Stationary Dynamic Acoustoelasticity Problems of a Thin Plate in a Perfect Compressible Fluid, Taking into Account the Dissipation of Energy in the Plate and Liquid
We propose the refined equations of motion of the plate and the fluid with additional accounting of the energy dissipation in the material of the plate and fluid based on the Thompson–Kelvin–Voight hysteresis model. These equations are used for the formulation of stationary dynamic problems in the field of acoustoelasticity of thin plates surrounded on both sides by acoustic media, which is represented as a perfect compressible fluid. Refinement of fluid behavior is based on the assumption that the pressure increment in fluid is proportional not only to volumetric deformation, but also to its velocity. This assumption allows us to obtain the generalized Helmholtz wave equation by introducing into consideration the complex velocity of sound according to the representation of Skudrzyk to account for energy dissipation. The equations of the plate motion are based on the classical Kirchhoff-Love model.
KeywordsProblems of acoustoelasticity Perfect compressible fluid Energy dissipation Thompson–Kelvin–Voight model Complex sound velocity Generalized helmholtz equation
This research was supported by a grant from the Russian Science Foundation (project № 19-19-00058).
- 1.Panovko, Y.G.: Vnutrennee trenie pri kolebaniyah uprugih sistem [Internal Friction at Vibrating of Elastic Systems]. Fizmatgiz, Moscow (1960). (in Russian)Google Scholar
- 2.Pisarenko, G.S., Yakovlev, A.P., Matveev, V.V.: Vibropogloshchayushchie svojstva konstrukcionnyh materialov: Spravochnik [Vibration Absorption Properties of Structural Materials: A Handbook]. Naukova Dumka, Kiev (1971). (in Russian)Google Scholar
- 3.Grigolyuk, E.I., Gorshkov, A.G.: Nestacionarnaya gidrouprugost’ obolochek [Nonstationary Hydroelasticity of Shells]. Sudostroenie, Leningrad (1974). (in Russian)Google Scholar
- 4.Guz, A.N., Kubenko, V.D.: Metody rascheta obolochek. Tom 5. Teoriya nestacionarnoj aehrogidrouprugosti obolochek [Methods for Calculating Shells. Volume 5 Theory of Nonstationary Aerohydroelasticity of Shells]. Naukova Dumka, Kiev (1982). (in Russian)Google Scholar
- 5.Gorshkov, A.G., Morozov, V.I., Ponomarev, A.T., Shklyarchuk, F.N.: Aehrogidrouprugost’ kostrukcij [Aerohydroelasticity of Constructions]. Fizmatgiz, Moscow (2000). (in Russian)Google Scholar
- 6.Shklyarchuk, F.N., Grishanina, T.V.: Primenenie metoda otsekov k raschetu kolebanij zhidkostnyh raket-nositelej [Application of the Compartment Method to the Calculation of Liquid Launch Vehicles Oscillations]. MAI Publishing House, Moscow (2017). (in Russian)Google Scholar
- 7.Skudrzyk, E.: The Foundations of Acoustics. Basic Mathematics and Basic Acoustics. Springer, New York (1971)Google Scholar