An influence of shear and longitudinal waves on sound insulation in the third range of the standard frequency spectrum
Abstract
An influence of shear and longitudinal waves on sound insulation in the third range of the standard frequency spectrum
Incoming article date: 10.02.2022The standard frequency spectrum according to regulatory documents is divided into three frequency bands. The third frequency range is currently not well studied and is represented on the standard sound insulation graph by a straight line. When sound is applied to the plate, at a certain frequency, bending waves in the plate are replaced by shear and longitudinal vibrations. Having considered the processes of propagation of shear and longitudinal waves in a soundproof barrier, it is possible to obtain an adequate physical model of wave propagation in the third frequency range, as well as to form an effective method for calculating the sound insulation of air noise. The physical model of sound insulation in the third frequency range is based on the use of objects in wave propagation media with concentrated parameters: coordinates, weight and velocity. The concepts of "concentrated" and "reduced" masses are introduced. Using the law of conservation of the amount of motion and the law of conservation of kinetic energy, formulas are derived for finding sound insulation in the third section of the standard frequency spectrum. The influence of shear waves on the third frequency range of the standard spectrum is considered. Formulas are given for calculating the initial frequency of occurrence of these waves and for finding sound insulation. The regularities of the appearance of the third section of the standard frequency spectrum are determined. The influence of longitudinal waves on the third frequency range is considered. Formulas for finding the limiting frequency, after which longitudinal waves appear in the partition, and formulas for finding sound insulation due to the action of longitudinal waves are obtained. The refinement of the sound insulation formulas using the modulus of elasticity, taking into account the creep of concrete, is shown. A computational experiment is being carried out to calculate sound insulation for building partitions made of heavy concrete of different thicknesses. Examples of graphs for calculating the sound insulation of air noise according to the method under consideration and according to the methodology of regulatory documents are presented.
Keywords: sound insulation of air noise, reduced mass, concentrated mass, method of discrete (concentrated) parameters, longitudinal waves, shear waves