Dynamics of the oscillating moving load acting on the hydroelastic system consisting of the elastic plate, compressible viscous fluid and rigid wall

2016 ◽  
Vol 59 (3) ◽  
pp. 403-430 ◽  
Author(s):  
Surkay D. Akbarov ◽  
Meftun I. Ismailov
Keyword(s):  
Viscous Fluid ◽  
Elastic Plate ◽  
Moving Load ◽  
Rigid Wall ◽  
Compressible Viscous Fluid ◽  
Hydroelastic System

The forced vibration of the system consisting of an elastic plate, compressible viscous fluid and rigid wall

2015 ◽  
Vol 23 (11) ◽  
pp. 1809-1827 ◽  
Author(s):  
Surkay D Akbarov ◽  
Meftun I Ismailov
Keyword(s):  
Viscous Fluid ◽  
Elastic Plate ◽  
Forced Vibration ◽  
Stokes Equations ◽  
Excitation Frequency ◽  
Rigid Wall ◽  
Navier Stokes ◽  
Fluid Viscosity ◽  
Compressible Viscous Fluid ◽  
Plane Flow

The forced vibration of the system consisting of a pre-stressed elastic plate, barotropic compressible Newtonian viscous fluid and rigid wall is considered. The space between the plate and rigid wall is filled by the fluid. It is assumed that the forced vibration is caused by the lineally-located time-harmonic force acting on the free face plane of the plate. The motion of the plate is written by utilizing the exact equations of elastodynamics, but the motion of the compressible viscous fluid is described by the linearized Navier-Stokes equations. Moreover, it is assumed that the velocities and stresses of the constituents are continuous on the contact plane between the plate and fluid, and that the impermeability conditions on the rigid wall are satisfied. The dimensionless parameters which characterize the compressibility and viscosity of the fluid as well as the elasticity constants of the plate are introduced. Plane strain state in the plate and two-dimensional plane flow of the fluid are considered. Numerical results on the interface normal stress and velocities are presented. The influence of the problem parameters is also discussed, including the fluid viscosity and compressibility, thickness of the plate and fluid depth as well as the excitation frequency. In this discussion the focus is on the influence of the fluid depth on the studied quantities. This is the parameter through which the main difference arises between the present and previous works by the authors.

Wave Motion of a Compressible Viscous Fluid Contained in a Cylindrical Shell

1993 ◽  
Vol 115 (3) ◽  
pp. 302-312 ◽  
Author(s):  
J. H. Terhune ◽  
K. Karim-Panahi
Keyword(s):  
Velocity Field ◽  
Viscous Fluid ◽  
Imaginary Part ◽  
Fluid Velocity ◽  
Wave Number ◽  
Mode Shapes ◽  
Infinite Length ◽  
Complex Frequency ◽  
Compressible Viscous Fluid ◽  
Fluid Velocity Field

The free vibration of cylindrical shells filled with a compressible viscous fluid has been studied by numerous workers using the linearized Navier-Stokes equations, the fluid continuity equation, and Flu¨gge ’s equations of motion for thin shells. It happens that solutions can be obtained for which the interface conditions at the shell surface are satisfied. Formally, a characteristic equation for the system eigenvalues can be written down, and solutions are usually obtained numerically providing some insight into the physical mechanisms. In this paper, we modify the usual approach to this problem, use a more rigorous mathematical solution and limit the discussion to a single thin shell of infinite length and finite radius, totally filled with a viscous, compressible fluid. It is shown that separable solutions are obtained only in a particular gage, defined by the divergence of the fluid velocity vector potential, and the solutions are unique to that gage. The complex frequency dependence for the transverse component of the fluid velocity field is shown to be a result of surface interaction between the compressional and vortex motions in the fluid and that this motion is confined to the boundary layer near the surface. Numerical results are obtained for the first few wave modes of a large shell, which illustrate the general approach to the solution. The axial wave number is complex for wave propagation, the imaginary part being the spatial attenuation coefficient. The frequency is also complex, the imaginary part of which is the temporal damping coefficient. The wave phase velocity is related to the real part of the axial wave number and turns out to be independent of frequency, with numerical value lying between the sonic velocities in the fluid and the shell. The frequency dependencies of these parameters and fluid velocity field mode shapes are computed for a typical case and displayed in non-dimensional graphs.

scholarly journals Analytical Expressions of Hydro-Seismic Forces on Dams

2018 ◽  
Author(s):  
Abdelmadjid Tadjadit ◽  
Boualem Tiliouine
Keyword(s):  
Viscous Fluid ◽  
Linear Combination ◽  
Upstream Face ◽  
Compressible Viscous Fluid ◽  
Natural Modes ◽  
Boundary Method ◽  
Complete Sets ◽  
Seismic Forces ◽  
Analytical Expressions

Analytical expressions for the determination of hydro-seismic forces acting on a rigid dam with irregular upstream face geometry in presence of a compressible viscous fluid are derived through a linear combination of the natural modes of water in the reservoir based on a boundary method making use of complete sets of complex T-functions.Analytical expressions for the determination of hydro-seismic forces acting on a rigid dam with irregular upstream face geometry in presence of a compressible viscous fluid are derived through a linear combination of the natural modes of water in the reservoir based on a boundary method making use of complete sets of complex T-functions. The formulas obtained for distributions of both shear forces and overturning moments are simple, computationally effective and useful for the preliminary design of dams. They show clearly the separate and combined effects of compressibility and viscosity of water. They also have the advantage of being able to cover a wide range of excitation frequencies even beyond the cut-off frequencies of the natural modes of the reservoir. Key results obtained using the proposed analytical expressions of the hydrodynamic forces are validated using numerical and experimental solutions published for some particular cases available in the specialized literature.

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