Vibration and dynamic buckling of shear beam-columns on elastic foundation under moving harmonic loads

The vibration and buckling of an infinite shear beam-column, which considers the effects of shear and the axial compressive force, resting on an elastic foundation have been investigated when the system is subjected to moving loads of either constant amplitude or harmonic amplitude variation with a constant advance velocity. Damping of a linear hysteretic nature for the foundation was considered. Formulations in the transformed field domains of time and moving space were developed, and the response to moving loads of constant amplitude and the steady-state response to moving harmonic loads were obtained using a Fourier transform. Analyses were performed to examine how the shear deformation of the beam and the axial compression affect the stability and vibration of the system, and to investigate the effects of various parameters, such as the load velocity, load frequency, shear rigidity, and damping, on the deflected shape, maximum displacement, and critical values of the velocity, frequency, and axial compression. Expressions to predict the critical (resonance) velocity, critical frequency, and axial buckling force were proposed.     

Dynamic problems for and stress–strain state of inhomogeneous shell structures under stationary and nonstationary loads

This paper reviews studies and analyzes results on the effect of discrete ribs on the dynamic characteristics of rectangular plates and cylindrical shells. Use is made of the vibration equations derived from the classical theories of beams, plates, and shells. The effect of Pasternak’s elastic foundation on the critical velocities of a structurally orthotropic model of a ribbed cylindrical shell is determined. Nonstationary problems are solved for perforated and ribbed shells of revolution filled with a fluid or resting on an elastic foundation and subjected to moving or impulsive loads. Results from studies of the behavior of sandwich shell structures under impulsive loads of various types are presented     

Analysis of coupled-mode flutter of pipes conveying fluid on the elastic foundation

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Stability analysis of cylindrical shells containing a fluid with axial and circumferential velocity components

The stability of an elastic circular cylindrical shell of revolution interacting with a compressible liquid (gas) flow having both axial and tangential components is analyzed. The behavior of the fluid is studied within the framework of potential theory. The elastic shell is described in terms of the classical theory of shells. Numerical solution of the problem is performed using a semianalytical finite element method. Results of numerical experiments for shells with different boundary conditions and geometric dimensions are presented. The effects of fluid rotation on the critical flow velocity and the effect of axial fluid flow on the critical angular velocity of fluid rotation were estimated.     

移动周期载荷作用下孔隙热弹性地基的动力学响应

根据孔隙热弹性线性理论,本文首先建立了在移动周期载荷作用下孔隙热弹性地基动力学响应分析的数学模型,其中提出了在周期性边界上必须满足的6类适当的条件,即界面位移相等、应力相等、孔隙百分比相等、温度相等以及在外法线方向孔隙发展相等和温度导数相等。在此基础上,分别采用微分求积法(DQM)和有限差分法(FDM)对控制方程进行空间和时间离散,并求解。作为算例,分别研究了在移动周期载荷和极限车载作用下孔隙热弹性地基的动力学响应,考察了车速对沉降、孔隙体积百分比和温度的影响。可以看到,本文提出的处理周期性问题DQM,具有精度高、收敛性好,计算效率高等特点。     

Swelling effect on the dynamic behaviour of composite cylindrical shells conveying fluid

This paper presents a semi‐analytical investigation of a fluid–structure system. Both isotropic and composite cylindrical shells filled with or subjected to a flowing fluid have been considered in this study. The structure may be uniform or non‐uniform in the circumferential direction. The hybrid finite element approach, shearable shell theory and velocity potential flow theory have been combined to establish the dynamic equations of the coupled system. The set of matrices describing their relative contributions to equilibrium is determined by exact analytical integration of the equilibrium equations. The linear potential flow theory is applied to describe the fluid effects that lead to the inertial, centrifugal and Coriolis forces. The axisymmetric, beam‐like and shell modes of vibrations in both cases of uniform and non‐uniform cylindrical shells are investigated. Fluid elastic stability of a structure subjected to a flowing fluid is also studied. This theory yields the high and the low eigenvalues and eigenmodes with comparably high accuracy. Reasonable agreement is found with other theories and experiments. Copyright © 2005 John Wiley & Sons, Ltd.     

Dynamical response of hyper-elastic cylindrical shells under periodic load

Dynamical responses, such as motion and destruction of hyper-elastic cylindrical shells subject to periodic or suddenly applied constant load on the inner surface, are studied within a framework of finite elasto-dynamics. By numerical computation and dynamic qualitative analysis of the nonlinear differential equation, it is shown that there exists a certain critical value for the internal load describing motion of the inner surface of the shell. Motion of the shell is nonlinear periodic or quasi-periodic oscillation when the average load of the periodic load or the constant load is less than its critical value. However, the shell will be destroyed when the load exceeds the critical value. Solution to the static equilibrium problem is a fixed point for the dynamical response of the corresponding system under a suddenly applied constant load. The property of fixed point is related to the property of the dynamical solution and motion of the shell. The effects of thickness and load parameters on the critical value and oscillation of the shell are discussed.     

Flow-induced flutter instability of cantilever carbon nanotubes

Carbon nanotubes are finding significant application to nanofluidic devices. This work studies the influence of internal moving fluid on free vibration and flow-induced flutter instability of cantilever carbon nanotubes based on a continuum elastic model. Since the flow-induced vibration of cantilever pipes is non-conservative in nature, cantilever carbon nanotubes conveying fluid are damped with decaying amplitude for flow velocity below a certain critical value. Beyond this critical flow velocity, flutter instability occurs and vibration becomes amplified with growing amplitude. Our results indicate that internal moving fluid substantially affects vibrational frequencies and the decaying rate of amplitude especially for longer cantilever carbon nanotubes of larger innermost radius at higher flow velocity, and the critical flow velocity for flutter instability in some cases may fall within the practical range. On the other hand, a moderately stiff surrounding elastic medium (such as polymers) can significantly suppress the effect of internal moving fluid on vibrational frequencies and suppress or eliminate flutter instability within the practical range of flow velocity.     

Non-linear stability problem of an open conical sandwich shell under external pressure and compression

The stability problem of a shallow sandwich shell of conical segment shape, subjected to uniform external pressure and compression along generators is analysed based on the finitedeformation theory. With the help of the Ritz method the system of five non-linear, heterogeneous equations is obtained. They are the basic equations of elastic stability of the shell under consideration. The results of numerical calculations are presented in diagrams, which show the influence of basic mechanical properties and geometric parameters of the shell on the value of the upper and lower critical load.     

Torsional vibration and stability of functionally graded orthotropic cylindrical shells on elastic foundations

In this study, the torsional vibration and stability problems of functionally graded (FG) orthotropic cylindrical shells in the elastic medium, using the Galerkin method was investigated. Pasternak model is used to describe the reaction of the elastic medium on the cylindrical shell. Mixed boundary conditions are considered. The material properties and density of the orthotropic cylindrical shell are assumed to vary exponentially in the thickness direction. The basic equations of the FG orthotropic cylindrical shell under the torsional load resting on the Pasternak-type elastic foundation are derived. The expressions for the critical torsional load and dimensionless torsional frequency parameter of the FG orthotropic cylindrical shell resting on elastic foundations are obtained. The effects of variations of shell parameters, the exponential factor characterizing the degree of material gradient, orthotropy, foundation stiffness and shear subgrade modulus of the foundation on the critical torsional load and dimensionless torsional frequency parameter are examined.     

Response of railway track system on poroelastic half-space soil medium subjected to a moving train load

Based on the dynamic poroelastic theory of Biot, dynamic responses of a track system and poroelastic half-space soil medium subjected to moving train passages are investigated by the substructure method. The whole system is divided into two separately formulated substructures, the track and the ground, and the rail is described by introducing the Green function for an infinitely long Euler beam subjected to the action of moving axle loads of the train and the reactions of the sleeper. Sleepers are represented by a continuous mass and the effect of the ballast is considered by introducing the Cosserat model for granular medium. Using the double Fourier transform, the governing equations of motion are then solved analytically in the frequency-wave-number domain. The time domain responses are evaluated by the inverse Fourier transform computation for a certain train speed. Computed results show that the shape of the rail displacements of the elastic and poroelastic soil medium are in good agreement with each other of the low train velocity, but the result of the poroelastic soil medium is significantly different to that of the elastic soil medium for the high train velocity which is higher than Rayleigh-wave speed in the soil. The influence of the soil intrinsic permeability on soil responses is discussed with great care in both time domain and frequency domain. The dynamic responses of the soil medium are considerably affected by the fluid phase as well as the load velocity.     

移动简谐力作用下三维多孔饱和半空间的动力问题

研究了移动荷载作用下多孔饱和地基的动力问题.应用Fourier变换求解该问题的控制偏微分方程,考虑了荷载的移动速度及振动频率对多孔饱和地基动力响应的影响,重点研究了移动速度达地基表面波速时多孔饱和半空间的振动问题(马赫效应),并与相应的弹性介质的解答进行了比较.结果显示当移动速度与多孔饱和半空间的表面波速相近时,地基会产生很大的振动;当移动速度大于表面波速时,多孔饱和半空间的动力响应与弹性半空间的动力响应有较大的差别.     

Nonlinear vibrations of cylindrical shells filled with a fluid and subjected to longitudinal and transverse periodic excitation

The paper proposes an approach to studying the nonlinear vibrations of thin cylindrical shells filled with a fluid and subjected to a combined transverse–longitudinal load. Methods of nonlinear mechanics are used to find and analyze periodic solutions of the system of equations that describes the dynamic behavior of the shell when the natural frequencies of the shell and the frequencies of both periodic forces are in resonance relations.     

受移动简谐力作用的多孔弹性半平面问题

研究了匀速移动的振动荷载作用下半无限多孔饱和固体中产生的应力和孔隙水压力．应用Fourier变换求解该问题的控制偏微分方程,考虑了荷载的移动速度及振动频率对多孔饱和固体中应力与孔隙水压力的影响,并与相应的弹性介质的解答进行了比较．结果显示多孔饱和半平面中应力和孔隙水压力随荷载的移动速度与振动频率的增加而增大,多孔饱和固体在移动荷载下的动力响应与相应的单相弹性固体的动力响应有较大的差别。     

Modeling and dynamic analysis of bolted joined cylindrical shell

Based on Sanders shell theory, modeling and dynamic analysis of bolted joined cylindrical shell were studied in this paper. When subjected to external excitations, contact state such as stick, slip and separation may occur at those locations of bolts. Considering these three contact states, an analytical model of cylindrical shell with a piecewise-linear boundary was established for the bolted joined cylindrical shell. First, the model was verified by the simplified line system, and the effects of stiffness in connecting interface and the number of bolts on natural frequency and mode shape were investigated. Then, through the response under instantaneous excitation, damping characteristic of the system was proved which is caused by the friction model. Last, the effects of external load frequency, response location, excitation amplitude and connecting parameters including stiffness and preload were numerically investigated and fully explained by 3-D frequency spectrum. The results indicated that periodic motion, times periodic motion and even chaotic motion were observed based on different parameters.     

Forced nonlinear oscillations of cylindrical shells interacting with fluid flow

The dynamic interaction of thin cylindrical shells with the fluid flow inside them under external periodic loads is studied. A technique is proposed to calculate the parameters of forced nonlinear oscillations of shells with a fluid moving with nearly critical velocities. The amplitude-frequency characteristics of the fluid-shell system under steady-state oscillation are plotted __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 4, pp. 91–99, April 2006.     

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.     

移动荷载作用下非局部地基梁动力响应分析的有限元法Dynamic response of beams with nonlocal foundations subjected to moving loads using finite element method

基于非局部地基理论,推导了移动荷载作用下非局部地基梁动力响应问题的有限元解,分别讨论了地基的非局部参数、刚度、阻尼系数以及移动荷载速度对非局部地基梁动力响应的影响,并比较了非局部结果与局部结果的差异。结果表明,地基的非局部参数、刚度和阻尼是地基梁的动力响应的主要影响参数,地基梁最大响应及其发生的时刻与移动荷载速度有关。研究成果可为轨道地基系统设计提供参考。     

EFFECT OF ELASTIC FOUNDATIONS ON DIVERGENCE AND FLUTTER OF AN ARTICULATED PIPE CONVEYING FLUID

In this study, we generalize earlier investigations of Benjamin and Sugiyama & Paı̈doussis devoted to the stability of articulated pipes conveying fluid. The present study additionally incorporates the translational and rotational elastic foundations in an attempt to answer the following question: Do the elastic foundations increase the critical velocity of the fluid? It turns out that the attachment of the elastic foundation along the entire length of the pipe may either strengthen or weaken the system, with attendant increase or decrease in the critical velocity. The physical mechanism of the change of type of instability plays a crucial role in deciding whether or not the elastic foundation increases the critical velocity. If the elastic foundations are attached within the first pipe only, the instability mechanism is by flutter. If the elastic foundations are attached beyond the first pipe, then divergence may occur. The interplay of the two mechanisms may lead to a decrease of the critical velocity of the system with elastic foundations. A remarkable nonmonotonous dependence of the critical velocity with respect to the attachment foundation ratio is established.     

Dynamic displacements of an infinite beam on a poroelastic half space due to a moving oscillating load

This investigation is concerned with the dynamic displacements of a beam on a poroelastic half space under a periodic oscillating load of constant velocity. The governing equations for the proposed analysis are solved using Fourier transform. The expression for the vertical displacement is obtained according to the contact condition between a beam and a half space. The effects of the moving velocity and vibration frequency of the load on the dynamic displacement are considered in the numerical examples. The results show that the load velocity has significant influence on dynamic displacement. It is also noted that large differences exist between the dynamic responses for a beam on a poroelastic half space and on an elastic half space when the load velocity is larger than the shear wave speed of the medium. The reported work is supported by the National Natural Science Foundation of China (Project No. 10372073).