武汉理工大学结构力学课件5.ppt

结 构 动 力 学,DYNAMICS OF STRUCTURES,第十章,10-1 Overview Of Structural Dynamics 10-2 Free-Vibration of SDOF 10-3 Forced-Vibration of SDOF 10-4 The Influence of Damping 10-5 Free-Vibration of MDOF 10-6 Orthogonality Relationship and Matrix of Normal Mode Shape 10-7 Forced-Vibration of MDOF Due to Harmonic Loads 13-11 Approximate Method to Natural Frequency,Catalog,13-1. Overview Of Structural Dynamics 结 构 动 力 学 综 述,Research Content Types of Prescribed Loading Essential Characteristics of Dynamics Problem Dynamic Degree Of Freedom Of Structure Formulation of Motion (Vibration) Equation,To present methods for analyzing the stresses and deflections developed in any given type of structure, when it is subjected to an arbitrary loading. 当结构承受任意动荷载作用时，计算给定结构的应力与变形的变化特点。,Fundamental Objective of Structural Dynamics Analysis,Structural response (deflections and Stresses) is also time-varying, or dynamic.,Types of Prescribed Loading,Dynamic loads,The magnitude, direction, or position varies with time,Period loads,Harmonic Load,Unharmonic Load,Typical examples,Unbalanced rotating machine in building,Rotating propeller At stern of ship,Nonperiodic loads,Impulse Load,在很短的时间内，荷载值急剧增大或急剧减小。如爆炸荷载等,Typical examples,Bomb blast pressure on building,Random Load Earthquake ,Wind,唐山地震-北京饭店测点（南北向 部分） 1976 7.28 03:42 单位:cm/s2 时间间隔 0.01 s,Typical examples,Earthquake on water tank,Time-varying Nature Inertia Force Equilibrium Status,Essential Characteristics of Dynamics Problem,录像资料,唐山大地震 1976年7月28日3时42分54秒，在河北省唐山、丰南一带， 发生了7.8级强烈地震，震中区烈度11度，地震波及天津市 和北京市。 这次地震集中在工矿企业集中、人口稠密的城市，造成 242419人丧生(包括天津等受灾区)。,唐山地震后，房屋几乎全部坍塌,塘沽新河造船厂船体车间墙倒顶塌,开滦唐山煤矿一号井震后,被震毁的唐山市胜利桥,唐山大地震后被震弯的铁路,唐山开滦煤矿医院新建7层大楼 震后破坏情况。大部分塌平，残 存一角仍然直立,唐山市文化路青年宫，为砖混结构的 二层楼房，除四根门柱外，全部坍塌,唐山市河北省矿业学院图书馆 西头倒毁，东头框架幸存,Definition The number of displacement components which must be considered in order to represent the effects of all significant inertia forces of a structure. Discrete Method Lumped-Mass method,Dynamic Degree of Freedom of Structure 动力自由度, Mass Point in Plane,Elastic Support No-effect to DOF,axial deformation,为减少动力自由度，梁与刚架不计轴向变形。,W=1,5),W=2,自由度数与质点个数无关，但 不大于质点个数的2倍。,W=2,W=1,8) 平面上的一个刚体,W=3,9)弹性地面上的平面刚体,W=3,W=2,W=1,W=13,自由度为1的体系称作单自由度体系； 自由度大于1的体系称作多（有限）自由度体系; 自由度无限多的体系为无限自由度体系。,2个自由度,2个自由度,m,mm梁,m,+m梁,I,I,2I,m,+m柱,厂房排架水平振时的计算简图,单自由度体系,水平振动时的计算体系,多自由度体系,构架式基础顶板简化成刚性块,(t),v(t),u(t),4个自由度,m1,m2,m3,2个自由度, Generalized Displacement,无限自由度体系,如简支梁的变形曲线可用三角级数来表示,用几条函数曲线来描述体系的振动曲线就称它是几个自由度体系，其中:, 是根据边界约束条件选取的函数，称为形状函数。,ak(t) 称广义座标，为一组待定参数，其个数即为自由度数,a1， a2， an,(3) The finite-Element Method,1) Direct Equilibration Using dAlembert Principle 直接平衡法dAlembert原理 2) Principle of Virtual Displacements 虚位移原理 3 )Hamilton Principle Hamilton原理,Formulation of Equations of Motion,The rate of change of momentum of any mass M is equal to the force acting on it. 任何给定质量m的动量变化率等于作用在这个质量上的力,1) Direct Equilibration Using dAlembert Principle,For most problems in structural dynamics it may be Assumed that the mass does not vary with time,: The Inertia force resisting the acceleration,elastic constraints, viscous forces, independently defined external loads.,dAlembert Principle： Mass develops an inertia force proportional to its acceleration and opposing it,if an inertial force which resists acceleration is introduced, the equation of motion is merely an expression of equilibration of all forces acting on the mass.,2) Principle of Virtual Displacements,The principle of virtual displacements may be expressed as follows: If a System which is in equilibrium under the action of a set of externally applied forces is subjected to a virtual displacement, i.e., a displacement pattern compatible with the systems constraints, the total work done by the set of forces will