低重环境下俯仰运动圆柱贮箱中液体非线性晃动

在低重力环境下,用变分原理建立了液体晃动的压力体积分形式的Lagrange函数,并将速度势函数在自由液面处作波高函数的级数展开,从而导出自由液面运动学和动力学边界条件非线性方程组;最后用四阶Runge-Kutta法求解非线性方程组。计算结果表明,随俯仰激励频率的逐渐变化,由于面外主模态和次生模态同时失稳,致使整个系统各阶模态和波高函数由稳态运动过渡为不稳定运动。     

Experimental study of liquid sloshing dynamics in a barge carrying tank

An experimental work has been carried out to study the phenomena of sloshing of liquid in partially filled tanks mounted on a barge exposed to regular beam waves. Three liquid fill levels with liquid depth, h_s to length of tank, l ratio (h_s/l) of 0.163, 0.325 and 0.488, are studied. The time histories of sloshing oscillation are measured along the length of container at predefined locations. The nonlinear behaviour of sloshing oscillation is observed for the regular wave excitation. The spectra of the sloshing oscillation and their qualitative assessment are reported. Attempts are made to evaluate the harmonics present in the sloshing oscillation and compare with the results of earlier studies. The effects of wave excitation frequency and wave height on the sloshing oscillation as well as on the response of the barge are studied.     

Experimental findings of the suppression of rotary sloshing on the dynamic response of a liquid storage tank

In liquid storage tanks, rotary sloshing occurs when the frequency of the lateral harmonic load is near the lowest frequency of the tank–liquid system. Rotary sloshing is a type of sloshing that modifies the tank response, which may cause instabilities of the tank wall. However, the consequences of rotary sloshing for the development of strain in the tank wall have not been elucidated. This paper presents an experimental determination of the effects of rotary sloshing on the development of strain and acceleration at various locations of a storage tank. A low-density-polyethylene tank containing water was tested using a shake table. Nine excitations with frequencies near the first free-vibration frequency of the tank–water system were employed. To suppress rotary sloshing, a high-density foam floating lid was utilised as a barrier. Results reveal rotary sloshing boosts not only the development of both hoop and axial strain but also the acceleration in the horizontal direction perpendicular to the excitation. The lid reduced the maximum hoop and axial strain by 500% and 400%, respectively compared to that when rotary sloshing occurs. Moreover, the lid suppressed the nonplanar sloshing by erasing the first three free-vibration frequencies of the tank–water system without the lid.     

Free bending vibration of annular cylindrical tank partially filled with liquid in the consideration of surface wave

ＦＲＥＥＢＥＮＤＩＮＧＶＩＢＲＡＴＩＯＮＯＦＡＮＮＵＬＡＲＣＹＬＩＮＤＲＩＣＡＬＴＡＮＫＰＡＲＴＩＡＬＬＹＦＩＬＬＥＤＷＩＴＨＬＩＱＵＩＤＩＮＴＨＥＣＯＮＳＩＤＥＲＡＴＩＯＮＯＦＳＵＲＦＡＣＥＷＡＶＥＺｈｏｕＤｉｎｇ（周叮）（ＮａｎｊｉｎｇＵｎｉｖｅ...     

Termination of the starting problem of dynamic expansion of a spherical cavity in an infinite elastic-perfectly-plastic medium

Perhaps the simplest non-trivial problem in small deformation dynamic plasticity is expansion of a spherical cavity in an infinite elastic-perfectly-plastic medium. Here, example problems are considered with two boundary conditions at the cavity's surface: constant velocity and constant pressure. Attempts to obtain analytical solutions are complicated by the fact that, in general, the elastic-plastic boundary propagates with variable speed. However, it is known that the elastic-plastic boundary propagates at constant speed for the starting problem when the shocks due to the applied loads are large enough to cause inelastic response at the instant they are applied. When the value of the applied pressure equals the shock pressure due to the applied velocity the solutions of the two boundary value problems are initially identical and can be compared. The objective of this paper is to review the literature and to examine the termination conditions for the starting problem. Specifically, the starting problem terminates when either the jump in radial stress at the elastic-plastic boundary or the loading condition for plasticity vanishes there. These termination conditions depend on the applied load and on Poisson's ratio.     

Experimental and numerical studies on interactions of a spherical flame with incident and reflected shocks

Observations are presented from experiments and calculations where a laminar spherical CH4/air flame is perturbed successively by incident and reflected shock waves. The experiments are performed in a standard shock tube arrangement, in which a high-speed shadowgraph imaging system is used to record evolutions of the flame. Numerical simulations are conducted by using second-order wave propagation algorithms, based on two-dimensional axisymmetric Navier-Stokes equations with detailed chemical reactions. Qualitative agreements are obtained between the experimental and numerical results. Under actions of incident shock waves, Richtmyer-Meshkov instability responsible for the flame deformation is induced in the flame, and the distoned flame takes a barrel shape. Then, under subsequent actions of the shock wave reflected from a planar wall, the flame takes an inclined non-symmetrical kidney shape in a symmetric cross section, which means a mushroom-like shape of the flame comes finally into being. The vorticity direction in the ring cap has been altered by the reflected shock＇s action, which makes the head of the mushroom-like flame extend quickly to the side wall.     

Chaos of liquid surface waves in a vessel under vertical excitation with slowly modulated amplitude

Free surface waves in a cylinder of liquid under vertical excitation with slowly modulated amplitude are investigated in the current paper. It is shown by both theoretical analysis and numerical simulation that chaos may occur even for a single mode with modulation which can be used to explain Gollub and Meyer's experiment. The implied resonant mechanism accounting for this phenomenon is further elucidated.     

A linear stability analysis of thermal convection in spherical shells with variable radial gravity based on the Tau-Chebyshev method

The onset of thermal convection in a non-rotating spherical shell is investigated using linear theory. The Tau-Chebyshev spectral method is used to integrate the linearized equations. We investigate the onset of thermal convection by considering two cases of the radial gravitational field (i) a local acceleration, acting radially inward, that is proportional to the distance from the center r, and (ii) a radial gravitational central force that is proportional to r⁻ⁿ. The former case has been widely analyzed in the literature, because it constitutes a simplified model that is usually used, in astrophysics and geophysics, and is studied here to validate the numerical method. The latter case was analyzed since the case n = 5 has been experimentally realized (by means of the dielectrophoretic effect) under microgravity condition, in the experimental container called GeoFlow, inside the International Space Station. Our study is aimed to clarify the role of (i) a radially inward central force (either proportional to r or to r⁻ⁿ), (ii) a base conductive temperature distribution provided by either a uniform heat source or an imposed temperature difference between outer and inner spheres, and (iii) the aspect ratio η (ratio of the radii of the inner and outer spheres), on the critical Rayleigh number. In all cases the surface of the spheres has been assumed to be rigid. The results obtained with the linear theory based on the Tau-Chebyshev spectral method are compared with those of the integration of the full non-linear equations solved by using the spectral element method. By using the Tau-Chebyshev method, we were able to explore new cases that have not been previously reported in the literature.     

Experimental study on the added mass and damping of a disk submerged in a partially fluid-filled tank with small radial confinement

The dynamic response of submerged and confined disk-like structures is of interest in engineering applications, such as in hydraulic turbine runners. This response is difficult to be estimated with accuracy due to the strong influence of the boundary conditions. Small radial gaps as well as short axial distances to rigid surfaces greatly modify the dynamic response because of the added mass and damping effects.In this paper, the influence of the axial nearby rigid distance on the dynamic response of a submerged disk is evaluated when the radial gap is very small. Moreover, the effects of the fluid depth and fluid viscosity on the natural frequencies and damping ratio of the submerged disk are studied. The study has been performed experimentally and numerically using structural–acoustic simulations.For the experimental investigation a test rig has been developed. It consists of a disk attached to a shaft and confined with a small radial gap inside a cylindrical container full of water. The disk can be moved up and down along the shaft to vary the axial distance to the nearby rigid surface. Piezoelectric patches are used to excite the disk and the response is measured with submersible accelerometers. Several excitation patterns can be used due to the disposition of these piezoelectric patches. For each configuration tested, the dynamic response of the structure is studied analyzing the natural frequencies and damping ratio of the disk attached to the shaft. The numerical results have been compared with the experimental results.