移动的线源平稳随机荷载激励下梁的随机响应

利用广义Ｄｕｈａｍｅｌ积分和积分变换，研究了粘弹性Ｋｅｌｖｉｎ地基上无限长梁在运动的线源平稳随机荷载作用下的随机响应．发现此时梁的挠度响应为非平稳随机过程．通过引入随动坐标系，建立了有明确物理意义的随动谱分析方法，使随机位移响应在随动坐标系下成为平稳随机过程     

地基土—多自由度非线性结构相互作用体系的非平稳随机动力响应分析

本文应用一个改进的等效线性化方法探讨了地基土——多自由度非线性结构相互作用体系在随机地震荷载作用下的非平稳动力响应问题。对非线性恢复力模型采用一个具有三线性滞回特性的非线性系统。最后将在平稳Gauss过滤白噪声激励下的非平稳随机响应与Monte-carlo法的统计结果进行了比较,得出了较为满意的结果。     

桥梁结构移动平稳随机荷载识别新方法

移动的平稳随机荷载对简支梁的作用,相当于固定的调制函数已知的非平稳随机荷载对简支梁结构的作用.本文以此为基础,研究了移动平稳随机荷载的识别问题.首先基于虚拟激励法的思想,利用特征值分解及奇异值分解技术,由虚拟位移响应反演虚拟广义坐标,有效地避免了矩阵求逆,得到高精度的广义坐标谱;同时利用Wiener-Khintchine关系及Duhamel积分,由广义坐标谱值反演得到平稳随机激励谱密度.仿真算例表明,只要适当地选取参振振型及测点位置,本文方法可以有效地识别桥梁结构的移动平稳随机荷载.     

广义密度演化方程与经典随机振动分析的比较研究

以结构随机风振响应分析为背景,考察了线性体系在平稳风荷载激励下的随机动力反应,进行了广义密度演化方程与经典随机振动分析的比较.基于物理随机系统研究框架,平稳脉动风荷载模型化为随机Fourier谱.分别以线性单自由度体系和线性多自由度体系为研究对象,比较分析了系统响应的概率密度演化解、理论平稳解和虚拟激励法解答.结果表明,分析系统有限时间内的随机动力反应,概率密度演化方法不仅能够获得渐近平稳段的稳态响应,而且能够反映响应非平稳初始效应的影响,与经典随机振动理论的虚拟激励法解答在均方特征意义上是等价的.     

线性随机桁架结构的平稳随机响应分析

研究了随机桁架结构的平稳随机响应问题。同时考虑结构的物理参数、几何尺寸的随机性，从结构平稳随机响应在频域上的表达式出发，利用求解随机变量函数矩的方法，导出了随机桁架结构在平稳随机激励下位移响应均方值的均值、均方差和变异系数的计算表达式。通过算例考察了随机荷载激励下结构物理参数、几何尺寸的随机性对结构随机响应的影响。     

线性随机结构的非平稳随机响应变异性分析

对于具有随机参数的结构受到非平稳随机激励的问题，给出了结构随机响应变异系数的虚拟激励摄动算法。它应用虚拟激励法先将随机荷载转化为确定性荷载，以使随机问题精确地转化为仅结构参数具有随机性的问题，从而将问题归结为应用随机摄动法求解单随机问题。求解过程简单高效，且有较高的精度。     

线性随机结构的平稳随机响应

对于不仅结构参数具有随机性,而且外载是平稳随机激励的问题,给出了随机响应变异系数的计算方法。应用虚拟激励法先将随机荷载转化为确定性的简谐荷载,使双随机问题得以精确地转化为单随机问题进行分析。求解过程显著简化,而且包含了二种随机因素之间的耦合效应。用数值模拟法对方法的精度作了估计。     

梁式结构受移动荷载作用非平稳随机振动的DQ-PEM方法

针对梁式结构受移动荷载作用的非平稳随机振动问题,提出了一种综合利用微分求积法和虚拟激励法DQ-PEM的新方法。梁式结构受移动荷载作用的振动控制方程为含Dirac函数的偏微分方程,利用微分求积(DQ)-积分求积法(IQ)法将其振动控制方程转化为不含Dirac函数的常微分方程。同时,将表示荷载位置变化的Dirac函数视为移动荷载的非平稳化函数,再结合虚拟激励法的思想,可得梁式结构在确定性荷载作用下的虚拟响应,进而得到其非平稳随机响应。通过工程算例验证了该方法的准确性与有效性,并进一步讨论了不同速度和不同边界条件下梁式结构受移动荷载作用的随机振动问题。     

挡土结构物随机地震响应分析及动力可靠度研究

本文提供了一种简单的确定性数值方法,来分析在平稳随机地震荷载作用下的结构随机地震响应及动力可靠度。该方法基于有限元动力分析软件,以单位加速度脉冲函数作为地震荷载的输入,当计算出结构的脉冲响应函数后,再运用傅立叶变换得到随机激励和结构响应之间的传递函数,由此来计算结构的均方根响应和峰值响应。基于此方法,分析了挡土结构物在平稳随机地震荷载作用下的位移、弯矩、基底水平合力、基底竖向合力以及沿墙高的土压力极值的随机地震响应及动力可靠度。从分析结果可以看出:用Kanai谱模型的计算值比欧进萍谱模型的计算值更趋保守,而把响应过程当作马尔可夫过程似比泊松过程更精确。     

平稳随机激励下随机智能桁架结构振动主动控制中的优化

研究了平稳随机激励下随机智能桁架结构振动主动控制中主动杆的配置位置和闭环控制系统增益的优化问题。考虑结构物理参数、几何尺寸、阻尼同时具有随机性以及作用荷载为平稳随机激励，基于系统最小储存能，构建了具有位移响应均方值、应力响应均方值可靠性约束的主动杆配置和控制增益的优化模型；并对结构平稳随机动力响应的数字特征进行了推导。通过算例，验证了该优化配置模型的合理性和有效性，获得了若干有意义的结论。     

Dynamic analysis of an axially moving plate subjected to thermal loading

Dynamic analysis of axially moving thermally loaded two-dimensional system is presented in this paper. Using the Hamilton's principle, the differential equation of the transverse motion of the moving plate is derived. Using the extended Galerkin method the approximate solution is determined in this work. To verify the present approach, the calculation results of buckling thermal load for stationary plate are compared with the results published in literature. Dynamic analysis of axially moving aluminum plate subjected to thermal loading is presented. Besides the thermal critical loading the effects of transport speed and axial tension on dynamic behavior of axially moving aluminum plate are presented.     

Nonlinear waves generated by a steadily moving line load on an elastic plate

The steady-state response of an infinite plate to a steadily moving line load is studied. The nonlinear plate theory of Herrmann is used. The plate response is governed by a set of nonlinear differential equations and, in addition, must satisfy the “radiation” conditions. Appropriate radiation conditions for the present nonlinear problem are developed. Exact solutions representing nonlinear waves generated by the moving load are constructed.     

Analytical dynamic displacement response of rigid pavements to moving concentrated and line loads

This paper presents the formulation of a plate of infinite dimensions (without boundary conditions) on an elastic foundation, subjected to a moving concentrated and line load of constant amplitude and speed, using a triple Fourier transform. The solution is carried out integration by residues. A closed-form solution of displacement field has been obtained for a moving load with subsonic, transonic and supersonic speeds. It is found that the maximum response of the slab occurs beneath the moving load and travels with the load at the same speed. It is also shown that a critical speed exists. If the moving load travels at critical speed, slab displacement becomes infinite in amplitude.     

Rigid Plastic Plates under a Concentrated Moving Load∗

A rigid-plastic rectangular plate subjected to a moving transverse load is analyzed. The load is too large for the plate to be supported under static conditions. The present study indicates that there is a critical value for the moving load, above which the crossing cannot be made, irrespective of its speed. The relation between the moving load and its speed is given for values less than ciritical, as well as the distribution of displacement for a simply supported rectangular plate.     

Transient responses of beams and plates subject to travelling load. Miscellaneous results

The steady-state response of a free and infinite Timoshenko beam is specified analytically in terms of non-dimensional displacements and stresses. The beam is supposed loaded by a travelling concentrated force or a moving step load. By a validated explicit numerical calculation, it is shown how a load travelling on a beam at constant velocity, from defined time and abscissa, generates a response which evolves towards the steady-state solution for a part, and towards a quantified transient solution for another part. Asymptotic values are given for the transient displacements and stresses according to the time and the speed of the loading. The solution is also found for a plate subject to a pressure, which spreads respecting the cylindrical symmetry. It is possible to identify in the response a part which follows the pressure front, and which is comparable with the steady-state response of a beam, and another transient part, which generates displacements and stresses with a much less oscillating character. An asymptotic solution is also presented for the plate.The whole series of the results makes it possible to better understand qualitatively the beginning of the transient response of a beam or of a plate to a moving load, and also makes it possible to estimate the stresses and displacements without needing specialised numerical codes.     

The probability stability of viscoelastic plates

The almost sure stability of homogeneous viscoelastic plates subjected to a random wide-band stationary in-plane load is investigated. The viscoelastic behavior of the plate is described in terms of the Boltzmann superposition principle, the relaxation kemels of which are represented by the sums of exponents. On the assumption that the in-plane load is random wide-band stationary process, sufficient conditions for almost sure stability of viscoelastic plates are obtained by the applications of Lyapunov's direct method. Project supported by the National Natural Science Foundation of China (No. 59635140) and the National Postdoctoral Foundation.     

Three Dimensional Vibration Transmission of a Plate on a Layer of Porous Medium Due to a Moving Load

Three-dimensional (3D) transmission of vibration in an infinite elastic thin plate on a layer of poroviscoelastic medium, due to a harmonic, rectangular moving load, is investigated theoretically based on Biot’s theory. The material of the medium is idealized as a uniform, fully saturated poroviscoelastic layer on bedrock. By introducing four scalar potential functions and Helmholtz decomposition theorem, analytical solutions of stress, displacement, and pore pressure with and without thin plate are derived using Fourier transform technique. Numerical results are obtained with the help of inverse Fourier transform and are used to analyze the influence of load velocity, porosity, permeability, relative stiffness of plate versus ground, and the thickness of plate on the vibration. Furthermore, the results are compared with the available dynamic response results of a non-moving load on a layer of viscoelastic material.     

不确定性移动载荷激励下弹性简支梁的动态响应边界分析及应用

不确定性移动载荷激励下的弹性梁振动是土木、机械和航空航天等工程领域普遍存在的一类重要问题。在许多实际工程中,不确定移动载荷的样本测试数据有限或测试成本较高,本文引入区间过程模型对此类动态不确定性参数进行描述,提出了一种求解不确定移动载荷激励下弹性梁振动响应边界的非随机振动分析方法。首先,介绍了确定性移动载荷激励下弹性梁的振动微分方程及其解析求解方法;其次,引入区间过程模型,以上下边界函数的形式对不确定性移动载荷进行度量,进而基于模态叠加法发展出弹性梁振动响应边界求解的非随机振动分析方法;最后,将上述非随机振动分析方法应用于车桥耦合振动问题。