水浮力对浮桥动力响应特性的分析

为了研究水介质的浮力对桥梁静态响应、特别是动态响应的影响,了解水浮力在桥梁动力响应上的作用及其大小,利用虚功原理和振型叠加法对桥梁运动的控制方程进行求解,并编制了通用的求解程序,通过对比简支梁桥和浮桥各阶振型的传播速度、静力作用、单阶荷载作用以及移动荷载作用下的动力响应,得出水浮力的存在大大降低了浮桥的挠度,使得浮桥的动力响应存在临界长度,即简支梁桥的运动整体性强,而浮桥的运动局部性强,对浮桥进行动力分析时,可以在临界长度以内进行处理,而不必对整个桥梁进行求解.     

Dynamic analysis of suspended cables carrying moving oscillators

An efficient procedure for analyzing in-plane vibrations of flat-sag suspended cables carrying an array of moving oscillators with arbitrarily varying velocities is presented. The cable is modelled as a mono-dimensional elastic continuum, fully accounting for geometrical nonlinearities. By eliminating the horizontal displacement component through a standard condensation procedure, the nonlinear integro-differential equation governing vertical cable vibrations is derived. Due to the dynamic interaction at the contact points with the moving oscillators, such equation is coupled to the set of ordinary differential equations ruling the response of the travelling sub-systems. An improved series representation of vertical cable displacement is proposed, which allows to overcome the inability of the traditional Galerkin method to reproduce the kinks and abrupt changes of cable configuration at the interface with the moving sub-systems. Following the philosophy of the well-known “mode-acceleration” method, the convergence of the series expansion of cable response in terms of appropriate basis functions is improved through the introduction of the so-called “quasi-static” solution. Numerical results demonstrate that, despite the basis functions are continuous, the improved series enables to capture with very few terms the abrupt changes of cable profile at the contact points between the cable and the moving oscillators.     

Vibration suppression for high-speed railway bridges using tuned mass dampers

This paper deals with the applicability of passive tuned mass dampers (PTMDs) to suppress train-induced vibration on bridges. A railway bridge is modeled as an Euler–Bernouli beam and a train is simulated as series of moving forces, moving masses or moving suspension masses to investigate the influence of various vehicle models on the bridge features with or without PTMD. According to the train load frequency analysis, the resonant effects will occur as the modal frequencies of the bridges are close to the multiple of the impact frequency of the train load to the bridge. A single PTMD system is then designed to alter the bridge dynamic characteristics to avoid excessive vibrations. Numerical results from simply supported bridges of Taiwan High-Speed Railway (THSR) under German I.C.E., Japanese S.K.S. and French T.G.V. trains show that the proposed PTMD is a useful vibration control device in reducing bridge vertical displacements, absolute accelerations, end rotations and train accelerations during resonant speeds, as the train axle arrangement is regular. It is also found that the inner space of bridge box girder of THSR is wide and deep enough for the installation and movement of PTMD.     

Unilaterality and Dry Friction: A Geometric Formulation for Two-Dimensional Rigid Body Dynamics

The dynamics of a rigid body simply supported on a moving rigid ground in the presence of dry friction is investigated. Rigid body kinematics, in terms of generalized coordinates, and features of contact are discussed. According to the contact laws, a variational formulation is adopted to describe the dynamics and to analyze, in the case of contact, the connection between dynamically possible motions and actual evolution of the system. A geometric method is then proposed which allows the dynamic evolution to be determined without any direct evaluation of the contact forces. Though different situations are possible, depending on the instantaneous values of relative position, velocity and active forces, a unique solution is identified. Examples illustrating applications of the theory are presented.     

任意有限个平行移动荷载作用下简支梁绝对最大挠度的解析算法研究

利用能量原理中的最小势能原理以及多元函数的极值原理，得到了简支梁在任意有限个平行移动荷载作用下的挠度方程与绝对最大挠度的解析算式。建立的可能位移函数既满足了位移几何边界条件，又满足了静力边界条件，故足可以保证简支梁的挠度计算精度。     

Charged droplets evaporation and motion in an electric field

Monodisperse spray evaporation is investigated theoretically when a pure liquid or an electrolyte solution spray is charged and moves through an electric field. The solution of the equations in the case of electrolyte solutions gives the droplet size evolution down to the “equilibrium radius” when the relative humidity is high and down to the saline kernel when the humidity is lower. This solution also gives the dynamic behaviour in an electric field when the droplets are charged and are moving in a gas stream. A non dimensional curve is obtained for a given humidity, molality and temperature, independently of the electric field. With this curve it is possible to predict the droplet evolution only knowing a “middle time” of evaporation, calculated for a given electric force and a given initial radius.     

Nonlinear analysis of high-speed trains moving on bridges during earthquakes

This paper investigates the derailment of high-speed trains moving on multispan simply supported bridges. A?moving wheel finite element containing contact and separation modes was developed to simulate vehicle?Cbridge interaction problems under seismic loads. Rail irregularities and bridge?Crail?Ctrain interactions were appropriately considered in the nonlinear finite element analysis, which indicates that the derailment coefficients are enlarged with the increase of train speeds for high-speed trains moving on multispan simply supported bridges. The accelerations of elevated bridge girders may be significantly magnified during the seismic load; moreover, gaps between simply supported girders during seismic loads will produce large derailment coefficients.     

Natural frequencies of thin,rectangular plates with holes or orthotropic “patches” carrying an elastically mounted mass

The approximate solution for the title problem is obtained in the case of simply supported and clamped rectangular plates made of isotropic or orthotropic materials. A variational approach (the well known Rayleigh–Ritz method) is used, where the displacement amplitude is expressed in terms of beam functions. This means that each coordinate function satisfies identically all the boundary conditions at the outer edge of the plate. Free vibration analysis has been performed on various different cases; solid isotropic and orthotropic plates, orthotropic plates with a hole and isotropic plates with an orthotropic inclusion or “patch”, carrying an elastically mounted concentrated mass. It is important to point out that the case of an orthotropic patch is interesting from a technological viewpoint since it constitutes a model of a repair implemented on the virgin structural element when it has suffered damage. This approach has been implemented by the aeronautical industry in some instances. The obtained results are in very good agreement with those of particular cases of simply supported plates available in the literature.     

基于车桥耦合理论的梁式桥阻尼比识别研究

提出一种基于车桥耦合动力学理论的梁式桥阻尼比识别方法. 首先按照动力学理论将测试车设计为单自由度体系, 然后利用安装在测试车上的传感器采集信号, 从测试车与桥梁接触点响应信号中得到梁式桥响应的信号, 基于车桥耦合动力学原理滤波处理得到包含梁式桥第一阶频率的信号, 最后假定梁式桥阻尼比值, 通过假定的梁式桥阻尼比值获取假定的梁式桥第一阶振型, 不断循环直至假定的阻尼比值下计算的第一阶振型最大值点居中, 即为识别的梁式桥真实阻尼比. 本文首先从车桥耦合动力学理论推导上说明了该方法的可行性, 然后考虑在不同车速与非恒定车速、路面粗糙度、环境噪音等影响因素下进行车桥耦合动力学模型分析, 最后通过实桥试验进行了初步验证. 研究结果表明: 该方法能一定程度上克服外界不利因素的影响, 达到识别梁式桥阻尼比的目的, 为识别梁式桥阻尼比提供一种更优方法, 其具有参数设置较少、操作简单方便以及更高测试精度等优点, 同时有助于推动基于车桥耦合的车桥耦合动力学理论技术在梁式桥模态参数识别工作中的实际工程应用.      

Transverse vibration characteristics of axially moving viscoelastic plate

The dynamic characteristics and stability of axially moving viscoelastic rect- angular thin plate are investigated.Based on the two dimensional viscoelastic differential constitutive relation,the differential equations of motion of the axially moving viscoelastic plate are established.Dimensionless complex frequencies of an axially moving viscoelastic plate with four edges simply supported,two opposite edges simply supported and other two edges clamped are calculated by the differential quadrature method.The effects of the aspect ratio,moving speed and dimensionless delay time of the material on the trans- verse vibration and stability of the axially moving viscoelastic plate are analyzed.     

Application of active piezoelectric patches in controlling the dynamic response of a thin rectangular plate under a moving mass

The governing differential equation of motion for an undamped thin rectangular plate with a number of bonded piezoelectric patches on its surface and arbitrary boundary conditions is derived using Hamilton’s principle. A moving mass traveling on an arbitrary trajectory acts as an external excitation for the system. The effect of the moving mass inertia is considered using all the out-of-plane translational acceleration components. The method of eigenfunction expansion is used to transform the equation of motion into a number of coupled ordinary differential equations. A classical closed-loop optimal control algorithm is employed to suppress the dynamic response of the system, determining the required voltage of each piezoactuator at any time interval. In a numerical example for a simply supported square plate under two different loading paths, the effect of the mass velocity and mass weight of the moving load on the dynamic behavior of the uncontrolled system is investigated. The results show that, depending on the path of the moving mass, the inertia effect is very important, causing different behaviors of the system. In addition, the number of vibrational modes involved in determining the dynamic response of the system is crucial. The inertia effect is more important for an orbiting mass loading case compared to the case in which the moving mass is traversing the plate on a straight line. A number of equally spaced piezo patches are used on the lower surface of the plate to control the displacement of the center point of the plate. The implemented control mechanism proves to be very efficient in suppressing the near resonant dynamic response of the system, requiring fairly low levels of voltage for each patch. Increasing the area of the employed piezo patches would reduce the required maximum voltage for controlling the response of the system.     

Elastic structural response of prismatic metal sandwich tubes to internal moving pressure loading

The analytical and numerical modeling of the structural response of a prismatic metal sandwich tube subjected to internal moving pressure loading is investigated in this paper. The prismatic core is equivalent to homogeneous and cylindrical orthotropic solids via homogenization procedure. The sandwich tube with the “effective” homogenized core is modeled using multi-layer sandwich theory considering the effects of transverse shear deformation and compressibility of the core; moreover, the solutions are obtained by using the precise integration method. Several dynamic elastic finite element (FE) simulations are carried out to obtain the structural response of the tube to shock loading moving at different velocities. The comparison between analytic solutions and FE simulations demonstrates that the transient analytical model, based on the proposed sandwich model, is capable of predicting the critical velocity and the dynamic structural response of the sandwich tube with the “effective” homogenized core with a high degree of accuracy. In addition, the critical velocity predicted using FE simulations of the complete model is not in agreement with that of the effective model. However, the structural response and the maximum amplification factors obtained using FE simulations of the complete model are nearly similar to that of the effective model, when the shock loading moves at the critical velocity. The influences of the relative density on the structural response are studied, and the capabilities of load bearing for sandwich tubes with different cores are compared with each other and with the monolithic tube. The results indicate that Kagome and triangle-6 are preferred among five topologies.     

Finite-Element Dynamic Analysis of a Rotating Shaft with or without Nonlinear Boundary Conditions Subject to a Moving Load

A C ⁰ continuity isoparametricfinite-element formulation is presented for the dynamic analysis of arotating or nonrotating beam with or without nonlinear boundaryconditions subject to a moving load. The nonlinear end conditions arisefrom nonlinear rolling bearings (both the nonlinear stiffness andclearance(s) are accounted for) supporting a rotating shaft. The shaftfinite-element model includes shear deformation, rotary inertia, elasticbending, and gyroscopic effect. Lagrange's equations are employed toderive system equations of motion which, in turn, are decoupled usingmodal analysis expressed in the normal coordinate representation. Theanalyses are implemented in the finite-element program DAMRO 1.Dynamic deflections under the moving load of rotating and nonrotatingsimply supported shafts are compared with those obtained using exactsolutions and other published methods and a typical coincidence isobtained. Samples of the results, in both the time and frequencydomains, of a rotating shaft incorporating ball bearings are presentedfor different values of the bearing clearance. And the results show thatsystems incorporating ball bearings with tight (zero) clearance have thesmallest amplitude-smoothest profile dynamic deflections. Moreover, fora system with bearing clearance, the vibration spectra of the shaftresponse under a moving load show modulation of the system naturalfrequencies by a combination of shaft rotational and bearing cagefrequencies. However, for a simply supported rotating shaft, the firstnatural frequency in bending dominates the response spectrum. The paperpresents the first finite-element formulation for the dynamic analysisof a rotating shaft with or without nonlinear boundary conditions underthe action of a moving load.     

Dynamic behavior of bridge-erecting machine subjected to moving mass suspended by wire ropes

The dynamic behavior of a bridge-erecting machine, carrying a moving mass suspended by a wire rope, is investigated. The bridge-erecting machine is modelled by a simply supported uniform beam, and a massless equivalent “spring-damper” system with an effective spring constant and an effective damping coefficient is used to model the moving mass suspended by the wire rope. The suddenly applied load is represented by a unitary Dirac Delta function. With the expansion method, a simple closed-form solution for the equation of motion with the replaced spring-damper-mass system is formulated. The characters of the rope are included in the derivation of the differential equation of motion for the system. The numerical examples show that the effects of the damping coefficient and the spring constant of the rope on the deflection have significant variations with the loading frequency. The effects of the damping coefficient and the spring constant under different beam lengths are also examined. The obtained results validate the presented approach, and provide significant references in the design process of bridgeerecting machines.     

Three dimensional solution of thick rectangular simply supported plates under a moving load

Dynamic behavior of continuous systems such as beams and plates, under a moving load is an important engineering subject. In this paper, 3D elasticity equations are solved by use of the displacement potential functions and the exact solution of a simply supported thick rectangular plate under moving load is presented. For this purpose, the governing equations in terms of displacements, Navier’s equations, are converted to two linear partial differential equations of forth and second order using displacement potential functions. Then the governing equations in terms of the potential functions are solved using the separation of variables and Laplace integral transform, satisfying exact initial and boundary conditions. In order to validate the present approach, the obtained results of this study are compared with the results of the classical theory of plates for thin and existing solutions for moderately thick plates. Also, it is observed that the speed of a moving load has an important effect on the dynamic response of plate.     

Reconstructing the transient,dissipative dynamics of a bistable Duffing oscillator with an enhanced averaging method and Jacobian elliptic functions

Systems characterized by the governing equation of the bistable, double-well Duffing oscillator are ever-present throughout the fields of science and engineering. While the prediction of the transient dynamics of these strongly nonlinear oscillators has been a particular research interest, the sufficiently accurate reconstruction of the dissipative behaviors continues to be an unrealized goal. In this study, an enhanced averaging method using Jacobian elliptic functions is presented to faithfully predict the transient, dissipative dynamics of a bistable Duffing oscillator. The analytical approach is uniquely applied to reconstruct the intrawell and interwell dynamic regimes. By relaxing the requirement for small variation of the transient, averaged parameters in the proposed solution formulation, the resulting analytical predictions are in excellent agreement with exact trajectories of displacement and velocity determined via numerical integration of the governing equation. A wide range of system parameters and initial conditions are utilized to assess the accuracy and computational efficiency of the analytical method, and the consistent agreement between numerical and analytical results verifies the robustness of the proposed method. Although the analytical formulations are distinct for the two dynamic regimes, it is found that directly splicing the inter- and intrawell predictions facilitates good agreement with the exact dynamics of the full reconstructed, transient trajectory.     

Geometrically non-linear free and forced vibrations of simply supported circular cylindrical shells: A semi-analytical approach

The non-linear free and forced vibrations of simply supported thin circular cylindrical shells are investigated using Lagrange's equations and an improved transverse displacement expansion. The purpose of this approach was to provide engineers and designers with an easy method for determining the shell non-linear mode shapes, with their corresponding amplitude dependent non-linear frequencies. The Donnell non-linear shell theory has been used and the flexural deformations at large vibration amplitudes have been taken into account. The transverse displacement expansion has been made using two terms including both the driven and the axisymmetric modes, and satisfying the simply supported boundary conditions. The non-linear dynamic variational problem obtained by applying Lagrange's equations was then transformed into a static case by adopting the harmonic balance method. Minimisation of the energy functional with respect to the basic function contribution coefficients has led to a simple non-linear multi-modal equation, the solution of which gives in the case of a single mode assumption an expression for the non-linear frequencies which is much simpler than that derived from the non-linear partial differential equation obtained previously by several authors. Quantitative results based on the present approach have been computed and compared with experimental data. The good agreement found was very satisfactory, in comparison with previous old and recent theoretical approaches, based on sophisticated numerical methods, such as the finite element method (FEM), the method of normal forms (MNF), and analytical methods, such as the perturbation method.     

Numerical and analytical methods for in-plane dynamic response of annular disk

A new method called the moving element method is formulated to solve two problems in a unified framework: (a) rotating disk subjected to stationary load and (b) stationary disk subjected to rotating load. The method involves discretization of the disk into “moving elements”. But unlike in the conventional finite element method, these elements rotate relative to the disk and are not attached to material points. Analytical solutions in terms of complex Fourier–Hankel series are also presented. Numerical examples show good agreement between the proposed numerical method and the analytical method. The advantages of the proposed method over the analytical method and the finite element method are illustrated.     

Almost sure stochastic stability of a viscoelastic double-beam system

This paper investigates the dynamic stability of a viscoelastic double-beam system under parametric excitations. It is assumed that the two beams, made from Voigt–Kelvin material, are simply supported and continuously joined by a Winkler elastic layer. Each pair of axial forces consists of a constant part and a time-dependent stochastic function. In the case of “non-white” excitations, by using the direct Liapunov method, bounds of the almost sure stability of the double-beam system as a function of retardation time, bending stiffness, stiffness modulus of the Winkler layer, variances of the stochastic forces and the intensity of the deterministic components of axial loading are obtained. Numerical calculations are performed for the Gaussian process with a zero mean, as well as a harmonic process with a random phase. When the excitations are wideband noises, almost sure stability is obtained within the concept of the Liapunov exponent. White noise and Ornstein–Uhlenbeck processes are considered as models of wideband noises.     

Stability analysis of the moving interface in piston- and non-piston-like displacements

From the macroscopic point of view, expressions involving reservoir and operational parameters are established for investigating the stability of moving interface in piston- and non-piston-like displacements. In the case of axisymmetrical piston-like displacement, the stability is related to the moving interface position and water to oil mobility ratio. The capillary effect on the stability of moving interface depends on whether or not the moving interface is already stable and correlates with the wettability of the reservoir rock. In the case of non-piston-like displacement, the stability of the front is governed by both the relative permeability and the mobility ratio.