Free and forced bending vibrations of a thin plate in a perfect compressible fluid with energy dissipation taken into account

Abstract

A refined statement of stationary dynamic acoustoelasticity problems of thin isotropic plates surrounded from both sides by acoustic media assumed to be perfect compressible fluids has been studed. The problem statement takes into account the energy dissipation in the material of the plate and fluid on the basis of the Kelvin-Voigt hysteresis model. The refinement of the fluid behavior is based on the assumption that the pressure increment is proportional not only to volumetric strain, but also to the rate of its volumetric strain. This assumption allows us to obtain the generalized Helmholtz wave equation by introducing Skudrzyk's complex sound velocity into consideration to take account of the energy dissipation. The motion equations of the plate are based on the classical Kirchhoff-Love model and are obtained in two versions. In the first version unsimplified three-dimensional wave equations are used to determine the aerohydrodynamic load acting on a plate. The second version is based on simplifying the equations of fluid motion by the introduction of the well-known hypothesis of plane reflection and emission of sound waves. On the basis of the derived equations, exact analytical solutions of two types of problems are obtained. The first type is related to the problem of free vibrations of a rectangular plate hinged around the contour when complex eigenfrequencies were defined. The second type is related to the problem of forced vibrations of the plate under the action of a flat mono-harmonic incident sound wave when sound transmission loss, the stress-strain state parameters of the plate as well as the laws of change in sound pressure in a fluid were determined. It is shown that correct and more meaningful solutions of acoustoelasticity problems of the considered class are possible only in case of describing the behavior of a fluid with unsimplified three-dimensional wave equations with consideration of the energy dissipation. K E Y W O R D Sacoustoelasticity problems, complex oscillation frequency, complex sound velocity, energy dissipation, free and forced vibrations, generalized Helmholtz equation, Kelvin-Voigt model, perfect compressible fluid, plate, sound pressure, sound transmission loss

Vibration of a Two-Layer “Metal+PZT” Plate Contacting with Viscous Fluid

“…Finally, we obtain a system of 14 linear algebraic equations which contains 14 unknown constants by substituting the expressions in ( 34), ( 36) and ( 42) into the Fourier transforms of the boundary conditions in (10), contact conditions in (11), compatibility conditions in (12), and impermeability conditions in (13). The explicit expressions of this system of equations are not written here to reduce the volume of the paper.…”

“…Since then, a lot of further research has been done. For a detailed review, as well as some recent results, see the works of Amabili [2], Akbarov [3,4], Akbarov et al [5][6][7], Guz [8], Guz et al [9], Paimushin et al [10], Paimushin et al [11], Shuaib et al [12], Sorokin et al [13], Zamanov et al [14] and many others listed therein.…”

“…Note that these investigations can be classified according to various aspects, such as the theories applied to describe the motion of the plate (approximate plate theories, which are described, for example in [1,2,[10][11][12] and many other theories discussed in the work of Akbarov [3]); the exact equations of elastodynamics discussed for example in [5][6][7][8][9]; and modeling of the plate material as elastic, for example, in the work of Akbarov et al [6] and many other works listed therein, or viscoelastic, for example, in the works [7,14]. Moreover, these works can be classified according to the type of dynamic problems considered (wave dispersion, free vibration, and forced vibration), the modeling of the fluid (inviscid fluid, viscous fluid, compressible and incompressible fluid), and so on.…”

On the dispersion of axisymmetric waves propagating in the initially strained highly elastic plate under two side contact with various fluids

“…The treatises [1][2][3][4][5][6][7][8] give an overview of the relevant research. From these papers, it is clear that before the work in papers [9] and [10] published this year, all the investigations on the wave dispersion problems related to the plate+fluid system consider the case of plane strain.…”

Analytical bending solutions of thin plates by two‐dimensional generalized integral transform method

“…Rectangular plates have been frequently used as crucial components of structures in many different engineering applications such as automobile, mechanical, aerospace and civil engineering during the past few decades [1–5]. As playing the important role in structure safety, the mechanical behaviour of such plate has attracted keen interest of many researchers [6–9].…”