Free longitudinal vibrations of tall buildings and high-rise structures

In this paper, tall buildings and high-rise structures are considered as cantilever bars with variable cross-section for the analysis of their free vibrations. The differential equations of free longitudinal vibrations of bars with variable cross-section are reduced to Bessel's equations by selecting suitable expressions, such as power functions and exponential functions, for the distribution of stiffness and mass. An approach is proposed for determining the natural frequencies and mode shapes in the vertical direction for tall buildings and high-rise structures with variably distributed stiffness and variably distributed mass. The derived solutions are expressed in terms of Bessel functions. A numerical example shows that the value of the natural frequency computed by the proposed method is close to full scale measured data. It is shown that the selected expressions are suitable for describing the distributions of stiffness and mass of tall buildings and high-rise structures. It is demonstrated that the proposed method has practical significance for free longitudinal vibration analysis. © 1998 John Wiley & Sons, Ltd.     

与圆弧形曲梁连结的框架柱侧移刚度

从悬臂直梁出发,可以推导出线刚度与固定端弯矩及铰支端转角的相互关系,进而通过该关系推导出曲梁的折算线刚度.如果考虑楼板的刚度足够大,利用传统的D值法可以直接计算出相关柱的侧移刚度.如果考虑楼板的刚度是有限的,则可以通过建立平衡方程和协调方程得出曲梁中部柱子的位移与其它柱子位移之间的关系,进而可以对曲梁中部柱子侧移刚度的修正系数进行调整,最终可以求出曲梁中部柱子的侧移刚度.     

Vibration analysis of tall buildings with narrow rectangular plane configuration

In this paper, tall buildings of narrow rectangular plane configuration are treated as one-step or multi-step cantilever flexural-shear plates for the analysis of their free vibrations. The governing differential equations for the vibration of flexural-shear plates considering the effects of both flexural and shear deformation are established. The general solutions for one-step flexural-shear plates are derived and used to obtain the eigenvalue equation for multi-step cantilever flexural-shear plates. A new exact approach is presented which combines the transfer matrix method and a closed-form solution for a uniform flexural-shear plate. A numerical example demonstrates that the calculated natural frequencies and mode shapes of a tall building are in good agreement with the experimentally measured data. It is also shown that the effect of shear deformation on the fundamental natural frequency can be ignored, but its effect on the higher natural frequencies should be considered. Copyright © 1998 John Wiley & Sons, Ltd.     

轴压组合叠合梁自由振动的动态刚度分析

采用动态刚度分析方法,对自由振动和轴压组合叠合梁的屈曲性能进行研究。在公式中考虑了轴力、泊松效应、轴向变形、剪切变形和转动惯量的影响。通过直接求解轴压组合叠合梁自由振动的控制微分方程,建立严格的动态刚度矩阵,并用该矩阵对已有文献中其他组合梁进行计算比较,证明了动态刚度矩阵的适应性。同时,论证了轴力和边界条件对自然频率、屈曲荷载和叠合梁模式的影响。     

考虑轴向位移的压弯Π形梁剪力滞分析

在截面纵向位移函数中引入截面轴向位移,以描述压弯作用下Π形梁截面的变形状态。基于能量变分法导出轴向位移、竖向位移和剪力滞位移之间相互耦合的控制微分方程组,求得压弯作用下Π形梁的位移解及其相应的边界条件。结合ANSYS软件,利用实体单元和导出的位移解及其边界条件分别对简支梁和悬臂梁进行分析,验证其有效性和可靠性。结果表明:剪力滞效应使得Π形梁中性轴和形心轴相互分离,截面不再绕形心轴转动;在弯曲作用下,剪力滞使简支梁截面弯曲刚度减小,悬臂梁固定端一侧1/4跨度内截面弯曲刚度减小,悬臂梁自由端一侧3/4跨度内截面弯曲刚度增加;在压弯作用下,轴向压力引起的剪力滞使简支梁梁端附近截面弯曲刚度减小,悬臂梁自由端一侧截面弯曲刚度增加。     

Nonlinear vibration of laminated plates on an elastic foundation

This paper studies the effects of initial stresses on the nonlinear vibrations of laminated plates on elastic foundations. The nonlinear partial differential equations based on Mindlin plate theory are derived for the nonlinear vibration of laminated plates in a general state of nonuniform initial stress. Both rotary inertia and transverse stress are considered. Using the derived governing equations, the nonlinear vibration behavior of an initially stressed cross-ply plate on a Pasternak or Winkler elastic foundation is studied. The Galerkin's approximate method is applied to the governing partial differential equations to yield ordinary differential equations. The ordinary differential equations are solved by Runge–Kutta method to obtain the ratio of nonlinear frequency to linear frequency. The initial stress is taken to be a combination of a pure bending stress and an extensional stress in the plane of the plate. It is found that the foundation stiffness and initial stresses may result in a drastic change of the nonlinear vibration behavior. The frequency responses of nonlinear vibration are sensitive to the initial stress, vibration amplitude, modulus ratio and foundation stiffness. The effects of various parameters on the nonlinear vibration are discussed.     

A new method for the design of tall buildings: The mit design method

A new method for the design of tall and super-tall buildings is presented in this paper. The method is based on transforming the stiffness properties of the building to equivalent beam properties. The equivalent beam is allowed to deform both in bending and shear to capture the true behavior of the building. The method is a stiffness based approach that later requires checks for strength. This is quite appropriate since the design of tall and super-tall buildings is governed by stiffness and not by strength. Knowing the load and assuming a desired shape of the beam, the required shear and bending rigidities of the beam can be calculated. The method is robust and easy to apply, and is particularly suited for space truss systems. The simplicity and efficiency of the method are illustrated with an example.     

Coupled shear‐flexural model for dynamic analysis of fixed‐base tall buildings with tuned mass dampers

An equivalent discrete model is developed for time domain dynamic analysis of uniform high‐rise shear wall‐frame buildings with fixed base and carrying any number of tuned mass dampers (TMDs). The equivalent model consists of a flexural cantilever beam and a shear cantilever beam connected in parallel by a finite number of axially rigid members that allow the consideration of intermediate modes of lateral deformation. The proposed model was validated by a building whose lateral resisting system consists of a combination of shear walls and braced frames. The results showed the effectiveness of TMDs to reduce the peak displacements, interstory drift ratio, and accelerations when the building is subjected to a seismic load. The root mean square accelerations due to along‐wind loads also decrease if TMDs are attached to the building.     

Estimation of floor acceleration demands in high‐rise buildings during earthquakes

A simplified method to estimate lateral acceleration demands in high‐rise buildings subjected to earthquakes is presented. In the proposed method acceleration demands are obtained by approximating the dynamic characteristics of the building with those of a continuous model consisting of a combination of a flexural cantilever beam and a shear cantilever beam. Closed‐form solutions for mode shapes, period ratios and modal participation factors for the first six modes of vibration are presented. The method is evaluated by comparing peak floor acceleration demands and acceleration time histories computed with the proposed method to those recorded during earthquakes in six instrumented high‐rise buildings. A comparison of floor spectra computed with the approximate method and spectra computed with recorded motions is also presented. Results indicate that the proposed method produces relatively good results with a very small computational effort and requires only a small amount of information about the building. Variations of accelerations demands along the height are closely examined in each building for each component. It is shown that the variation of acceleration demands along the height of high‐rise buildings can differ significantly from that currently recommended in US seismic provisions for anchoring building nonstructural components. Copyright © 2005 John Wiley & Sons, Ltd.     

Dynamic analysis of combined system of framed tube and shear walls by Galerkin method using B‐spline functions

In this article, dynamic parameters (natural frequencies and mode shapes) of tall buildings that consist of framed tube and shear walls are obtained using a simple approximate method. The three‐dimensional structure is replaced by an equivalent cantilever beam, considering both bending and shear deformations. On the basis of dynamic equilibrium, the governing differential equation of motion is obtained and converted to its corresponding weak form. B‐spline functions are then utilized to approximate the weak form and to obtain the final matrix form of the problem. Finally, by applying essential boundary conditions, the natural frequencies and corresponding mode shapes are calculated. To demonstrate the accuracy of the proposed method, numerical examples are solved, and the results are compared with those obtained from SAP2000 computer analysis. The results show that the proposed method is efficient and accurate enough to be used in preliminary design. Copyright © 2014 John Wiley & Sons, Ltd.     

钢板夹层阻尼高频TMD两阶段设计方法

随着工业化的发展,建筑结构逐渐轻量化,机械设备逐渐重型化、高效化,这使得机械设备高频扰力导致的结构振动问题越来越突出;为了减轻结构的高频受迫振动响应,可以在结构振动响应较大的位置安装高频高阻尼比的钢板夹层阻尼悬臂梁式调谐质量阻尼器(tuned mass damper,TMD).由于TMD的弹性元件与阻尼元件相互耦合,因...     

Free vibration of partially supported piles with the effects of bending moment, axial and shear force

The pile parts above the soil and embedded in the soil are called the first region and the second region, respectively. The fourth order partial differential equations of both regions for free vibration of partially supported pile subjected to bending moment, axial force and shear force are obtained using the small-displacement theory and the Winkler model. It is assumed that the behavior of the material is linear-elastic, and that axial force along the pile length and modulus of subgrade reaction for the second region to be constant. Shear effect is included in the partial differential equations by the second derivative of the elastic curve function with respect to shear deformation. Natural circular frequencies and relative stiffness of the pile are calculated for non-trivial solution of linear homogeneous system of equations obtained due to the values of axial forces acting on the pile, the shape factors, and the boundary conditions of the pile with both ends free and both ends simply supported; the results are presented in graphs.     

开口截面双索面斜拉桥动力特性研究

开口截面斜拉桥的自由扭转刚度较低,其翘曲刚度和自由扭转刚度相比不可忽略,采用模型的不同将严重影响扭弯频率比,而扭弯频率比对颤振起至关重要的影响,故扭转刚度的正确计算是抗风分析的关键。在分析开口截面斜拉桥的结构构造特点的基础上,考虑各种参数（索的非线性,索的振动,主梁质量中心和剪切中心间的偏心）对斜拉桥的自振特性的影响,对开口截面的桥面采用三种有限元模型,建立了空间三维计算模型．并将其应用于江苏省灌河特大桥的动力特性的计算。通过对三种有限元建模方式的计算结果的比较,说明三主梁模型应用于开口截面双索面斜拉桥是适用的。     

A new approach for free vibration analysis of nonuniform tall building structures with axial force effects

Dynamic analysis of beam‐like structures is significantly important in modeling actual cases such as tall buildings and several other related applications as well. This article studies free vibration analysis of tall buildings with nonuniform cross‐section structures. A novel and simple approach is presented to solve natural frequencies of free vibration of cantilevered tall structures with variable flexural rigidity and mass densities. These systems could be replaced by a cantilever Timoshenko beam with varying cross‐sections. The governing partial differential equation for vibration of a nonuniform Timoshenko beam under variable axial loads is transformed with varying coefficients to its weak form of integral equations. Natural frequencies can be determined by requiring the resulting integral equation, which has a nontrivial solution. The presented method in this study has fast convergence. Including high accuracy for the obtained numerical results as well. Numerical examples including framed tube as well as tube‐in‐tube structures are carried out in the study and compared with available results in the literature, and also with the results obtained from finite element analysis in order to show the accuracy of the proposed method in the study. Obtained results indicate that the presented method in this study is powerful enough for the free vibration analysis of tall buildings.     

剪力墙和薄壁开口截面作为支撑的高层建筑抗震计算的简化方法

对高度方向性能恒定,不对称的建筑结构,提出了近似的抗震分析手算方法。通过剪力墙和薄壁开口截面结构的结合,增加了建筑物的刚度。基于连续技术和达朗伯原理,推导了自由振动的控制方程和相应的特征值问题。应用伽辽金技术,提出了一个通用的方法对剪力墙和薄壁开口截面结构的耦合振动进行自由振动分析。     

Free vibrations of stiffened coupled shear walls

This paper presents the free vibration analysis of stiffened coupled shear walls based on a discrete–continuous approach. The stiffened system is reinforced by an additional stiffening beam at some level of the structure. This induces additional axial forces, and thus reduces the bending moments in the walls, as well as helping to reduce the lateral deflection. The effect of the stiffening beam on the free vibration characteristics of coupled shear walls is studied, and numerical investigations show that the natural frequencies of vibration can be significantly increased. The optimal position for the stiffening beam to increase as far as possible the first natural frequency of vibration is also presented. © 1998 John Wiley & Sons, Ltd.     

Minimum‐weight design of high‐rise structures subjected to flexural vibration at a desired natural frequency

In this paper, a parametric approach for design of high‐rise structures subjected to flexural vibration is proposed. The optimization problem is formed based on a preselected value for the fundamental natural frequency, and it is formulated for minimum structural weight. In a two‐step approach, first, an alternative formulation aimed at maximizing structural stiffness that in turn maximizes structure's fundamental frequency is introduced. Then, optimized results are used in obtaining a closed‐form solution of the actual problem. Because the resulting equations are rather complicated, approximate forms are developed in order to simplify the design process. In all relations, contributions from shear forces to lateral displacement are assumed to be negligible; hence, bending resistance is the only design variable, and its optimal value is computable using simple relations. Two numerical examples are presented in order to illustrate the efficiency of this method in practice.     

框支剪力墙和落地剪力墙共同工作时的自振周期

本文将框支剪力墙和落地剪力墙合并成一个弹性支座上的Timoshenko悬臂粱,考虑截面的剪切和转动惯量的影响,求得了其水平振动时的自振周期计算公式。还讨论了各种因素的影响及简化的计算公式。     

Coupled‐two‐beam discrete model for dynamic analysis of tall buildings with tuned mass dampers including soil–structure interaction

An equivalent coupled‐two‐beam discrete model is developed for time‐domain dynamic analysis of high‐rise buildings with flexible base and carrying any number of tuned mass dampers (TMDs). The equivalent model consists of a flexural cantilever beam and a shear cantilever beam connected in parallel by a finite number of axially rigid members that allows the consideration of intermediate modes of lateral deformation. The equivalent model is applied to a shear wall–frame building located in the Valley of Mexico, where the effects of soil–structure interaction (SSI) are important. The effects of SSI and TMDs on the dynamic properties of the shear wall–frame building are shown considering four types of soil (hard rock, dense soil, stiff soil, and soft soil) and two passive damping systems: a single TMD on its top (1‐TMD) and five uniformly distributed TMDs (5‐TMD). The results showed a great effectiveness of the TMDs to reduce the lateral seismic response and along‐wind response of the shear wall–frame building for all types of soils. Generally speaking, the dynamic response increases as the flexibility of the foundation increases.     

TMD等强度悬臂梁实际应用时的频率精确分析

为了确定实际应用中调谐质量阻尼器（TMD）刚度单元的梯形悬臂梁参数,建立了梯形悬臂梁频率的精确计算公式,计算了梯形等强度悬臂梁与三角形等强度悬臂梁频率的误差,利用梯形悬臂梁频率计算公式确定了TMD等强度悬臂梁的设计步骤与程序,给出了工程示例,并使用仿真软件ANSYS进行了验证。结果表明:悬臂梁自由端的宽度小于固定端宽度的12.65%时,梯形等强度悬臂梁与三角形等强度悬臂梁的频率相对误差小于5%;所用程序可以用于确定满足频率精度要求的TMD等强度悬臂梁的参数,对工程实际有较大指导意义。