高层建筑自由振动近似计算

对于高层结构自由振动我们感兴趣的是其中心轴的振动情况。因此我们可以将其简化为一个与该结构具有相同刚度,质量分布的Timoshenko梁来进行研究。根据哈密顿原理推导出控制方程和边界条件,然后用常微分求解器进行求解。     

大底盘多塔楼连体结构的振动计算和动力特性

用沿高度方向分段连续化的方法,对底部为大底盘、上部为多塔楼、塔楼间带连廊的高层建筑结构,建立一个分段连续的串并联振动模型,导出其水平振动的弯扭耦连振动微分方程组,用常微分方程求解器COLSYS求解其自振频率及相应的振型.讨论了连廊不同刚度时的振动特性.为复杂结构提供了一种可用的动力计算简化方法.     

弹性地基分析的奇异函数方法研究

利用奇异函数对Winker弹性地基梁的静力响应问题进行了分析，对于弹性地基梁的动力问题，根据其振动微分方程采用分离变量法求得了其自由振动频率及其振动响应表达式，从而得到振动微分方程的解析解，为弹性地基梁的求解问题提供了一种新的方式。     

混凝土振捣滚平机振动辊振动特性的研究

本文给出了振动辊的力学模型并利用有限元理论建立了振动辊的动力学方程，求解其各阶固有频率及在激振力作用下垂向振动振幅。本文叙述的方法可为设计提供依据，以避免振动辊发生共振造成弹性支承的损坏，可使激振块的布置尽量合理以达到振动辊各处振幅接近一致。     

地震作用下高层建筑平移-扭转耦联振动的控制

本文根据结构振动控制的基本理论，提出了TMDLP（TunedMassDamperwithLeverandPendulum）控制系统，用其控制高层建筑的水平振动和扭转振动。运用摄动理论求解耦联振动的特征方程，节省了计算机的存贮空间，加快了计算速度。文中对TMDLP控制系统各参数进行了优化分析，并对一个刚心和质心偏离较大的20层框架一剪力墙结构施加TMDLP控制。结果表明，该控制系统能显著降低建筑物的水平地震反应和扭转地震反应，并克服了TMD控制系统用于实际工程结构时存在的若干问题，对工程设计和抗震加固具有重要意义。     

振动压路机名义振幅求解方法研究

该文以某型串联振动压路机和某型单轮振动压路机为研究对象，建立了逆转双幅双频振动压路机工作装置的虚拟样机模型，并利用该模型进行仿真，给出一种全新的求解振动压路机名义振幅的方法。     

基于ADAMS的路面激励下矿用汽车驱动桥动载荷分析

矿用汽车的油气悬架具有明显的非线性刚度和非线性阻尼特性，因此计算驱动桥壳在不平路面上运行时的动载荷是一个非线性振动问题，采用解析方法求解非常困难。在考虑阻尼和刚度的前提下，建立了首钢SGA3550矿用汽车驱动桥振动系统后轴物理和数学模型，利用机械动力学仿真软件ADAMS建立了驱动桥非线性振动系统的虚拟样机模型，得到了驱动桥在不平路面激励下所受到的动载荷。     

交叉梁系比拟求解薄板弯曲问题的相容性及其计算

文章用交叉梁系比拟求解薄板结构，讨论两种结构在静力分析和自由振动分析中的相容性和互异性，论证含有简支和固支边组合的边界属于相容问题，其解答随着交叉梁系网格加密可收敛到薄板理论解，而含有自由边界的非相容问题则不能。文中给出了采用3D结构力学求解器求解的算法实施和数值算例，包括矩形、三角形和圆形板问题，用以验证理论分析的正确性，展示并拓展了3D求解器的出色性能。     

大底盘多塔楼结构的振动计算

本文用沿高度方向分段连续化的方法,对底部为大底盘、上部为多塔楼的高层建筑结构,建立了其水平振动的微分方程组.用常微分方程求解器COLSYS求解其自振频率及相应的振型,讨论了其振动的特性,为复杂结构提供了一种可用于设计的动力计算简化方法.     

介绍一种计算方法——用偏微分方程解塔状结构物的地震反应分析

本文介绍变截面塔状结构的地震反应分析的一个实用和有效的解法.其特点是引用了拉格朗日(Lagrange)内插公式并用不等区格的有限差分法来求解弹性杆件的振动方程,其数学要求不高,实际应用时可用计算机进行计算。     

变截面框架-剪力墙-薄壁筒斜交结构考虑竖向荷载作用时的弯扭耦连振动

用沿高度方向分段连续化的方法,对沿高度方向为阶形变截面、在平面内为任意斜向布置的框架-剪力墙-薄壁筒协同工作体系,考虑竖向荷载作用的影响,建立了弯扭耦连的振动方程,用常微分方程求解器COLSYS求解了自振频率及相应的振型.讨论了高层建筑结构竖向荷载对水平振动的影响.     

大底盘多塔楼连体结构的受力分析

用沿高度方向分段连续化的方法,对底部为大底盘、上部为多塔楼、塔楼间带连廊的高层建筑结构,建立一个分段连续的串并联模型,导出其在水平荷载作用下的平衡微分方程组.用常微分方程求解器COLSYS求解其位移和内力.为复杂结构设计提供了一种简化的算法.     

大底盘多塔楼结构的整体稳定计算

用沿高度方向分段连续化的方法,对底部为大底盘、上部为多塔楼的高层建筑结构建立了整体的稳定方程,用常微分方程求解器COLSYS求解,为这种复杂的高层建筑结构的整体稳定计算提供了一种简化算法.     

Bending analysis of thin annular sector plates using extended Kantorovich method

Highly accurate approximate closed-form solution is presented for bending of thin sector plates with clamped edges subjected to uniform and non-uniform loading using the extended Kantorovich method (EKM). Successive application of EKM converts the governing equation which is a forth-order partial differential equation (PDE) to two separate ordinary differential equations (ODE) in terms of r and θ. The obtained ODE systems are then solved iteratively with very fast convergence. In every iteration, exact closed-form solutions are obtained for both ODE systems. It is shown that the method provides sufficiently accurate results not only for deflections but also for stress components. Comparison of the deflection and stresses at various points of the plate shows very good agreement with results of other analytical and numerical analyses.     

变截面高层建筑结构考虑楼板变形时的二阶分析

对考虑楼板变形的变截面框－剪结构的二阶分析问题建立了一个分段连续化的串并联模型，导出其二阶分析的微分方程组，用常微分方程求解器求解。讨论了影响二阶效应的一些因素。     

非刚性楼板对高层建筑结构内力和位移的影响分析

考虑高层建筑结构楼板的非刚性，将框架-剪力墙结构连续化，建立结构的平衡微分方程，采用通用的常微分方程求解器求解，得到了高层建筑结构考虑非刚性楼板与刚性楼板的内力和位移。     

Nonlinear behaviour of a coupled shear wall and shear core system under random ground excitation

Nonlinear behaviour of a coupled shear wall and shear core system under random ground excitation is presented. Random vibrational theory is used for the response analysis of hysteretic structural systems under stochastic earthquake excitation. An equivalent linearization technique, based on Wen's model, is used to convert the nonlinear differential equations to the equivalent linear differential equations, under bi-axial hysteretic restoring forces. The damping is assumed to be linear and a Clough–Penzien double filter is used to calculate the input ground excitation forces on the structure. A comparison has been made between coupled shear wall and shear core systems, to get a best model for a 15 storey building. © 1997 John Wiley & Sons, Ltd.     

A consistent modelling methodology for secondary settling tanks in wastewater treatment

The aim of this contribution is partly to build consensus on a consistent modelling methodology (CMM) of complex real processes in wastewater treatment by combining classical concepts with results from applied mathematics, and partly to apply it to the clarification-thickening process in the secondary settling tank. In the CMM, the real process should be approximated by a mathematical model (process model; ordinary or partial differential equation (ODE or PDE)), which in turn is approximated by a simulation model (numerical method) implemented on a computer. These steps have often not been carried out in a correct way. The secondary settling tank was chosen as a case since this is one of the most complex processes in a wastewater treatment plant and simulation models developed decades ago have no guarantee of satisfying fundamental mathematical and physical properties. Nevertheless, such methods are still used in commercial tools to date. This particularly becomes of interest as the state-of-the-art practice is moving towards plant-wide modelling. Then all submodels interact and errors propagate through the model and severely hamper any calibration effort and, hence, the predictive purpose of the model. The CMM is described by applying it first to a simple conversion process in the biological reactor yielding an ODE solver, and then to the solid-liquid separation in the secondary settling tank, yielding a PDE solver. Time has come to incorporate established mathematical techniques into environmental engineering, and wastewater treatment modelling in particular, and to use proven reliable and consistent simulation models.