Dynamics and Stability of Coaxial Cylindrical Shells Conveying Viscous Fluid

1985 ◽  
Vol 52 (2) ◽  
pp. 389-396 ◽  
Author(s):  
M. P. Paidoussis ◽  
A. K. Misra ◽  
S. P. Chan
Keyword(s):  
Viscous Fluid ◽  
Annular Flow ◽  
Cylindrical Shells ◽  
Inviscid Flow ◽  
Viscous Effects ◽  
Fluid Forces ◽  
Frictional Pressure Drop ◽  
Generalized Force ◽  
Shell Equations ◽  
Shell Vibration

In this paper the dynamics and stability characteristics of coaxial cylindrical shells containing incompressible, viscous fluid flow are examined in contrast to previous studies where the fluid has been considered to be inviscid. Specifically, upstream pressurization of the flow (to overcome frictional pressure drop) and skin friction on the shell surfaces are taken into account, generating time-mean normal and tangential loading on the shells. Shell motions are described by Flu¨gge’s thin shell equations, suitably modified to incorporate the time-mean stress resultants arising from viscous effects. The fluctuating fluid forces, coupled to shell vibration, are determined entirely by means of linearized potential flow theory and formulated with the aid of generalized-force Fourier-transform techniques. It is found that the effect of viscosity in the annular flow generally tends to destabilize the system, vis-a`-vis inviscid flow, whereas viscous effects in the inner flow stabilize the system. These effects can be quantitatively very important, so that, generally, neglect of viscous effects cannot be justified.

A theoretical description of viscous flow along a flat plate

2005 ◽  
Vol 109 (1101) ◽  
pp. 585-589
Author(s):  
R. C. Hastings
Keyword(s):  
Heat Conduction ◽  
Viscous Fluid ◽  
Flat Plate ◽  
Stokes Equations ◽  
Heat Conduction Problem ◽  
Inviscid Flow ◽  
Theoretical Description ◽  
Successive Approximations ◽  
Navier Stokes ◽  
Viscous Effects

Theoretical quantification of viscous effects in fluid flows is difficult, even if turbulence is absent, except when it is legitimate to simplify the Navier-Stokes equations in some way; for example by invoking the boundary-layer approximation in appropriate cases of interacting viscous and inviscid flow. The technical importance of viscous effects was thought sufficient incentive to re-examine a very simple flow configuration — namely plane, uniform and steady flow of an incompressible, viscous fluid toward a vanishingly-thin flat plate aligned with the undisturbed stream — in search of fresh insights into the general theory for viscous-inviscid interactions. The strategy was to exploit the analogy between vorticity transport in a viscous fluid and heat conduction in a moving solid. The key to doing so was the realization that, if the perturbation of the undisturbed flow by the plate might be represented as the sum of a series of successive approximations, then the stream function of the viscous part of the flow field — not merely the vorticity which resulted from its existence — might be expressible at every stage as the solution of an analogous heat conduction problem.

scholarly journals Dynamical analysis of multilayered reinforced composite cylindrical shells

2005 ◽  
Vol 27 (4) ◽  
pp. 220-228
Author(s):  
Dao Huy Bich ◽  
Tran Thanh Tuan
Keyword(s):  
Linear Problem ◽  
Cylindrical Shells ◽  
Dynamical Analysis ◽  
Dynamical Equations ◽  
Fundamental Frequencies ◽  
Reinforced Composite ◽  
Longitudinal Stiffeners ◽  
Shell Vibration ◽  
Shell Geometry ◽  
Composite Cylindrical Shells

In the present paper the governing dynamical equations for multilayered reinforced composite cylindrical shells based on Kirchhoff-Love's theory and Lekhnitsky's smeared stiffeners technique are derived. The shell is reinforced by longitudinal and ring stiffeners. The longitudinal stiffeners may be composite or sleeves with SMA wire. The linear problem of shell vibration is considered for illustrating the effects of the stiffeners, the shell geometry and altering the lamination scheme on fundamental frequencies of the shell.

Parametrically Excited Vibrations and Auto-Parametric Resonance in Cylindrical Shells

2000 ◽  
Author(s):  
A. A. Popov ◽  
J. M. T. Thompson ◽  
F. A. McRobie
Keyword(s):  
Internal Resonance ◽  
Cylindrical Shells ◽  
Mode Interaction ◽  
Geometric Description ◽  
Modal Interactions ◽  
Structural Behaviour ◽  
Parametrically Excited ◽  
Parametric Resonances ◽  
Shell Vibration ◽  
Low Dimensional

Abstract Vibrations of cylindrical shells parametrically excited by external axial forcing or by internal auto-parametric resonances are considered. A Rayleigh-Ritz discretization of the von Kármán-Donnell equations through symbolic computations leads to low dimensional models of shell vibration. After applying methods and ideas of modern dynamical systems theory, complete bifurcation diagrams are constructed and analyzed with an emphasis on modal interactions and their relevance to structural behaviour. In the case of free shell vibrations, the Hamiltonian and a transformation into action-angle coordinates followed by averaging provides readily a geometric description of the interaction between concertina and chequerboard modes. It was established that the interaction should be most pronounced when there are slightly less than 2 N square chequerboard panels circumferentially, where N is the ratio of shell radius to thickness. The two mode interaction leads to preferred vibration patterns with larger deflection inwards than outwards, and at internal resonance, significant energy transfer occurs between the modes. The regular and chaotic features of this interaction are studied analytically and numerically.

scholarly journals Decomposition of the forces on a body moving in an incompressible fluid

2019 ◽  
Vol 881 ◽  
pp. 1097-1122
Author(s):  
W. R. Graham
Keyword(s):  
Velocity Field ◽  
Pressure Field ◽  
Rotational Velocity ◽  
Inviscid Flow ◽  
Added Mass ◽  
The Body ◽  
Mass Force ◽  
Natural Approach ◽  
Fluid Forces ◽  
Point Pressure

In analysing fluid forces on a moving body, a natural approach is to seek a component due to viscosity and an ‘inviscid’ remainder. It is also attractive to decompose the velocity field into irrotational and rotational parts, and apportion the force resultants accordingly. The ‘irrotational’ resultants can then be identified as classical ‘added mass’, but the remaining, ‘rotational’, resultants appear not to be consistent with the physical interpretation of the rotational velocity field (as that arising from the fluid vorticity with the body stationary). The alternative presented here splits the inviscid resultants into components that are unquestionably due to independent aspects of the problem: ‘convective’ and ‘accelerative’. The former are associated with the pressure field that would arise in an inviscid flow with (instantaneously) the same velocities as the real one, and with the body’s velocity parameters – angular and translational – unchanging. The latter correspond to the pressure generated when the body accelerates from rest in quiescent fluid with its given rates of change of angular and translational velocity. They are reminiscent of the added-mass force resultants, but are simpler, and closer to the standard rigid-body inertia formulae, than the developed expressions for added-mass force and moment. Finally, the force resultants due to viscosity also include a contribution from pressure. Its presence is necessary in order to satisfy the equations governing the pressure field, and it has previously been recognised in the context of ‘excess’ stagnation-point pressure. However, its existence does not yet seem to be widely appreciated.

scholarly journals Length-scale effect in stability problems for thin biperiodic cylindrical shells: extended tolerance modelling

2020 ◽  
Author(s):  
B. Tomczyk ◽  
M. Gołąbczak ◽  
A. Litawska ◽  
A. Gołąbczak
Keyword(s):  
Scale Effect ◽  
Cylindrical Shells ◽  
Length Scale ◽  
Stability Problems ◽  
Constant Coefficients ◽  
A Cell ◽  
Circular Cylindrical Shells ◽  
Tolerance Modelling ◽  
Tolerance Model ◽  
Shell Equations

Abstract Thin linearly elastic Kirchhoff–Love-type circular cylindrical shells of periodically micro-inhomogeneous structure in circumferential and axial directions (biperiodic shells) are investigated. The aim of this contribution is to formulate and discuss a new averaged nonasymptotic model for the analysis of selected stability problems for these shells. This, so-called, general nonasymptotic tolerance model is derived by applying a certain extended version of the known tolerance modelling procedure. Contrary to the starting exact shell equations with highly oscillating, noncontinuous and periodic coefficients, governing equations of the tolerance model have constant coefficients depending also on a cell size. Hence, the model makes it possible to investigate the effect of a microstructure size on the global shell stability (the length-scale effect).

Design of Aerofoils for Prescribed Pressure Distribution in Viscous Incompressible Flows

1980 ◽  
Vol 31 (1) ◽  
pp. 42-55 ◽  
Author(s):  
H.N.V. Dutt ◽  
A.K. Sreekanth
Keyword(s):  
Incompressible Flows ◽  
Design Procedure ◽  
Inviscid Flow ◽  
Viscous Effects ◽  
Inviscid Flows ◽  
Numerical Examples ◽  
Pressure Distributions ◽  
Displacement Thickness ◽  
Viscous Incompressible Flows ◽  
Attached Flow

SummaryA design procedure has been developed to generate aerofoil shapes for prescribed pressure distributions in an incompressible viscous attached flow. It is based on the method of singularities, originally proposed by Chen and later modified by Kennedy and Marsden, for inviscid flows. The classical approach of adding the displacement thickness of the boundary layer and wake to the aerofoil contour is used to account for viscous effects. Several numerical examples are worked out and are compared with the inviscid flow results. Significant changes in aerofoil contours due to viscous effects are observed and these are discussed.

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