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# On the Discrete-Analytical Solution Method of the Problems Related to the Dynamics of Hydro-Elastic Systems Consisting of a Pre-Strained Moving Elastic Plate, Compressible Viscous Fluid and RigidWall

Surkay D. Akbarov1,2,3, Panakh G. Panakhlı4

Yildiz Technical University, Faculty of Mechanical Engineering, Department of Mechanical Engineering, Yildiz Campus, 34349, Besiktas, Istanbul-TURKEY.
Institute of Mathematics and Mechanics of the National Academy of Sciences of Azerbaijan,37041, Baku, Azerbaijan.
Corresponding author. Email: akbarov@yildiz.edu.tr.
Azerbaijan Architecture and Civil Engineering University, Faculty of Mechanical and Information Technologies, Dep. Computing Hardware and Software, Baku, Azerbaijan. Email:panakh@yahoo.com

Computer Modeling in Engineering & Sciences 2015, 108(2), 89-112. https://doi.org/10.3970/cmes.2015.108.089

## Abstract

The discrete-analytical solution method is proposed for the solution to problems related to the dynamics of the hydro-elastic system consisting of an axially-moving pre-stressed plate, compressible viscous fluid and rigid wall. The fluid flow caused by the axial movement of the plate and the pre-stresses in the plate are taken into consideration as the initial state of the system under consideration. It is assumed that the additional lineally-located time-harmonic forces act on the plate and these forces cause additional flow field in the fluid and an additional stress-strain state in the plate. The additional stress-strain state in the plate is described by utilizing the equations and relations of the three-dimensional linearized theory of elastic waves in initially stressed elastic bodies. The additional fluid flow field is described with linearized Navier-Stokes equations for compressible viscous fluid. As the fluid flow velocities in the initial state are non-homogeneous, the linearized Navier-Stokes equations have variable coefficients and this situation causes difficulties in obtaining an analytical solution to these equations. The proposed discrete-analytical solution method allows this difficulty to be overcome and for approximate analytical solutions for these types of problems to be obtained. The proposed solution method is examined with respect to concrete problems. Numerical results obtained with the proposed approach are presented and discussed.

## Keywords

Akbarov, S. D., Panakhlı, P. G. (2015). On the Discrete-Analytical Solution Method of the Problems Related to the Dynamics of Hydro-Elastic Systems Consisting of a Pre-Strained Moving Elastic Plate, Compressible Viscous Fluid and RigidWall. CMES-Computer Modeling in Engineering & Sciences, 108(2), 89–112.

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