Free vibrations of a liquid in a rectangular channel with an elastic membrane on the free surface

1995 ◽  
Vol 31 (8) ◽  
pp. 661-667
Author(s):  
V. A. Trotsenko
Keyword(s):  
Free Surface ◽  
Rectangular Channel ◽  
Free Vibrations ◽  
Elastic Membrane

Surface folds during the penetration of a viscoelastic fluid by a sphere

2002 ◽  
Vol 460 ◽  
pp. 337-348 ◽  
Author(s):  
THOMAS PODGORSKI ◽  
ANDREW BELMONTE
Keyword(s):  
Relaxation Time ◽  
Free Surface ◽  
Physical Mechanism ◽  
Pressure Field ◽  
Elastic Membrane ◽  
Anisotropic Elastic ◽  
The Stability ◽  
Stress Boundary ◽  
Settling Process ◽  
Present Experimental Evidence

When a sphere settles through the free surface of a viscous fluid, the interface is deformed and assumes a funnel shape behind the sphere. If the fluid is viscoelastic and the settling process is fast compared to the relaxation time of the fluid, elastic effects are dominant and an instability occurs. The interface loses its original axisymmetry and buckles, leading to a particular mode of pinch-off unseen in Newtonian fluids. We present experimental evidence that stress boundary layers form in this type of flow, and argue that a physical mechanism for this instability can be recovered, at least qualitatively, by considering the stability of a stretched anisotropic elastic membrane in a pressure field.

Surface folding of viscoelastic fluids: finite elasticity membrane model

2004 ◽  
Vol 15 (4) ◽  
pp. 385-408 ◽  
Author(s):  
T. PODGORSKI ◽  
A. BELMONTE
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Pressure Field ◽  
Numerical Study ◽  
Finite Elasticity ◽  
Viscoelastic Fluids ◽  
Deborah Number ◽  
Elastic Membrane ◽  
Surface Wetting ◽  
Qualitative Behaviour

When a dry sphere sinks into a fluid, a funnel-shaped free surface develops behind the sphere if the sinking occurs faster than the surface wetting. If the fluid is viscoelastic, the interface can become unstable to a loss of axisymmetry. The stress near this surface concentrates into boundary layers, as also seen in other free surface extensional flows of viscoelastic fluids. At high Deborah number and low Reynolds number, the qualitative behaviour can be recovered by considering the static equilibrium of a stretched elastic membrane in an hydrostatic pressure field. We treat this problem in the framework of finite elasticity using a neo-Hookean constitutive model, and show how the conditions of instability can be recovered. A numerical study of this model is presented.

scholarly journals EIGENFREQUENCIES OF OSCILLATIONS OF A PLATE WHICH SEPARATES A TWO-LAYER IDEAL FLUID WITH A FREE SURFACE IN A RECTANGULAR CHANNEL

2021 ◽  
Vol 3 (2) ◽  
pp. 75-87
Author(s):  
О. Lymar ◽  
Keyword(s):  
Free Surface ◽  
Frequency Spectrum ◽  
Ideal Fluid ◽  
Elastic Plate ◽  
Homogeneous Equation ◽  
Rectangular Channel ◽  
Partial Solution ◽  
Fundamental Solutions ◽  
Frequency Equation ◽  
Inhomogeneous Equation

The frequency spectrum of plane vibrations of an elastic plate separating a two-layer ideal fluid with a free surface in a rectangular channel is investigated analytically and numerically. For an arbitrary fixing of the contours of a rectangular plate, it is shown that the frequency spectrum of the problem under consideration consists of two sets of frequencies describing the vibrations of the free surface of the liquid and the elastic plate. The equations of coupled vibrations of the plate and the fluid are presented using a system of integro-differential equations with the boundary conditions for fixing the contours of the plate and the condition for the conservation of the volume of the fluid. When solving a boundary value problem for eigenvalues, the shape of the plate deflection is represented by the sum of the fundamental solutions of a homogeneous equation for a loose plate and a partial solution of an inhomogeneous equation by expanding in terms of eigenfunctions of oscillations of an ideal fluid in a rectangular channel. The frequency equation of free compatible vibrations of a plate and a liquid is obtained in the form of a fourth-order determinant. In the case of a clamped plate, its simplification is made and detailed numerical studies of the first and second sets of frequencies from the main mechanical parameters of the system are carried out. A weak interaction of plate vibrations on vibrations of the free surface and vice versa is noted. It is shown that with a decrease in the mass of the plate, the frequencies of the second set increase and take the greatest value for inertialess plates or membranes. A decrease in the frequencies of the second set occurs with an increase in the filling depth of the upper liquid or a decrease in the filling depth of the lower liquid. Taking into account two terms of the series in the frequency equation, approximate formulas for the second set of frequencies are obtained and their efficiency is shown. With an increase in the number of terms in the series of the frequency equation, the previous roots of the first and second sets are refined and new ones appear.

scholarly journals Forced liquid vibrations in prismatic tanks under vertical and horizontal loads

2019 ◽  
Keyword(s):  
Free Surface ◽  
Velocity Potential ◽  
Excitation Frequency ◽  
Free Vibrations ◽  
Phase Portraits ◽  
Design Stage ◽  
Kinematic Condition ◽  
Vertical Excitation ◽  
Basic Functions ◽  
Static Conditions

The method of studying forced vibrations of a liquid in rigid prismatic tanks partially filed by a liquid is offered. It is supposed that the liquid is an ideal and incompressible one, and its motion, caused by the action of external influences, is irrotational. In these assumptions, there exists a velocity potential that satisfies the Laplace equation. The boundary value problem for this potential is formulated. On the wetted surfaces of the tank the non-penetration conditions are chosen. On the free surface of the liquid, the kinematic and static conditions are specified. The static condition consists in the equality of pressure on the free surface to atmospheric one. The liquid pressure is determined from the Cauchy-Lagrange integral. To formulate the kinematic condition, an additional unknown function is introduced, which describes the motion of the free surface. The kinematic condition is the equality of the velocity of the liquid, which is described by the velocity potential, and the velocity of the free surface itself. These modes of free vibrations are used as a system of basic functions in solving problems of forced fluid vibrations in reservoirs. Unknown functions are presented as series of the basic functions. The coefficients of these series are generalized coordinates. Periodic excitation forces acting in the vertical and horizontal directions are considered. If vertical excitation is studied, this leads to appearance of additional acceleration. Here we obtain a system of unbounded differential equations of the Mathieu type. This allows us to investigate the phenomena of parametric resonance. The effect of parametrical resonance is considered when the vertical excitation frequency is equal to double own frequency of liquid vibrations Dependences of change in the level of free surface via time under both separate and mutual action of horizontal and, vertical forces of are obtained. The phase portraits of a dynamic system with indication of resonances are presented. The method allows us to carry out the adjustment of undesired excitation frequencies at the design stage at reservoir producing in order to prevent the loss of stability.

scholarly journals Bulging Modes of Circular Bottom Plates in Rigid Cylindrical Containers Filled with a Liquid

1997 ◽  
Vol 4 (1) ◽  
pp. 51-68 ◽  
Author(s):  
Marco Amabili
Keyword(s):  
Free Surface ◽  
Liquid Surface ◽  
Dynamic Pressure ◽  
Ritz Method ◽  
Free Vibrations ◽  
Free Liquid Surface ◽  
Mode Shapes ◽  
Bottom Plate ◽  
Free Surface Waves ◽  
Theoretical Approaches

In this article the free vibrations of the bottom plate of an otherwise rigid circular cylindrical tank filled with liquid are studied, considering only the bulging modes (when the amplitude of the plate displacement is predominant with respect to that of the free surface). The tank axis is vertical, thus the free liquid surface is orthogonal to the tank axis. The liquid is assumed to be inviscid, and the contribution of the free surface waves to the dynamic pressure on the free liquid surface is neglected. Wet and dry mode shapes of the plate are assumed to be the same, so that the natural frequencies are obtained by using the nondimensionalized added virtual mass incremental (NA VMI) factors and the modal properties of dry plates. This simplifies computations compared to other existing theoretical approaches. NAVMI factors express the nondimensionalized ratio between the reference kinetic energy of the liquid and that of the plate and have the advantage that, due to their nondimensional form, they can be computed once and for all. Numerical results for simply supported and clamped bottom plates, as well as for supported plates with an elastic moment edge constraint are given. For more accurate results, and to exceed the limits of the assumed modes approach, the Rayleigh-Ritz method is applied and results are compared to those obtained by using the NAVMI factors and other existing methods in the literature.

scholarly journals Three-Dimensional Simulation of a Tank Filling With a Viscous Fluid Using the VOF Method

2020 ◽  
pp. 670-677
Author(s):  
Evgeny I. Borzenko ◽  
Efim I. Hegaj
Keyword(s):  
Free Surface ◽  
Constant Velocity ◽  
Rectangular Channel ◽  
Three Dimensional ◽  
Fluid Flows ◽  
Surface Shape ◽  
Convex Shape ◽  
Parametric Studies ◽  
Free Surface Shape ◽  
Dimensional Simulation

This paper presents the results of 3D modeling of a Newtonian fluid flow with a free surface. The PLIC-VOF algorithm, which is developed to solve the problems of two-dimensional fluid flows with a free surface, is generalized to the case of three-dimensional flows. Efficiency of the developed algorithm and reliability of the obtained results are justified by comparing with available data in literature and by testing approximation convergence. Parametric calculations of a rectangular channel filling show that the free surface assumes a steady convex shape over time and then moves along the channel at a constant velocity. As a result of parametric studies, the dependences of geometric characteristics of the free surface shape on problem parameters have been plotted

scholarly journals Study of Free Surface Flows in Rectangular Channel over Rough Beds

2016 ◽  
Vol 9 (6) ◽  
pp. 3023-3031 ◽  
Author(s):  
S. H. Talbi ◽  
A. Soualmia ◽  
L. Cassan ◽  
L. Masbernat ◽  
◽  
...  
Keyword(s):  
Free Surface ◽  
Rectangular Channel ◽  
Free Surface Flows ◽  
Surface Flows ◽  
Rough Beds

On the role of tin underlays for the prevention of thermal grooving in thin gold films

1986 ◽  
Vol 44 ◽  
pp. 732-733
Author(s):  
Jin Young Kim ◽  
R. E. Hummel ◽  
R. T. DeHoff
Keyword(s):  
Thin Film ◽  
Free Surface ◽  
Grain Boundary ◽  
Beneficial Effect ◽  
Failure Mechanism ◽  
Failure Mechanisms ◽  
Distinct Advantage ◽  
Gold Films ◽  
Gold Thin Film

Gold thin film metallizations in microelectronic circuits have a distinct advantage over those consisting of aluminum because they are less susceptible to electromigration. When electromigration is no longer the principal failure mechanism, other failure mechanisms caused by d.c. stressing might become important. In gold thin-film metallizations, grain boundary grooving is the principal failure mechanism.Previous studies have shown that grain boundary grooving in gold films can be prevented by an indium underlay between the substrate and gold. The beneficial effect of the In/Au composite film is mainly due to roughening of the surface of the gold films, redistribution of indium on the gold films and formation of In2O3 on the free surface and along the grain boundaries of the gold films during air annealing.

Sign in / Sign up

Export Citation Format

Share Document