbounded logarithmic, linear, or quadratic growth of the total absorption cross section with an increase in the number of monopoles comprising them are considered for the case of the wave size of the absorbing structures being as small as desired. Characteristic features of the cooperative and individual strategies of absorbing oscillators are described. The results are applicable to waves of various physical natures.