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Thin-walled structures, plate included, interacting with fluid have found wide application in real technical objects such, for example, as pipelines, storage reservoirs for fuel and chemically aggressive fluids, heat exchangers of different configurations, aircraft propellant containers. The above objects require special attention in relation to safety of their operation under conditions of high operational loads, vibrations, or seismic action. In the majority of studies, the liquid medium is considered ideal, and its perturbed motion is assumed to be vortex-free. However, it has been known that in the process of hydrodynamic interaction the damping properties of the system essentially depend on the viscous characteristics of the fluid. The primary purpose of this study is to develop a numerical algorithm for solving the problem on spatial vibrations of one or several parallel plates interacting with viscous fluid and its subsequent verification through comparison of the obtained results with the experimental data.
The experimental technique used to investigate the modal characteristics of rectangular plates interacting with the fluid is based on the laser vibrometry method. The oscillations are excited in the non-contact manner by the loudspeaker. Such an approach allows one to obtain the “purest” data, because no associated mass and contact interactions are introduced in the system. The measurements are taken by a Polytec PDV-100 digital laser vibrometer. The recorded values of vibration velocity are processed using the Fast Fourier Transform procedure. The values of eigenfrequencies are determined from the analysis of Fourier images of the signals.
The perturbed vortex-free motion of the viscous fluid is described in the framework of acoustic approximation in terms of the velocity potential. The corresponding finite-element relations are constructed using Bubnov-Galerkin method. The deformations of the plate are determined based on Timoshenko theory. The mathematical formulation of the elastic structure dynamics problem relies on the principle of virtual displacements, taking into account the inertia forces and forces exerted on the system by the fluid. The solution of the problem involves the computation and analysis of the complex eigenvalues of the coupled system of equations and is implemented with the use of ARPACK procedure, which is based on the implicitly restarted Arnoldi method. Reliability of the finite-element solution of the problem is verified by comparing the results of calculation with the experimental data obtained for a single plate interacting with the fluid layer.
The developed numerical algorithm was used to derive new data about the dynamic characteristics of the plates interacting with different kinds of viscous fluids. The paper presents the results of computation of eigenfrequencies, vibration modes and damping decrements obtained for single and two parallel plates for different geometrical dimensions, boundary conditions and heights of the fluid layer. It has been found that viscosity has a minor impact on the vibration frequencies of the examined systems and, conversely, exerts a considerable effect on the damping decrement. It has been shown that increase in the height of the fluid layer enclosed between two parallel plates leads to a nonmonotonic dependence of the lowest vibration frequency, showing a pronounced extremum. By contrast, the behavior of the single plate is of asymptotic nature.

The work is supported by the Russian Foundation for Basic Research grant (project 16-41-590646).