Horizontal dynamic response of a large-diameter pipe pile considering the second-order effect of axial force

The second-order effect of axial force on horizontal vibrating characteristics of a large-diameter pipe pile is theoretically investigated. Governing equations of the pile-soil system are established based on elastodynamics. Three-dimensional wave equations of soil are decoupled through differential transformation and variable separation. Consequently, expressions of soil displacements and horizontal resistances can be obtained. An analytical solution of the pile is derived based on continuity conditions between the pile and soil, subsequently from which expressions of the complex impedances are deduced. Analyses are carried out to examine the second-order effect of axial force on the horizontal vibrating behavior of the pipe pile. Some conclusions can be summarized as follows: stiffness and damping factors are decreased with the application of axial force on the pile head; distributions of the pile horizontal displacement and rotation angle are regenerated due to the second-order effect of the applied axial force; and redistributions of the bending moment and shearing force occur due to the second-order effect of the applied axial force.     

On axisymmetric vibration in a transversely isotropic finite cylindrical shell acted upon by a magnetic field

Summary The present note seeks to investigate the axisymmetric vibration in a transversely isotropic finite cylindrical shell in presence of axial magnetic field by making use of the electromagnetic equations of Maxwell and the equations of elasticity. The frequency with its minimum value is obtained.     

Propagation of Rayleigh waves on cylindrical surfaces of transversely isotropic material and of varying density in a magnetic field

Summary Three dimensional magneto-elastic equations pertaining to the problem of propagation of axial Rayleigh waves on the surface of elastic cylinder of isotropic material have been solved. Two cases have been considered — first, when the density varies linearly and second, when it varies inversely as the radius vector and frequency equations for both the cases have been obtained.     

Numerical study on factors that influence the in‐plane drift capacity of unreinforced masonry walls

Displacement‐based assessment procedures require as input reliable estimates of the deformation capacity of all structural elements. For unreinforced masonry (URM) walls, current design codes specify the in‐plane deformation capacity as empirical equations of interstory drift. National codes differ with regard to the parameters that are considered in these empirical drift capacity equations, but the inhomogeneity of datasets on URM wall tests renders it difficult to validate the hypotheses with the currently available experimental data. This paper contributes to the future development of such empirical relationships by investigating the sensitivity of the drift capacity to the shear span, the aspect ratio, the axial load ratio, and the size of the wall. For this purpose, finite element models of URM walls are developed in Abaqus/Explicit and validated against a set of experimental results. The results show that the axial load ratio, the shear span, and the wall size are among the factors that influence the drift capacity the most. Empirical equations are mainly derived from test results on small walls, and the numerical results suggest that this can lead to a significant overestimation of the drift capacity for larger walls.     

拉索端部弹性约束振动控制研究(I)——理论模型

本文建立了拉索振动的轴向被动控制理论模型。在拉索端部沿轴向设置弹性约束,通过影响索端支座的移动,从而改变拉索的振动特性,最终达到减振效果。通过D’Alembert原理建立拉索-弹性约束系统振动方程,通过Galerkin方法将偏微分方程转化为常微分方程,应用龙格-库塔积分法求解方程;经过仿真分析,验证了该振动控制具有明显的减振效果,并且讨论了初始拉力、支座质量、振动频率及弹簧刚度对减振效果的影响;最后给出了计算最优阻尼参数的近似解析式,为工程师提供了简便有效的参考依据及设计方法。     

The effect of axial inertia on the bending eigenfrequencies of a timoshenko two-bar frame

The equations of free lateral vibrations of a uniform Timoshenko two-bar frame including the effects of axial motion and joint mass with its rotational inertia are presented. The influence on the flexural eigenfrequencies of the axial motion alone or in combination with other parameters is fully assessed and thoroughly discussed. These parameters are: the translational and rotational inertia of the joint mass, the transverse shear deformation and rotatory inertia, the length, stiffness and slenderness ratios of the two bars of the frame. The variety of numerical results presented herein leads to the important finding that for framed structures the effect of axial inertia on the flexural eigenfrequencies alone or in combination with the foregoing parameters may be considerable. In particular, if the joint mass should be accounted for, the foregoing effect cannot be ignored, since it leads, in general, to considerable errors even for frames with relatively slender bars.     

Seismic analysis of a rotor-bearing system

The seismic analysis of a rotor-bearing system is presented in the time domain. The governing equations of motion for the rotor are derived including the effects of rotatory inertia, shear deformation, gyroscopic effects, axial force, axial torque, stiffness and damping provided by the lubricants in the bearings, base translation and base rotation. A simple and efficient finite rotor element based on a Galerkin formulation is proposed to model the rotor. The effects of disks and flywheels mounted on the rotor are also included in the analysis. An example problem for a rotor-bearing system is solved using El Centro earthquake data. Four cases are investigated that will permit one to study the influence of spin, base rotation, comparison between rigid body model and beam model and the influence of axial force and axial torque. The results of the above study show that the gyroscopic effects amplify the response of the rotor-bearing system. The base rotations of the rotor-bearing system under seismic excitation contribute significantly to the response.     

Free vibrations of foundation beams on Green soil in the presence of conservative and nonconservative axial loads

In this paper a general dynamic analysis of a foundation beam on Green-Boussinesq soil is performed, taking into account the instabilizing effect of conservative and nonconservative applied axial loads.The beam is reduced to a finite number of rigid bars, linked together by elastic springs; the equations of motion are written by means of the Lagrange equations. The kinetic energy and the total potential energy are calculated first, and emphasis is placed on the strain energy of the Green soil; then the virtual work of the applied follower loads is detected, which allow us to define the generalized forces. The resulting equations of motion lead to an eigenvalue problem with unsymmetric matrix.Initially, the first free vibration frequencies of simply supported beams, clamped beams and free beams are plotted as functions of the two soil parameters. A more complex beam is also examined, in order to show the method potentialities. A stability analysis in the presence of conservative axial loads is then performed, and the influence of the soil on the critical load is discussed, both for simply supported beams and clamped beams. Finally, the instability mechanism of a clamped - clamped beam subjected to a uniformly distributed follower force is shown to be deeply influenced by the presence of the soil. (A number of graphs and examples conclude the paper.)     

Estimating bearing response in symmetric and asymmetric‐plan isolated buildings with rocking and torsion

A comprehensive approach is developed to estimate relevant design quantities—lateral deformations and axial forces—in isolation systems composed of lead–rubber bearings. The approach, applicable to symmetric and asymmetric‐plan systems, includes the effects of bidirectional excitation, rocking, and torsion; and is the culmination of previous work on this topic. The approach is based on nonlinear response history analysis of an isolated block using an advanced bearing model that incorporates the interaction between axial force and lateral response of the bearing, known as axial‐load effects. The rocking response of the system and peak axial forces are shown to depend on the isolation period, the normalized strength—or yield strength normalized by peak ground velocity, the ratios of rocking frequency about each horizontal axis to vertical frequency, and the normalized stiffness eccentricity. In an attempt to develop results widely applicable to asymmetric‐plan systems, eccentricity is introduced by varying the stiffnesses and strengths of individual bearings in an idealized, rectangular plan. This idealized system approach is shown to have limited success; when applied to actual asymmetric‐plan systems the design equations to estimate response are accurate for lateral deformations but err by up to 25% for axial forces. Copyright © 2006 John Wiley & Sons, Ltd.     

关于日本框架柱受剪承载力公式的讨论

通过对日本抗震设计规范中有关钢筋混凝土框架柱受剪承载力代表性公式的研究，凸现了由经验公式到基于桁架一拱模型建立的发展趋势。对各公式中所包括的影响框架柱受剪承载力的主要因素(如剪跨比、轴压比、配箍率、混凝土强度、纵筋率等)进行了深入讨论，并采用框架柱受剪承载力试验数据考察了各个公式的有效性。     

The coupling effect of axial motion and joint mass on the lateral vibrations of a rigid-jointed triangular frame

In this investigation, the coupling effects of the axial motion and other parameters on the bending eigenfrequencies and eigenmodes of laterally vibrating frames are re-examined. To this end an energy variational approach is performed on a rigid-jointed triangular frame, whose joint mass is eccentrically located with respect to its theoretical position. The governing partial differential equations subject to the appropriate boundary conditions are very conveniently formulated and successfully solved in a closed form by using generalized functions and Laplace transforms. Contrary to the usual assumptions of the standard dynamic analysis of continuous systems, herein the effect of axial contraction and extension is accounted for when establishing the translational kinematic boundary conditions. This may lead to considerable discrepancies that reveal the decisive role of the axial motion effect on the dynamic response of framed structures. Such discrepancies are clearly confirmed through a thorough numerical discussion of the governing parameters: joint mass and its rotatory inertia, joint angle, positioning of the mass, slenderness ratios, stiffness and length ratios.     

Non-linear steady state vibration and dynamic snap through of shallow arch beams

The non-linear steady state vibration of shallow arch beams is studied by a finite element method based on the principle of virtual work. Both the free and forced periodic vibrations are considered. The axial and flexural deformations are coupled by the induced axial force along the beam element. The spatial discretization is achieved by the usual finite element method and the steady state nodal displacements are expanded into a Fourier series. The harmonic balance method gives a set of non-linear algebraic equations in terms of the vibrating frequency and the Fourier coefficients of nodal displacements. The non-linear algebraic equations are solved by the Newtonian algorithm iteratively. The combined algorithm is called the incremental harmonic balance method. The importance of the conditions of completeness and balanceability is presented. Since the non-linearity is essentially softening, different orders of internal resonances between two modes can occur repeatedly. Isolated response curves are possible and are connected to the bifurcation of a particular excited mode.     

Note on the propagation of waves from a spherical cavity in an infinite solid

Summary The present note, as its title implies, is concerned with the investigation of disturbances in an infinite elastic medium containing an initial magnetic field in the axial direction. The equations ofMaxwell, those of elasticity have been effectively made use of to solve the problem.     

长型大截面地下结构的横向自由振动方程

文中综合考虑了内阻尼、外阻尼、剪切变形、横截面转动惯性、轴力和地基模型参数的影响,推得了弹性地基梁的一般自由振动方程。由这一方程可以得到一系列特殊情况下地下结构的自由振动方程。这一方程不仅能从理论上扩展了Timoshenko粱理论,而且在后续的研究中,为研究上述因素对于地下结构的自由振动和强迫振动的影响奠定了理论基础。     

The galactic dynamo: Axisymmetric and non-axisymmetric modes

Abstract

We discuss recent developments in the theory of large-scale magnetic structures in spiral galaxies. In addition to a review of galactic dynamo models developed for axisymmetric disks of variable thickness, we consider the possibility of dominance of non-axisymmetric magnetic modes in disks with weak deviations from axial symmetry. Difficulties of straightforward numerical simulation of galactic dynamos are discussed and asymptotic solutions of the dynamo equations relevant for galactic conditions are considered. Theoretical results are compared with observational data.     

Research on seismic behavior and shear strength of SRHC frame columns

The seismic behavior of steel reinforced high strength and high performance concrete(SRHC)frame columns was investigated through pseudo-static experiments of 16 frame columns with various shear span ratios,axial compression ratios,concrete strengths,steel ratios and stirrup ratios.Three kinds of failure mechanisms are presented and the characteristics of experimental hysteretic curves and skeleton curves with different design parameters are discussed.The columns’ductility and energy dissipation were quantitatively evaluated based on seismic resistance.The research results indicate that SRHC frame columns can withstand extreme bearing capacity,but the abilities of ductility and energy dissipation are inferior because of SRHC’s natural brittleness.As a result,the axial load ratio should be restricted and some construction measures adopted,such as increasing the stirrup ratio.This research established effect factors on the bearing capacity of SPHC columns.Finally,an algorithm for obtaining ultimate bearing capacity using the flexural failure mode is established based on a modified planesection assumption.The authors also established equations to determine shearing baroclinic failure and shear bond failure based on the accumulation of the axial load force distribution ratio.The calculated results of shear bearing capacity for different failure modes were in good agreement with the experimental results.     

摩擦摆支座在单层球面网壳结构中的隔震分析

将摩擦摆支座（FPS）应用于单层球面网壳结构的隔震，给出了隔震网壳结构的运动方程。通过对比分析不同强度地震动输入条件下的结构动力响应特征，考察了FPS支座应用于网壳结构隔震的有效性和适用性。研究结果表明，在不同强度的地震动作用下，隔震结构的节点加速度峰值和杆件轴力峰值都得到了有效控制，且地震动强度越大，控制效果越好。     

Seismic wave propagation effects on buried segmented pipelines

This paper deals with seismic wave propagation effects on buried segmented pipelines. A finite element model is developed for estimating the axial pipe strain and relative joint displacement of segmented pipelines. The model accounts for the effects of peak ground strain, shear transfer between soil and pipeline, axial stiffness of the pipeline, joint characteristics of the pipeline, and variability of the joint capacity and stiffness. For engineering applications, simplified analytical equations are developed for estimating the maximum pipe strain and relative joint displacement. The finite element and analytical solutions show that the segmented pipeline is relatively flexible with respect to ground deformation induced by seismic waves and deforms together with the ground. The ground strain within each pipe segmental length is shared by the joint displacement and pipe barrel strain. When the maximum ground strain is higher than 0.001, the pipe barrel strain is relatively small and can be ignored. The relative joint displacement of the segmented pipeline is mainly affected by the variability of the joint pullout capacity and accumulates at locally weak joints.     

An experimental study on active control of in-plane cable vibration by axial support motion

Active control of slightly sagged cables using the axial motion at the cable support is studied experimentally and analytically. Non-linear modal equations of a cable are presented, and two control schemes are identified, i.e. active stiffness control and active sag-induced force control. In this study, emphasis is placed on the active sag-induced force control. Additional damping is analytically expressed when a velocity feedback control is used. Although the active sag-induced force control can be applicable only for in-plane symmetric modes, it is shown that it is very efficient for the first mode. An experiment is conducted using a scaled cable model of 2 m length. First, it is shown by the experiment that the analytical model can predict well the non-linear cable motion. Next, sag-induced force control is examined using free vibration and harmonic excitations. The results agree well with the analytical predictions and confirm that additional damping can be obtained efficiently from the axial support motion.     

横向同性地层中井间电磁响应的三维频域耦合势正演模拟研究

本文针对电导率横向同性地层中三轴发射-接收线圈系的井间电磁响应,开展三维正演算法及模拟研究.首先将发射线圈简化为三轴正交磁偶极子源.为克服低频电磁产生的数值迭代收敛缓慢问题,利用低感应数预处理方法将频域Maxwell方程组转化为基于矢势与标势的Helmholtz方程.采用非等间距的Yee氏交错网格、电导率的体积加权平均技术以及积分形式的有限差分格式实现对控制方程的离散化.借助于不完全LU分解预处理的稳定双共轭梯度法计算井间电磁响应的数值解,并通过与有限元软件COMSOL的数值结果对比验证本文模型与算法的有效性.数值计算结果表明：在横向同性地层的垂直井模型中,测井响应横向分量xx和yy能反映出地层电导率各向异性信息,但横向探测能力较差.轴向分量zz虽只反映地层水平电阻率信息,但具有较好的横向探测能力,且对地层中异常体非常敏感,而交叉分量xz、zx则具备较强的层边界识别能力.