用薄层法分析高架轨道交通引发的环境振动

薄层法是分析和模拟弹性波在层状介质中传播的一种半解析半数值方法。将由车辆一桥梁动力分析程序算得的高架轨道支架动反力作为支架的激振荷载。在支架上激振荷载作用下，利用薄层法计算位于上海典型场地上的高架轨道线路承台群桩基础周围地基的频率响应函数。根据频率响应函数和激振荷载可算得高架轨道线路周围场地的加速度响应及振级。分别采用单支架模型和多支架模型计算高架轨道交通引发的环境振动。振级计算结果与实测回归公式的比较表明，多支架模型中相邻基础的影响不大，实用时可采用单支架模型进行计算。本文提出的高架轨道交通环境振动分析模型可以应用于高架轨道交通引发环境振动的分析和预测。     

Topology optimization of dynamics problems with Padé approximants

An efficient procedure for topology optimization of dynamics problems is proposed. The method is based on frequency responses represented by Padé approximants and analytical sensitivity analysis derived using the adjoint method. This gives an accurate approximation of the frequency response over wide frequency ranges and a formulation that allows for design sensitivities to be computed at low computational cost also for a large number of design variables. Two examples that deal with optimization of forced vibrations are included. Copyright © 2007 John Wiley & Sons, Ltd.     

压电纤维复合材料层合壳的非线性动力学研究

本文对横向激励作用下的1-3型压电纤维复合材料层合壳进行了非线性动力学分析,并研究了压电特性对结构振动响应的影响.首先建立了压电纤维复合材料层合壳的非线性动力学方程,并且在已知的几何结构和材料特性基础上考虑了电场属性.然后根据位移边界条件,选择合适的振型函数,通过Galerkin方法将运动控制方程转化成两自由度的非线性常微分方程.通过数值模拟方法分析了横向激励和压电系数对压电纤维复合材料层合壳非线性振动特性的影响.通过波形图、三维相图、庞加莱图和分叉图等来研究壳体不同类型的周期和混沌运动.结果表明,外激励作用下结构存在复杂的非线性振动响应,同时压电参数对层合壳结构振动响应具有很强的调节作用.     

Dynamic response of a beam to the train of moving forces driven by an Erlang renewal process

Dynamic response of a beam to a random train of moving forces moving with the same velocity is considered. Unlike a widely used Poisson process model, a more adequate Erlang renewal process is used as a process driving the train of forces. Normal-mode approach is used to convert the problem into that of a renewal driven train of general pulses. Consequently the modal responses are the filtered renewal processes and are expressed as integrals with respect to the response to a single pulse (passage of a force) and to the increments of the counting renewal process. The expressions for the mean values and cross-correlations of modal responses are obtained as single and double integrals, respectively. The results are presented in terms of the renewal density of the underlying Erlang counting process. Mean value and variance of the mid-span deflection of the beam are determined by numerical evaluation of the pertinent integrals. Numerical analysis is carried out for the Erlang processes with integer parameter $k=2$, $k=3$ and 4 and, for comparison, also for a Poisson process. Different traffic conditions such as the velocity and the mean arrival rate of vehicles are taken into account.     

在定常流动下混流式水轮机叶片横向振动特性分析

使用一般壳体理论及ALE描述下叶片近壁区流动控制方程，在正交流线坐标系中建立了描述混流式水轮机叶片振动的一般方程，并将叶片在流向与展向的振动对横向振动的影响表示为参数函数，构造出描述叶片横向振动的Mathieu方程，从而可利用数学上熟知的Mathieu方程的特性分析叶片的横向振动。     

g‐Jitter–Induced Electrothermoconvection in a Dielectric Fluid Saturated Porous Layer

This paper presents linear and nonlinear stability analyses of thermal convection in a dielectric fluid saturated sparsely packed porous layer subject to the combined effect of time‐periodic gravity modulation (GM) and an AC electric field. In the domain of linear theory, the critical stability parameters are computed by the regular perturbation method in the form of a perturbation series in powers of frequency of modulation. The local nonlinear theory based on the truncated Fourier series method gives information on convection amplitudes and heat transfer. The principle of the exchange of stabilities is found to be valid and subcritical instability is ruled out. Based on the governing linear autonomous system, several qualitative results on stability are discussed. The sensitive dependence of the solution of a Lorenz system of electrothermal convection subject to the choice of initial conditions points to the possibility of chaos. Low‐frequency g‐jitter is found to have a significant stabilizing influence, which is in turn diminished by an imposed AC electric field. The role of sparseness of the porous layer, viscosity ratio, and normalized porosity on the stability criterion and on heat transport is determined.     

非同轴质量偏心结构平扭耦合风振响应的研究

为了详细地对比分析结构各质量中心不在同一轴线上的偏心对结构风致平移一扭转耦合响应的影响,提出了分析非同轴质量偏心结构风振响应的基本框架.首先,建立了两层六自由度非同轴质量偏心结构的动力方程,并将其推广至N层3N自由度的非同轴质量偏心结构动力方程;然后,基于高频力平衡(HFFB)技术和多点同步扫描(MPSS)技术获得的顺风向、横风向以及扭转风荷载功率谱,考虑横风向和扭转风荷载之间的相关性以及模态之间的耦合,在频域内进行非同轴质量偏心结构的风致平移一扭转耦合响应分析.一栋120 m高的矩形钢结构建筑,被简化为15个自由度的三维分析模型作为数值研究案例.通过设置不同位置的结构质量偏心,分析研究了单轴质量偏心、非同轴质量偏心对矩形建筑结构平移一扭转风振的影响.     

Vibrations of stretched damped beams under non-ideal boundary conditions

A simply supported damped Euler-Bernoulli beam with immovable end conditions are considered. The concept of non-ideal boundary conditions is applied to the beam problem. In accordance, the boundaries are assumed to allow small deflections and moments. Approximate analytical solution of the problem is found using the method of multiple scales, a perturbation technique.     

Characterising heave,pitch, and roll motion of road vehicles with principal component and frequency analysis

For the great majority of transport vehicles, the magnitude of the heave vibration is generally more severe than pitch and roll. Consequently, the measurement, analysis, and simulation of the vehicle vibrations have been focused on vertical vibration. Despite this, it is now being increasingly recognised that the combination of heave, pitch, and roll vibratory motion can induce more severe damage to shipments than vertical vibration alone. Although the pitch and roll motion of road vehicles can now be readily measured, there is little information on how to analyse the data to produce meaningful statistical relationships between the three variables. This paper builds upon previous work that showed that there is some correlation between pitch, roll, and heave motion and that these relationships are dependent on vehicle geometry, including payload mass, centre of mass, vehicle roll centre, and moments of inertia as well as vehicle speed and the road surface. In this paper, data from a range of quasi‐controlled experiments, which involved driving vehicles at constant‐speed on selected roads, were analysed using principal component analysis as well as frequency domain analysis to reveal the relationship between heave, pitch, and roll motion. This was undertaken for a variety of vehicle speeds and routes in order to establish if they influence pitch and roll response. Results are presented in the form of distribution functions, statistical coefficients, and frequency response functions, all of which are useful for helping to define parameters for the simulation of complete, three‐axis vibrations using multi‐axis vibration test systems.     

Geometrically Non-Linear Rapid Heating of Temperature-Dependent Circular FGM Plates

Based on the uncoupled thermoelasticity assumptions, axisymmetric thermally induced vibrations of a circular plate made of functionally graded materials (FGMs) are analyzed. Each thermomechanical property of the circular plate is assumed to be functions of temperature and thickness coordinate. Solution of the transient one-dimensional heat conduction equation with the arbitrary type of time-dependent boundary conditions is carried out employing the central finite difference method combined with the Crank–Nicolson time marching scheme. Afterwards, with the establishment of the associated Hamilton's principle and the accountancy of the von Kármán type of geometrical non-linearity, the motion equations are obtained with the aid of the conventional multi-term Ritz method. The solution of highly coupled non-linear motion equations is obtained utilizing a hybrid iterative Newton–Raphson–Newmark scheme. After validating the developed computer code, some parametric studies are accomplished to show the influences of various involved parameters. It is shown that temperature dependency, geometrical non-linearity, plate thickness, power law index, and the type of thermal in-plane and out-of-plane mechanical boundary conditions, all affect the temporal evolution of plate characteristics.