Coupled vibration of a partially fluid-filled cylindrical container with a cylindrical internal body

In the present paper a method is proposed to investigate the effects of a rigid internal body on the coupled vibration of a partially fluid-filled cylindrical container. The internal body is a thin-walled and open-ended cylindrical shell. The internal body is concentrically and partially submerged inside a container. The radial and axial distances between the internal body and the container are filled with fluid. Along the contact surface between the container and the fluid, the compatibility requirement for the fluid–structure interactions is applied and the Rayleigh–Ritz method is used to calculate the natural frequencies and modes of a partially fluid-filled cylindrical container. The fluid domain is continuous, simply connected, and non-convex. The fluid is assumed to be incompressible and inviscid. The velocity potential for fluid motion is formulated in terms of eigenfunction expansions for two distinct fluid regions. The resulting equations are solved by using the Galerkin method. The results from the proposed method are in good agreement with experimental and numerical solutions available in the literature for the partially water-filled cylindrical container without internal body. A finite element analysis is also used to check the validity of the present method for the partially water-filled cylindrical container with internal body. The effects of the fluid level, internal body radius, and internal body length on the natural frequencies of the coupled system are also investigated.     

Collapse of a cylindrical cavity in a fluid layer under impact

The case of impact on a thin annular fluid layer with a gas-filled cavity is considered. The solution of the problem reduces to integrating a system of two first-order ordinary differential equations. The equations are analyzed qualitatively, and some exact solutions are found. Cases are noted of pulsation of the cavity, and the influence of counter-pressure and viscosity is investigated. The experimental results obtained are in agreement with the numerical computations carried out herein.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 98–106, November–December, 1970.The authors are grateful to A. M. Kogan and L. V. Mostovaya for performing the computations.     

Free vibration of circular cylindrical shell with constrained layer damping

Free vibration characteristics of circular cylindrical shell with passive constrained layer damping (PCLD) are presented. Wave propagation approach rather than finite element method, transfer matrix method, and Rayleigh-Ritz method is used to solve the problem of vibration of PCLD circular cylindrical shell under a simply supported boundary condition at two ends. The governing equations of motion for the orthotropic cylindrical shell with PCLD are derived on the base of Sanders’ thin shell theory. Numerical results show that the present method is more effective in comparison with other methods. The effects of the thickness of viscoelastic core and constrained layer, the elastic modulus ratio of orthotropic constrained layer, the complex shear modulus of viscoelastic core on frequency parameter, and the loss factor are discussed.     

The turbulent boundary layer on the moving surface of a cylindrical body

A study is made of the problem of a two-dimensional turbulent boundary layer on the moving surface of a cylindrical body (a Rankine oval with a relative elongation of four) moving at constant velocity in an incompressible fluid. For the numerical simulation of the turbulent flow of the fluid, the boundary layer is divided into exterior and interior regions in accordance with a two-layer model, using different expressions for the coefficients of turbulent transfer for each region. A study was nade of the development of the boundary layer on the body at different speeds of the body surface and different Reynolds numbers. The following integral characteristics were found by numerical calculation: the work of friction as the body is displaced; the work expended on the movement of its surface; and, for a flow regime with separation, the work of the pressure force. In this case the following model of separation flow is assumed: beyond the singular point in the solution of the boundary layer equations that indicates the appearance of a region of reverse flow, the pressure and friction stress on the wall are constant and are determined by their values at the singular point.Translated from Izvestiya Akademii Nauk SSSH, Mekhanika Zhidkosti i Gaza, No. 5, pp. 61–67, September–October, 1984.Finally, the author would like to thank G. G. Chernyi and Yu. D. Shevelev for useful discussions and for their interest in this work.     

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.     

单层偏心圆柱薄壳的自由振动特性分析研究

论文从偏心圆柱壳截面的几何特性出发,将偏心圆柱壳问题转化为一个周向变厚度圆柱壳问题,随后利用其状态向量之间的传递矩阵将壳体的振动控制方程转化为矩阵微分方程形式,通过Magnus级数法求解传递矩阵得到频率方程.采用Lagrange插值法得到偏心圆柱壳体自由振动状态下的固有频率,并且与圆柱壳的固有频率进行了比较.对影响结构固有频率的主要参数进行了分析,得到了这些参数和固有频率之间的关系.论文不仅提出了一种有效求解偏心圆柱壳固有频率的新方法,同时亦可为检测偏心圆柱壳的偏心距提供一种新的思路和方法.     

Dynamics of a two-fluid system in a rotating horizontal cylinder under longitudinal vibration

The average dynamics of immiscible fluids with different densities in a horizontal axially vibrating cylinder are studied. The angular velocity is sufficient to sustain the centrifuged state of the fluids. The vibration and rotation frequencies are of the same order. The generation of toroidal vortices periodic along the rotation axis and the formation of quasi-steady interface relief with axially periodic axisymmetric crimps are detected. It is shown that the vortex flow is associated with the generation of an inertial axisymmetric standing wave. The formation of the quasi-steady relief is induced by the development of the Kelvin-Helmholtz instability on the fluid interface under tangential vibration.     

Research on nonlinear vibration control of laminated cylindrical shells with discontinuous piezoelectric layer

Nonlinear Dynamics - A model of laminated cylindrical shells with discontinuous piezoelectric layer is proposed. Based on the first-order shear nonlinear shell theory, the nonlinear vibration...     

Boundary layer on a circular sector

The finite difference method is used to investigate laminar and turbulent boundary layers on a flat surface in the case of circular streamlines of the exterior flow. It is shown that when the flow is turned through large angles the behavior of the boundary layer over a finite circular sector differs qualitatively from an infinite sector. A study is made of the influence of the Mach number, the angle through which the flow is turned, and the wall temperature on the secondary flows in the boundary layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 35–41, January–February, 1982.     

Stability of thermocapillary motion in a cylindrical layer

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 50–52, July–August, 1989.     

Dynamics of an elastic half-space with a reinforced cylindrical cavity under moving loads

Partial separation of variables and reexpansion of cylindrical and plane waves are used to find the solution describing the uniform motion of a load along a thin circular cylindrical shell in an elastic half-space with the free surface parallel to the axis of the shell. This is a model problem for studying the dynamics of tunnels and shallow-buried pipelines under transport loads. Dispersion curves for the cases of sliding and tight contact between the shell and the half-space are plotted and analyzed. The effect of the shell parameters on the stress–strain state of the half-space is examined     

Free vibration analysis of functionally graded laminated sandwich cylindrical shells integrated with piezoelectric layer

An analytical method for the three-dimensional vibration analysis of a functionally graded cylindrical shell integrated by two thin functionally graded piezoelectric (FGP) layers is presented. The first-order shear deformation theory is used to model the electromechanical system. Nonlinear equations of motion are derived by considering the von Karman nonlinear strain-displacement relations using Hamilton’s principle. The piezoelectric layers on the inner and outer surfaces of the core can be considered as a sensor and an actuator for controlling characteristic vibration of the system. The equations of motion are derived as partial differential equations and then discretized by the Navier method. Numerical simulation is performed to investigate the effect of different parameters of material and geometry on characteristic vibration of the cylinder. The results of this study show that the natural frequency of the system decreases by increasing the non-homogeneous index of FGP layers and decreases by increasing the non-homogeneous index of the functionally graded core. Furthermore, it is concluded that by increasing the ratio of core thickness to cylinder length, the natural frequencies of the cylinder increase considerably.     

Dynamics of discontinuity formation in a cavitating liquid layer under shock wave loading

The problem of experimental modeling of discontinuity formation in a cavitating liquid layer under shock wave loading is considered. It is shown that the discontinuity takes the shape of a spherical segment and retains it up to the closure instant. The discontinuity surface becomes covered with a dynamically growing thin boundary layer consisting of bubbles, which transforms to a ring-shaped vortex bubble cluster at the instant of the discontinuity closure, generating a secondary shock wave. Specific features of the structure of the cavitating flow discontinuity arising at loading intensities lower than 0.1 and 5 kJ are discussed.     

Performance improvement of the stochastic-resonance-based tri-stable energy harvester under random rotational vibration

In this paper, the stochastic-resonance-based tri-stable energy harvester (TEH) is proposed to enhance harvesting performance under random rotational vibration. An electromechanical coupled system interfaced with a standard rectifier circuit driven by colored noise is considered. The stationary probability density function (SPDF) of the harvester is obtained by the improved stochastic averaging. Then, with the adiabatic approximation theory, the analytical expression of signal-to-noise ratio (SNR) for the TEH is deduced to characterize stochastic resonance (SR). To enhance direct current (DC) power delivery from a rotational TEH, the influences of system parameters on SR is discussed. The obtained results suggest that there are damping-induced resonance and noise-intensity-induced SR in the tri-stable system. The TEH has higher harvesting performance under the optimal SR. That is, the optimal parameter combinations can induce optimal SR and maximize harvesting performance. Thus, the stochastic-resonance-based TEH can be optimized to enhance energy harvesting through choosing the optimal parameter.     

Free vibration of an elastic bottom plate of a partially fluid-filled cylindrical container with an internal body

An analytical method is developed to consider the free vibration of an elastic bottom plate of a partially fluid-filled cylindrical rigid container with an internal body. The internal body is a rigid cylindrical block that is concentrically and partially submerged inside the container. The developed method captured the analytical features of the velocity potential in a non-convex, continuous, and simply connected fluid domain including the interaction between the fluid and the structure. The interaction between the fluid and the bottom plate is included. The Galerkin method is used for matching the velocity potentials appropriate to two distinct fluid regions across the common horizontal boundary (artificial horizontal boundary). Then, the Rayleigh–Ritz method is also used to calculate the natural frequencies and modes of the bottom plate of the container. The results obtained for the problem without internal body are in close agreement with both experimental and numerical results available in the articles. A finite element analysis is also used to check the validity of the present method in the presence of the internal body. Furthermore, the influences of various variables such as fluid level, internal body radius, internal body length, and the number of nodal diameters and circles on the dynamic behaviour of the coupled system are investigated.     

圆柱形充液室中4股贴壁燃气射流扩展特性的实验研究

为了探索高温高压周向均布4股贴壁燃气射流在受限空间中的扩展特性,设计了贴壁燃气射流在圆柱形充液室内扩展的实验装置,借助数字高速录像系统,观察了4股贴壁燃气射流在充液室中的扩展过程,发现由Kelvin-Helmholtz不稳定性引起的表面不规则一直存在于整个射流扩展过程;通过处理拍摄记录的射流扩展序列图,获得不同时刻射流扩展的轴向和径向位移; 对比了不同破膜喷射压力和喷孔结构参数对4股贴壁燃气射流扩展过程的影响。实验结果表明:喷孔面积越大,贴壁射流初期轴向扩展速度越大,但由于径向扩展达到交汇的时间较早,湍流掺混和干涉强烈,衰减也越快;破膜喷射压力越高,射流径向扩展到达交汇的时间越短; 破膜喷射压力从12 MPa升高到20 MPa,射流轴向扩展速度大幅增加,气液湍流掺混效应增强。