Hydroelastic System Research Articles

Coupled Frequencies of a Hydroelastic System of an Elastic Two-Dimensional Sector-Shell and Frictionless Liquid in Zero Gravity

For a circular sector system consisting of an elastic shell and an incompressible frictionless liquid layer with a free surface, the coupled liquid-structure frequencies are determined and compared with the natural (uncoupled) frequencies of the shell and the liquid. The coupled frequencies always exhibit smaller values than those of liquid and shell alone. The deviation increases with decreasing thickness of the liquid layer.

Application of transition functions in problems of transient hydroelasticity for systems of cylindrical shells

Elsewhere we discussed the formulation of transient hydroelasticity problems for systems of reflecting surfaces and development of methods for solving them. An approach based on the use of transition functions, which have been defined for the case of individual shells, may be of interest in some cases, when solving such problems for systems of shells, particularly cylindrical. When this approach is taken a preliminary qualitative analysis of the elements of a hydroelastic system can be made from the form of the functions and in a number of cases less computer time is required. The main complication in this case is in obtaining exact analytical expressions for the transition functions. To date, for the greater part such expressions have been obtained for single shells. Relations analogous to the transition functions of the external problem of transient hydroelasticity for a system of two cylindrical shells were used in [11] when calculating their displacements.

Transients in a shock-excited hydroelastic system of cylindrical shells of finite length

Forced oscillations of a system of cylindrical shells filled with a liquid are considered. The initial—boundary-value problem is solved by Godunov's method. Plots of kinematic parameters of the hydroelastic system reflecting the behavior of the wave fields are given.

Coupled frequencies of a hydroelastic system of an elastic two-dimensional sector-shell and frictionless liquid in zero gravity

For a circular sector system consisting of an elastic shell and an incompressible frictionless liquid layer with a free surface, the coupled liquid-structure frequencies are determined and compared with the natural (uncoupled) frequencies of the shell and the liquid. The coupled frequencies always exhibit smaller values than those of liquid and shell alone. The deviation increases with decreasing thickness of the liquid layer.

An estimate of the time of a direct-axis collision of a body of finite mass and a semiinfinite cylindrical shell with fluid

The problem of a direct-axis collision of a body affinite mass and a semi-infinite cylindrical shell with fluid is considered, and is solved using an analytic-numerical method, which is based on an application of the Laplace-Carson transform with its subsequent numerical inverse. An expression is found for the interaction force for the body and the hydro-elastic system, which allows us to determine the time of collision. Numerical results of calculations of the interaction force and the time of collision are given.

Frequencies of a hydroelastic rectangular system

The coupled hydroelastic frequencies of a liquid in a rectangular channel covered by a membrane or plate (beam in the here treated two-dimensional case) have been obtained for various boundary conditions. The coupled eigenvalues have been obtained and show a decrease for increasing length of the beam to liquid heigh ratio, while for increasing mass ratio of the beam mass per unit length to the liquid mass per unit length exhibit an increase of the coupled eigenvalue.

Oscillations and stability of a finite shell containing a fluid

The problem of determining the natural vibration frequency of a hollow conical shell containing a fluid is solved. Regions of dynamic instability of the hydroelastic system are constructed as a function of the depth of filling and the taper angle of the cone.

Coupled frequencies of a rotating hydroelastic shell-liquid system under zero gravity

The coupled natural frequencies of solidly rotating axially independent (two-dimensional) liquid-structure systems have been determined. The hydroelastic systems under consideration are a liquid layer around an elastic center shell, two immiscible liquids inside a cylindrical shell and an elastic shell in an infinite medium. The system was considered in a zero-gravity environment, thus being held together by surface- or interfacial tension. Strong deviation of the coupled frequencies in comparison with the uncoupled frequencies of the liquid and shell alone was found. In addition instability may occur, depending on the magnitude of the physical and geometrical parameters of the system.

Hydroelastic oscillations of a viscous infinitely long liquid column

The coupled frequencies of hydroelastic systems in zero gravity consisting of an elastic shell and a viscous liquid layer with a free surface have been treated. The system exhibits either an annular liquid layer around an elastic cylindrical center shell or a liquid layer inside an elastic infinitely long container. The first case has been evaluated numerically, where the influence of the liquid surface tension parameter, the elasticity parameter of the shell, its axial deflection wave length l and the thickness of the layer have been determined. In contrast to the hydroelastic system with an ideal liquid, the system with viscous liquid exhibits instability of the liquid surface as well as the shell.

Propagation of axisymmetric waves in a hydroelastic system

In this article we study normal axisymmetric waves propagating in a system consisting of an elastic isotropic space, which has a cylindrical cavity with a space within which an orthotropic cylindrical shell is coaxially situated. Between the surface of a cavity of radius R, and a shell of radius R (R < R,) with velocity v 2 there is a translational displacement in the layer of a nonviscous liquid differing in its physical properties from the liquid moving with velocity v I inside the shell.

Coupled frequencies of a hydroelastic system, consisting of an elastic shell and frictionless liquid

For a frictionless liquid layer around a cylindrical shell and a frictionless liquid inside a shell in a zero-gravity condition the hydroelastic interaction of the shell- and liquid-motion is treated. The coupled frequencies for the two-dimensional and three-dimensional cases are presented for various elasticity parameters and liquid layer thicknesses. There are strong interactions in both cases.

Coupled frequencies of a hydroelastic viscous liquid system

The coupled frequencies of a hydroelastic system consisting of an elastic shell and a viscous liquid layer with a free surface have been treated. The system exhibits no z-dependency and may be either an annular liquid layer around an elastic center shell or a liquid layer inside an elastic container. The first case has been evaluated numerically, where the influence of the liquid surface tension parameter, the elasticity parameter of the shell and the thickness of the layer have been determined. In contrast to the hydroelastic system with an ideal liquid, the system with viscous liquid exhibits instability of the liquid surface as well as the shell.

Modes and waves in a cochlear model

A simplified model hydroelastic system having many features in common with the cochlea is studied theoretically and experimentally. The system consists of a slender rigid tube filled with a viscous incompressible fluid. The tube is divided lengthwise into two chambers (scala vestibuli, scala tympani) by an interior surface, part of which is rigid and part elastic. The elastic portion is an isotropic plate having variable width and is clamped on its edges. The system is driven by a sinusoidal input at the stapes end. The mechanical model is 24 times life size and dynamical similarity is maintained. Wave patterns in the plate are measured using time-averaged and stroboscopic holographic interferometry. At low frequency (corresponding to less than 500 cycles/s in the cochlea) the response can be adequately predicted by a one dimensional theory. The waves are a combination of travelling and standing waves. The traveling component is solely a dissipative effect. Discrete resonances are readily observed in the low frequency range.

A spectral problem in hydroelasticity

The present paper is concerned with the analysis of the small vibrations of a coupled fluid-elastic system. In a geometrical sense the problem consists of a liquid-filled body which contains an internal elastic structure, such as an elastic plate or membrane. The mathematical model which describes the resulting dynamic response of the fluid and container is coupled through the differential equations as well as through the kinematic boundary conditions. Because of this, and the geometrical complexity, the problem is approached using variational methods. An analysis of various hydroelastic systems, without internal structures, can be found in Tong [l], Berger [2], and Moiseyev [3]. However, aside from the geometrical differences to our problem these authors deal primarily with sloshing, that is, elastic tanks which are partially filled with liquid. The associated spectral problem for the hydroelastic system, which is of the Steklov type, is studied by introducing certain energy spaces on which the operators are compact and positive. Preceding this the motion of the fluid is examined independently of the problem for the elastic boundary. As a result of this the eigenvalue problem can be reduced to a single operator equation which is easily resolved in the defined function spaces. After establishing the existence of a discrete spectrum the forced initial-value problem can be studied with little difficulty. The problem discussed in this article arose in modeling the dynamics of the cochlea. As a component of the inner ear the cochlea is believed to be responsible for most of the frequency resolution in the hearing process. Consequently a viable theory of hearing must include a comprehensive investigation of the natural frequencies and corresponding eigenfunctions. A description of the problem, as it applies to the cochlea, can be found in either Cole and Chadwick [4] or Holmes [5].

An approach to mechanics of the cochlea

A central problem in cochlear mechanics is an assessment of the mechanical basis of the ability of the ear to distinguish tones of different frequency. The starting point here is a fairly complete description of the cochlea as a hydroelastic system. The equations of an incompressible inviscid fluid, coupled to those of an elastic plate lead to a linear eigenvalue problem. Since the cochlea has a slender geometry, asymptotic methods can be used to generate a sequence of simplified problems. In the first approximation an interaction problem must be solved in a cross-plane. Integral properties of the second order problem connect the cross-plane solutions. Mode shapes and eigenvalues can then be calculated. It is found that the spectrum is relatively dense, which has importance in terms of the frequency sensitivity of the ear.

Note on the spectrum and normal modes of a general hydroelastic system

Note on the spectrum and normal modes of a general hydroelastic system