Dynamic response of liquid-filled rectangular tank with elastic appendages under pitching excitation

Nonlinear dynamics of liquid-filled rectangular tank with elastic appendages are studied. Based on the assumption of ideal fluid, the coupling dynamic equations of rigid tank, elastic appendages and liquid fuel are derived using H-O principle. In the case of pitch excitation, the modified potential function and wave height function are introduced to describe the moving boundary of fluid, then Galerkin's method is used to discretize the dynamic equations into ordinary differential equations. The natural frequencies of the coupling system are formulated in liquid depth, the length of the tank, etc. The formulae are confirmed by numerical simulations, which also show that the effects of liquid and elastic appendages on the attitude angular of rigid.     

System with a non-linear negative self-excitation

A two-mass system is analyzed consisting of a self-excited basic system, which is mounted on a foundation subsystem consisting of a mass on a spring. The self-excitation is expressed in differential equations by a non-linear term of the second power. The efficiency of the self-excited vibration suppressing of different positive damping components in both the subsystems is investigated by means of analytical and numerical solution. Phase plane trajectories gained by numerical solution show the distortion of pure harmonic forms of oscillations presumed in analytical solution. Ranges of system parameters in which the approximate bifurcation diagrams coincide with numerical results are ascertained.     

充液矩形贮箱弹性箱底板应力与变形分析

基于相容拉格朗日-欧拉法,通过对流场与弹性固体间流固耦合作用的分析,得到了矩形贮箱弹性底板流固耦合系统的自由振动微分方程。将伯努利方程与外加激励条件、速度势函数耦合到自由振动方程中,采用迦辽金积分法,给出了矩形贮箱在流体作用下的应力与变形的解析解。讨论了弹性底板的抗弯刚度、结构尺寸、底板材料参数及流体深度等因素对底板应力与变形的影响。研究结果表明:在液体晃动非线性激励作用下,贮箱底板的应力和变形随着液体深度、板长的增大而增大,随着板厚的减小而增大,且成非线性变化关系;底板的变形及应力与底板的材料常数相关,其中板厚的变化对其变形和应力影响要比板长及液体深度的影响显著得多。本文结果可为工程实际中矩形贮箱的设计提供参考。     

Standing surface waves in a rectangular tank with local wall and bottom irregularities

The results of laboratory experiments on the estimation of the effect of wall and bottom geometry on the frequency, height, and decay rate of standing surface waves in a tank oscillating in the vertical direction are presented. The effect of one or two semi-cylindrical inserts mounted on the face and rear walls of the tank is considered in detail for the cases of a horizontal bottom and a linear shallow on the bottom. The experimental data are interpreted using a mathematical longwave model based on the method of accelerated convergence.     

Stability of a spinning liquid-filled spacecraft

Summary The stability of a spinning liquid-filled spacecraft has been investigated in the present paper. Using Galerkin's method, the attitude dynamic equations have been given. The Liapunov direct method was employed to obtain a sufficient condition for stability. Three kinds of characteristic modals were investigated: free motion of inviscid fluid, slosh motion and non-slosh motion. All characteristic problems can be solved numerically by the Finite Element Method or the Boundary Element Method. It has been demonstrated that the viscosity of the fluid has a dissipative effect at large Reynolds number, while the slosh motion plays a destabilizing role. The non-slosh model of fluid does not affect the stability criterion. Accepted for publication 19 October 1996     

Non-uniqueness of the motions of a friction oscillator with self-excitation

Self-exciting non-unique motions of a system with a finite number of degrees of freedom are investigated. By means of an example, analytically calculated limit cycles can be compared with numerically determined attractors. This procedure allows the discussion of the initial conditions, the initial state, the step size and the influence of switch time with regard to the valuation of numerical results.     

Waves in a solid medium with liquid-filled pores

The dynamic nonlinear theory of deformation of a two-phase medium, a solid with pores filled with a liquid, is developed. The variational principle is used to derive nonlinear equations that take into account the motions of the solid and liquid phases and the porosity variations. All types of nonlinearity, including nonlinear friction, are also taken into account. Formulas for the velocities of the linear and nonlinear waves and the absorption coefficient are derived. The one- and three-dimensional cases are considered. In the three-dimensional case, an equation describing the wave profile evolution is obtained as well as a nonlinear Schrödinger equation. Their solutions are analyzed; soliton-type solutions and solutions for narrow beams are obtained.     

Measurements of differential diffusion in a liquid-filled lung model

 A noninvasive method for obtaining quantitative images of differential diffusion in liquid-filled lung models is presented. The method utilizes planar fluorescence imaging to obtain differences in concentration fields and was tested on an oscillatory flow of water in a Y-shaped tube. Differences as large as 36% were measured between the concentration fields of two dyes having a factor of 15 difference in their diffusion coefficient. The method is applicable to the study of differential diffusion in any internal flow. The relevance to recent clinical studies of liquid phase respiration (Greenspan et al. 1990) is discussed. Received: 6 September 1996/Accepted: 7 April 1997     

Free and forced oscillations of a frictionless liquid in a long rectangular tank with structural obstructions at the free liquid surface

Summary If a free liquid surface is partly covered with a solid wall, the natural frequencies and the response of the liquid in the container may be drastically changed. The fundamental natural frequency of a frictionless and incompressible liquid in an infinitely long rectangular container is determined for increasing structural coverage of the free surface. With increasing coverage of the surface by a rigid structural member, the natural frequencies increase drastically and reduce the sloshing motion. The response to translational excitation is evaluated also numerically. The procedure may be applied to arbitrary coverages of a three-dimensional rectangular container, and may also be used as a test case for purely numerical procedures such as the finite element method. Received 13 July 1999; accepted for publication 26 October 1999     

Pressure wave breakdown of a gas film in a liquid-filled slit

In [1–4] the results of investigating the breakdown of gas bubbles by medium-intensity pressure waves are presented and various bubble breakdown mechanisms are proposed. It is shown that breakdown may occur as a result of the formation of a cumulative jet on the boundary of the bubble or as a result of instability due to the relative motion of the bubble in the wave. In [5] experimental data on the pressure wave breakdown of a gas film in a liquid on a solid wall are reported. It is shown that at wave amplitudes p/p₀1 a liquid jet is formed at the edge of the gas film. The jet, traveling along the wall, strips off the film and carries it into the surrounding liquid. Below we investigate the pressure wave behavior of a gas film in a liquid-filled slit.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 175–178, September–October, 1992.     

Vibrational dynamics of a light body in a liquid-filled rotating cylinder

The behavior of a light free cylindrical body in a rapidly rotating horizontal cylinder containing a liquid under vibrational action (the vibration direction is perpendicular to the rotation axis) is investigated. An intense rotation of the body relative to the cavity is detected. Depending on the vibration frequency, the body rotation velocity in the laboratory reference system may be higher or lower than the cavity rotation velocity and in the resonance region they may differ by several times. The mechanism of motion generation is theoretically described. It is shown that the motion is related with the excitation of inertial oscillations of the body: the cause of the motion is an average vibrational force generated due to nonlinear effects in the Stokes boundary layer near the oscillating body. The formation of large-scale axisymmetric vortex structures periodic along the rotation axis, which appear under conditions of inertial oscillation of the body during its motion, both leading and lagging, is detected.     

Flutter of a rectangular plate

We address theoretically the linear stability of a variable aspect ratio, rectangular plate in a uniform and incompressible axial flow. The flutter modes are assumed to be two-dimensional but the potential flow is calculated in three dimensions. For different values of aspect ratio, two boundary conditions are studied: a clamped-free plate and a pinned-free plate. We assume that the fluid viscosity and the plate viscoelastic damping are negligible. In this limit, the flutter instability arises from a competition between the destabilising fluid pressure and the stabilising flexural rigidity of the plate. Using a Galerkin method and Fourier transforms, we are able to predict the flutter modes, their frequencies and growth rates. The critical flow velocity is calculated as a function of the mass ratio and the aspect ratio of the plate. A new result is demonstrated: a plate of finite span is more stable than a plate of infinite span.     

On the chaotic rotation of a liquid-filled gyrostat via the Melnikov-Holmes-Marsden integral

The non-linear motions of a gyrostat with an axisymmetrical, fluid-filled cavity are investigated. The cavity is considered to be completely filled with an ideal incompressible liquid performing uniform rotational motion. Helmholtz theorem, Euler's angular momentum theorem and Poisson equations are used to develop the disturbed Hamiltonian equations of the motions of the liquid-filled gyrostat subjected to small perturbing moments. The equations are established in terms of a set of canonical variables comprised of Euler angles and the conjugate angular momenta in order to facilitate the application of the Melnikov-Holmes-Marsden (MHM) method to investigate homoclinic/heteroclinic transversal intersections. In such a way, a criterion for the onset of chaotic oscillations is formulated for liquid-filled gyrostats with ellipsoidal and torus-shaped cavities and the results are confirmed via numerical simulations.     

Attitude maneuver of liquid-filled spacecraft with a flexible appendage by momentum wheel

Attitude maneuver of liquid-filled spacecraft with an appendage as a cantilever beam by momentum wheel is studied.The dynamic equations are derived by conservation of angular momentum and force equilibrium principle.A feedback control strategy of the momentum wheel is applied for the attitude maneuver.The residual nutation of the spacecraft in maneuver process changes with some chosen parameters,such as steady state time,locations of the liquid container and the appendage,and appendage parameters.The results indicate that locations in the second and fourth quadrants of the body-fixed coordinate system and the second quadrant of the wall of the main body are better choices for placing the liquid containers and the appendage than other locations if they can be placed randomly.Higher density and thicker cross section are better for lowering the residual nutation if they can be changed.Light appendage can be modeled as a rigid body,which results in a larger residual nutation than a flexible model though.The residual nutation decreases with increasing absolute value of the initial sloshing angular height.     

Coupling dynamic analysis of a liquid-filled spherical container subject to arbitrary excitation

Using spherical coordinates, the coupling nonlin- ear dynamic system of a liquid-filled spherical tank, which can be excited discretionarily, is deduced by the H-O variational principle, and the viscous damping is introduced via the liquid dissipation function. The kinetic equations of the coupling system are deduced by the relationship between the velocity of liquid particles and the disturbed liquid surface equation. Normal differential equations are obtained through the Galerkin method. An equivalent mechanical model is developed for liquid sloshing in a spherical tank subject to arbitrary excitation. The fixed and slosh masses, as well as the spring and damping constants, are determined in such a way as to satisfy the principle of equivalence. Numerical simulations illustrate the theoretical results in this paper as well.