Transient Interaction of a Circular Plate and a Fluid Medium

1979 ◽  
Vol 46 (1) ◽  
pp. 26-30 ◽  
Author(s):  
J. W. Berglund
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Applied Pressure ◽  
Plate Boundary ◽  
Fluid Medium ◽  
Fluid Field ◽  
Elastic Circular Plate ◽  
Unstrained State ◽  
State Of Rest ◽  
Acoustic Fluid

The transient dynamic response of an elastic circular plate subjected to a suddenly applied pressure is determined for several edge boundary conditions. The plate boundary is attached to a semi-infinite, radially rigid tube which is filled with an acoustic fluid, and pressure is applied to the in-vacuo side of the plate. The transient solution is determined by using a technique in which the plate is subjected to a periodic pressure function constructed of appropriately signed and time-shifted Heaviside step functions, and by relying on a physical mechanism which returns the plate and fluid near the plate to an unstrained state of rest between pulses. The plate response is presented for a number of radius-to-thickness ratios and edge boundary conditions when interacting with water. Comparisons are also made with solutions obtained using a plane wave approximation to the fluid field.

scholarly journals Added Mass of Fluid and Fundamental Frequencies of a Horizontal Elastic Circular Plate Vibrating in Fluid of Constant Depth

2017 ◽  
Vol 64 (3-4) ◽  
pp. 163-186
Author(s):  
Kazimierz Szmidt ◽  
Benedykt Hedzielski
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Fluid Motion ◽  
Added Mass ◽  
Free Vibrations ◽  
Constant Depth ◽  
Infinite Layer ◽  
Pressure Load ◽  
Fundamental Frequencies ◽  
Elastic Circular Plate

AbstractThe paper deals with free vibrations of a horizontal thin elastic circular plate submerged in an infinite layer of fluid of constant depth. The motion of the plate is accompanied by the fluid motion, and thus, the pressure load on this plate results from displacements of the plate in time. The plate and fluid motions depend on boundary conditions, and, in particular, the pressure load depends on the gap between the plate and the fluid bottom. In theoretical description of this phenomenon, we deal with a coupled problem of hydrodynamics in which the plate and fluid motions are coupled through boundary conditions at the plate surfaces. This coupling leads to the so-called co-vibrating (added) mass of fluid, which significantly changes the fundamental frequencies (eigenfrequencies) of the plate. In formulation of the problem, a linear theory of small deflections of the plate is employed. At the same time, one assumes the potential fluid motion with the potential function satisfying Laplace’s equation within the fluid domain and appropriate boundary conditions at fluid boundaries. In order to solve the problem, the infinite fluid domain is divided into sub-domains of simple geometry, and the solution of problem equations is constructed separately for each of these domains. Numerical experiments have been conducted to illustrate the formulation developed in this paper.

scholarly journals Hydro-elastic vibration analysis of functionally graded rectangular plate in contact with stationary fluid

2018 ◽  
Author(s):  
Shahrouz Yousefzadeh ◽  
Ashkan Akbari ◽  
Mohammad Najafi
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Volume Fraction ◽  
Applied Pressure ◽  
Plate Boundary ◽  
Shear Deformation Theory ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Power Law Distribution

This study investigates the free vibration of a moderately thick rectangular plate, which is composed of functionally graded materials and floating on incompressible fluid. Material properties are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fraction of the constituent. The governing equations of the plate are analytically derived based on the first-order shear deformation theory with consideration of rotational inertial effects and transverse shear stresses. Applied pressure on the free surface of the plate is obtained by the velocity potential function together with Bernoulli’s equation. The equation governing on the oscillatory behaviour of the fluid is obtained by solving Laplace equation with satisfying the boundary conditions. The natural frequencies and shape modes of the rectangular plate are determined by decoupling and solving the motion equations system. Then, analyses of the numerical results of free vibrations and the effects of the different parameters such as thickness to length of the plate, boundary conditions, fluid density, index of volume fraction and the height of the fluid on the frequencies are investigated. Finally, the results of this research in limit case is compared and validated with the results of other researchers and finite element model.

scholarly journals Thermoelastic coupling vibration and stability analysis of rotating circular plate in friction clutch

2018 ◽  
Vol 38 (2) ◽  
pp. 558-573 ◽  
Author(s):  
Yongqiang Yang ◽  
Zhongmin Wang ◽  
Yongqin Wang
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Circular Plate ◽  
Coupling Coefficient ◽  
Inertial Force ◽  
Angular Speed ◽  
Circular Plates ◽  
Thermoelastic Coupling ◽  
Coupling Vibration ◽  
Friction Clutch

Rotating friction circular plates are the main components of a friction clutch. The vibration and temperature field of these friction circular plates in high speed affect the clutch operation. This study investigates the thermoelastic coupling vibration and stability of rotating friction circular plates. Firstly, based on the middle internal forces resulting from the action of normal inertial force, the differential equation of transverse vibration with variable coefficients for an axisymmetric rotating circular plate is established by thin plate theory and thermal conduction equation considering deformation effect. Secondly, the differential equation of vibration and corresponding boundary conditions are discretized by the differential quadrature method. Meanwhile, the thermoelastic coupling transverse vibrations with three different boundary conditions are calculated. In this case, the change curve of the first two-order dimensionless complex frequencies of the rotating circular plate with the dimensionless angular speed and thermoelastic coupling coefficient are analyzed. The effects of the critical dimensionless thermoelastic coupling coefficient and the critical angular speed on the stability of the rotating circular plate with simply supported and clamped edges are discussed. Finally, the relation between the critical divergence speed and the dimensionless thermoelastic coupling coefficient is obtained. The results provide the theoretical basis for optimizing the structure and improving the dynamic stability of friction clutches.

Hydroelastic Vibration of Rectangular Plates

1996 ◽  
Vol 63 (1) ◽  
pp. 110-115 ◽  
Author(s):  
Moon K. Kwak
Keyword(s):  
Boundary Conditions ◽  
Approximate Formula ◽  
Natural Frequencies ◽  
Mass Matrix ◽  
Ritz Method ◽  
Plate Boundary ◽  
Rigid Wall ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Virtual Mass

This paper is concerned with the virtual mass effect on the natural frequencies and mode shapes of rectangular plates due to the presence of the water on one side of the plate. The approximate formula, which mainly depends on the so-called nondimensionalized added virtual mass incremental factor, can be used to estimate natural frequencies in water from natural frequencies in vacuo. However, the approximate formula is valid only when the wet mode shapes are almost the same as the one in vacuo. Moreover, the nondimensionalized added virtual mass incremental factor is in general a function of geometry, material properties of the plate and mostly boundary conditions of the plate and water domain. In this paper, the added virtual mass incremental factors for rectangular plates are obtained using the Rayleigh-Ritz method combined with the Green function method. Two cases of interfacing boundary conditions, which are free-surface and rigid-wall conditions, and two cases of plate boundary conditions, simply supported and clamped cases, are considered in this paper. It is found that the theoretical results match the experimental results. To investigate the validity of the approximate formula, the exact natural frequencies and mode shapes in water are calculated by means of the virtual added mass matrix. It is found that the approximate formula predicts lower natural frequencies in water with a very good accuracy.

A Three-Equation Eddy-Viscosity Model for Reynolds-Averaged Navier–Stokes Simulations of Transitional Flow

2008 ◽  
Vol 130 (12) ◽  
Author(s):  
D. Keith Walters ◽  
Davor Cokljat
Keyword(s):  
Boundary Layer ◽  
Turbulent Flows ◽  
Eddy Viscosity ◽  
Flow Behavior ◽  
Applied Pressure ◽  
Plate Boundary ◽  
Low Frequency ◽  
Transitional Flow ◽  
Test Cases ◽  
Eddy Viscosity Model

An eddy-viscosity turbulence model employing three additional transport equations is presented and applied to a number of transitional flow test cases. The model is based on the k-ω framework and represents a substantial refinement to a transition-sensitive model that has been previously documented in the open literature. The third transport equation is included to predict the magnitude of low-frequency velocity fluctuations in the pretransitional boundary layer that have been identified as the precursors to transition. The closure of model terms is based on a phenomenological (i.e., physics-based) rather than a purely empirical approach and the rationale for the forms of these terms is discussed. The model has been implemented into a commercial computational fluid dynamics code and applied to a number of relevant test cases, including flat plate boundary layers with and without applied pressure gradients, as well as a variety of airfoil test cases with different geometries, Reynolds numbers, freestream turbulence conditions, and angles of attack. The test cases demonstrate the ability of the model to successfully reproduce transitional flow behavior with a reasonable degree of accuracy, particularly in comparison with commonly used models that exhibit no capability of predicting laminar-to-turbulent boundary layer development. While it is impossible to resolve all of the complex features of transitional and turbulent flows with a relatively simple Reynolds-averaged modeling approach, the results shown here demonstrate that the new model can provide a useful and practical tool for engineers addressing the simulation and prediction of transitional flow behavior in fluid systems.

Parameter Estimation for an Imperfectly Clamped Plate: Numerical Examples

1995 ◽  
Author(s):  
H. T. Banks ◽  
R. C. Smith ◽  
Yun Wang
Keyword(s):  
Parameter Estimation ◽  
Boundary Conditions ◽  
Circular Plate ◽  
Simple Zero ◽  
Numerical Examples ◽  
Vibrating Structures ◽  
Physical Experiments ◽  
Slight Rotation ◽  
Physical Manifestation ◽  
Clamped Edges

Abstract The problems associated with maintaining truly fixed (zero displacement and slope) or simple (zero displacement and moment) boundary conditions in applications involving vibrating structures have led to the development of models which admit slight rotation and displacement at the boundaries. In this paper, numerical examples demonstrating the dynamics of a model for a circular plate with imperfectly clamped boundary conditions are presented. The latitude gained when using the model for estimating parameters through fit-to-data techniques is also demonstrated. Through these examples, the manner in which the model accounts for the physical manifestation of imperfectly clamped edges is illustrated, and issues regarding the use of the model in physical experiments are defined.

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