Vibrations of a Cylindrical Shell Filled with a Liquid

The concurrent effect of a harmonic excitation and an airflow on the vibrations and vibroaccelerations of a thin-walled cylindrical shell filled with a liquid is studied     

Dynamics of Shell Systems Interacting with a Liquid

Results of studies into dynamic processes (both stationary and nonstationary) in differently excited shell systems interacting with a liquid are generalized and systematized. Problems related to this division of mechanics are formulated and methods developed for solving them are stated. Typical numerical results are presented.     

On the Chaotic Dynamics of a Spherical Pendulum with a Harmonically Vibrating Suspension

The equations of motion for a lightly damped spherical pendulum are considered. The suspension point is harmonically excited in both vertical and horizontal directions. The equations are approximated in the neighborhood of resonance by including the third order terms in the amplitude. The stability of equilibrium points of the modulation equations in a four-dimensional space is studied. The periodic orbits of the spherical pendulum without base excitations are revisited via the Jacobian elliptic integral to highlight the role played by homoclinic orbits. The homoclinic intersections of the stable and unstable manifolds of the perturbed spherical pendulum are investigated. The physical parameters leading to chaotic solutions in terms of the spherical angles are derived from the vanishing Melnikov–Holmes–Marsden (MHM) integral. The existence of real zeros of the MHM integral implies the possible chaotic motion of the harmonically forced spherical pendulum as a result from the transverse intersection between the stable and unstable manifolds of the weakly disturbed spherical pendulum within the regions of investigated parameters. The chaotic motion of the modulation equations is simulated via the 4th-order Runge–Kutta algorithms for certain cases to verify the analysis.     

Nonlinear Vibrations of a Cylindrical Shell Containing a Flowing Fluid

The Bogolyubov-Mitropolsky method is used to find approximate periodic solutions to the system of nonlinear equations that describes the large-amplitude vibrations of cylindrical shells interacting with a fluid flow. Three quantitatively different cases are studied: (i) the shell is subject to hydrodynamic pressure and external periodical loading, (ii) the shell executes parametric vibrations due to the pulsation of the fluid velocity, and (iii) the shell experiences both forced and parametric vibrations. For each of these cases, the first-order amplitude-frequency characteristic is derived and stability criteria for stationary vibrations are established__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 4, pp. 75–84, April 2005.     

Abnormal Frequencies in a Semi-Infinite Cylindrical Vessel Filled with a Fluid and Dynamically Excited by a Spherical Oscillator

International Applied Mechanics - A semi-infinite circular cylindrical cavity filled with a compressible ideal fluid and containing a spherical body near its end is considered. The body surface...     

Dynamics of a Spherical Microcavity in a Polymeric Liquid

The formation and collapse of a vapor microcavity (microbubble) in aqueous solutions of polyacrylamide with a molecular mass of 0.5–11 million and concentration of 0–6% is studied experimentally. A microbubble less than 100 m in size is formed as a result of local superheating of the liquid by a microheater. Using stroboscopic visualization, the microbubble evolution is investigated in detail. At high polymer concentrations and low molecular masses, a slowing of bubble collapse is noted. On the range of parameters considered, no radical change in microbubble dynamics due to the action of polymeric additives was observed.     

Dynamics of a Spherical Body in a Liquid with Rotational Vibration of the Cavity

The average dynamics of a single solid sphere in a liquid-filled cylindrical cavity in the presence of high-frequency rotational oscillation about the axis of symmetry is studied experimentally. In the cavity there is an impermeable membrane which forces the liquid as a whole to vibrates together with the cavity. Various orientations of the vessel in the gravity force field are considered. The action of an average force of vibrational nature on the sphere and the dependence of this force on the vibration parameters and the body dimensions and density are studied. The force is measured with respect to the floating threshold for the heavy body, when the average vibrational force balances or exceeds the action of the gravity force.     

含轴对称初始缺陷的具有正交各向异性表层的夹层圆柱壳的非线性屈曲

夹层圆柱壳具有很高的结构效能。在许多工程结构中被广泛采用。本文研究分析了含有轴对称初始缺陷的夹层圆柱壳在轴压下的非线性屈曲问题。该夹层壳具有正交各向异性表层和各向同性可承剪的夹心．利用Stein的前屈曲一致理论得出了前屈曲挠度随轴向载荷及缺陷参数的变化情况，运用Galerkin法导出了屈曲控制方程，并进行了数值计算，得到了屈曲载荷、缺陷幅值、缺陷波数、夹心模量等参量之间的关系．结果表明与壳体实际屈曲模态相同的初始缺陷具有很大的危害性，可以通过增加壳体表层的轴向弹性模量或优化夹心的有关参数等途径来提高屈曲载荷，改善壳体屈曲性能。     

Vibrations of a Rigid Body with Cylindrical Surface on a Vibrating Foundation

The analytic solution of the problem of forced vibrations of a rigid body with cylindrical surface on a horizontal foundation is given. It is assumed that the dry friction force acts at the point of contact between the cylindrical surface of the body and the foundation and the foundation moves by a harmonic law in the horizontal direction perpendicularly to the cylindrical surface element. The averaging method is used to determine the forced vibration mode near the natural frequency of the body vibrations on the fixed foundation. The results are presented as amplitude-frequency and phase-frequency characteristics.     

Spherical Vortex Structures with a Core and a Shell

In this paper we construct and investigate the vortex structure consisting of a spherical vortex (vortex core) inside a spherical vortex layer (shell). A partial case of this structure is a spherical vortex with uniformly helical motion of the fluid within the core and the shell. The strengths of the helical flows in the core and the shell are generally different. The case of identical strengths is analyzed in detail. The streamline pattern is presented. The vortex velocity limit at which the vortex does not collapse is found. This proves to be less by a factor 1.7 than the analogous quantity for a vortex without a shell and 4 times lower than the maximum velocity of the Hill vortex.     

Solution of Boundary-Value Problems of the Dynamics of a Liquid in Horizontal Cylindrical Cavities with Partitions

We propose methods for the construction of approximate solutions of main boundary-value problems. These methods enable one to determine frequencies and attached masses of an ideal liquid in a moving horizontal cylinder that has an arbitrary symmetric cross section and structural elements in the form of longitudinal edges-partitions.     

圆柱形弹性壳液耦合系统大幅低频重力波振动机理的研究

以圆柱形弹性壳液耦合系统为研究对象,根据非线性振动理论,建立了多自由度的非线性振动方程。通过数值计算,发现当激振力足够大,且激振力的频率在壳体固有频率与重力波固有频率之和的一个窄频带内时,会产生大幅低频重力波。从而解释了这一现象产生的振动机理。理论结果与实验结果基本吻合。     

Axisymmetric Interaction Problem for a Sphere Pulsating Inside an Elastic Cylindrical Shell Filled with and Immersed Into a Liquid

An interaction problem is formulated for a spherical body oscillating in a prescribed manner inside a thin elastic cylindrical shell filled with a perfect compressible liquid and submerged in a dissimilar infinite perfect compressible liquid. The geometrical center of the sphere is on the cylinder axis. The solution is based on the possibility of representing the partial solutions of the Helmholtz equations written in cylindrical coordinates for both media in terms of the partial solutions written in spherical coordinates, and vice versa. Satisfying the boundary conditions on the sphere and shell surfaces results in an infinite system of linear algebraic equations. This system is used to determine the coefficients of the Fourier-series expansions of the velocity potentials in terms of Legendre polynomials. The hydrodynamic characteristics of both liquids and the shell deflections are determined. The results obtained are compared with those for a sphere oscillating on the axis of an elastic cylindrical shell filled with a compressible liquid (the ambient medium being neglected).     

Natural Vibrations of a Cylindrical Shell Reinforced with Two-Layer Rings

The vibrations of a cylindrical shell reinforced with ring ribs attached to the shell by means of elastic elements are studied. The problem is solved by the finite-element method. The shell and ribs are modelled by a plane four-node finite element, which is a combination of a four-node plane stress element and a four-node flexural element. The effect of the stiffness of the elastic elements on the natural frequencies and modes is examined __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 8, pp. 105–110, August 2005.     

Vibrations of Cylindrical Shells Filled with a Liquid

The paper reports on experimental results for a dynamic system of two identical shells filled with a liquid and placed on a common elastic foundation. It is established that vibrations excited in one of the shells synchronize the vibrations of the whole system     

Dynamics of a Gas–Liquid Medium in a Torus-Like Shell Under Vibratory Actions

The results of experimental studies into the resonance vibration of a free liquid surface and gas–liquid medium in a torus-like shell are presented     

Interaction Between an Oscillating Sphere and a Thin Elastic Cylindrical Shell Filled with a Compressible Liquid. Internal Axisymmetric Problem

The problem on the interaction between a spherical body that oscillates in a prescribed manner and a thin elastic cylindrical shell filled with an ideal compressible liquid is formulated. It is assumed that the geometrical center of the sphere is located on the cylinder axis. The problem is solved based on the possibility of representing a partial solution of the Helmholtz equation written in cylindrical coordinates in terms of partial solutions in spherical coordinates, and vice versa. By satisfying the boundary conditions on the surfaces of the sphere and the shell, we obtain an infinite system of linear algebraic equations to determine the coefficients of expansion of the liquid-velocity potential into a Fourier series in terms of Legendre polynomials. The hydrodynamic characteristics of the liquid filling the cylindrical shell are determined and compared with the cases where a sphere oscillates in an infinite liquid and in a rigid cylindrical vessel