Free and Forced Vibrations of a Composite Plate in a Perfect Compressible Fluid, Taking into Account Energy Dissipation in the Plate and Fluid

The problem of the passage of a monoharmonic plane sound wave through a thin composite rectangular plate hingly supported in the aperture of an absolutely rigid partition has been considered. In this work, two-dimensional equations of motion constructed by reduction of three-dimensional equations we...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2021-08, Vol.42 (8), p.2016-2022
Main Authors: Paimushin, V. N., Gazizullin, R. K.
Format: Article
Language:English
Subjects:
Acoustic velocity
Algebra
Analysis
Composite structures
Compressible fluids
Deformation
Energy dissipation
Equations of motion
Exact solutions
Forced vibration
Geometry
Insulation
Internal friction
Mathematical Logic and Foundations
Mathematical models
Mathematics
Mathematics and Statistics
Multilayers
Probability Theory and Stochastic Processes
Rectangular plates
Sound pressure
Sound waves
Structural models
Wave equations
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Summary:The problem of the passage of a monoharmonic plane sound wave through a thin composite rectangular plate hingly supported in the aperture of an absolutely rigid partition has been considered. In this work, two-dimensional equations of motion constructed by reduction of three-dimensional equations were used. These equations were based on a discrete structural model of multilayer plates deformation at small displacements and deformations. Additionally there were taken into account the internal friction of layer materials according to the Kelvin–Voigt model. The behavior of acoustic media is described by the generalized Helmholtz wave equations, composed with the introduction of the complex sound velocity according to Skudrzyk to take into account the dissipation of energy. An exact analytical solution of the formulated problem has been obtained. On this basis, this work studies the insulation properties and the stress-strain parameters of a composite plate reinforced with carbon textile depending on the incident sound wave frequency. In addition to this, the laws that represent the change in the sound pressure in an acoustic medium with a distance from the plate were established.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080221080242