Stochastic Theory of Sound Insulation of Pipeline Cylindrical Shell

Abstract

In a number of cases having a certain practical significance, the question of the ability of a thin-walled shell to localize the wave energy near the recipient surrounded by this shell, that is, separated by it from the external medium, is of interest. This phenomenon allows us to talk about internal sound insulation. The spectral density of the pressure intensity from a random emitter is determined in the absence of a shell. The most interesting problem of passing a random wave field through a cylindrical shell from a point source was solved, and so on. The problem of sound insulation of cylindrical shells, located near the source of radiation is considered. It is shown that the sound insulation increases monotonically with the frequency; and it has gaps due to resonance phenomena. The obtained results allow us to conclude that here, as in the case of acoustic insulation of the shell from an external field (casing), the following physical phenomena are of great importance: sound insulation increases non-monotonically with the frequency; Dips in the spectrum of sound insulation are caused by resonant phenomena in the shell and air volume enclosed under the shell; During the experimental analysis of the internal sound insulation of the shells (according to the standard measuring method), the dips in the soundproofing are not observed because of averaging in octave frequency bands due to the non-monotonicity of the frequency course of the coefficient of sound insulation. This leads to a significant deviation from the elementary law of the masses. The degree of deviation in this case depends on the density of natural frequencies in a given octave.