武汉理工大学结构力学课件.ppt

第十章第十章10-1 Overview Of Structural Dynamics10-1 Overview Of Structural Dynamics10-2 Free-Vibration of SDOF10-2 Free-Vibration of SDOF10-3 Forced-Vibration of SDOF10-3 Forced-Vibration of SDOF10-4 The Influence of Damping10-4 The Influence of Damping10-5 Free-Vibration of MDOF10-5 Free-Vibration of MDOF10-6 Orthogonality Relationship and Matrix of Normal Mode Shape 10-6 Orthogonality Relationship and Matrix of Normal Mode Shape 10-7 Forced-Vibration of MDOF Due to Harmonic Loads10-7 Forced-Vibration of MDOF Due to Harmonic Loads13-11 Approximate Method to Natural Frequency13-11 Approximate Method to Natural FrequencyCatalog13-1. Overview Of Structural Dynamics结结 构构 动动 力力 学学 综综 述述¯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 AnalysisFundamental Objective of Structural Dynamics AnalysisStructural response (deflections and Stresses) is also time-varying, or dynamic.¯Types of Prescribed Loading Dynamic loadsThe magnitude, direction, or position varies with timeØPeriod loadsHarmonic LoadUnharmonic LoadTypical examplesUnbalanced rotating Unbalanced rotating machine in building machine in building Rotating propellerRotating propellerAt stern of ship At stern of ship ØNonperiodic 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 examplesBomb blast pressure on buildingØRandom 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 examplesEarthquake on water tankEarthquake on water tankèTime-varying Nature èInertia ForceèEquilibrium Status¯Essential Characteristics of Dynamics Problem录像资料J 塔科马大桥J地震影响 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 ØDefinition The number of displacement components which must be considered in order to represent the effects of all significant inertia forces of a structure. ØDiscrete Method ⑴ Lumped-Mass method ¯Dynamic Degree of Freedom of Structure动力自由度动力自由度⒈⒈⒈⒈ Mass Point in Plane Mass Point in Plane⒉⒉⒉⒉Elastic Support No-effect to DOF⒊⒊⒊⒊axial deformationaxial deformation为减少动力自由度，梁与刚架不计轴向变形为减少动力自由度，梁与刚架不计轴向变形为减少动力自由度，梁与刚架不计轴向变形。

为减少动力自由度，梁与刚架不计轴向变形4) W=15) W=2自由度数与质点个数无关，但不大于质点个数的2倍6) W=27) W=18) 平面上的一个刚体W=39)弹性地面上的平面刚体W=3W=210) 4) W=15) W=2自由度数与质点个数无关，但不大于质点个数的2倍6) W=27) W=1W=18) 平面上的一个刚体W=39)弹性地面上的平面刚体W=310) W=211) 12) W=13自由度为自由度为1 1的体系称作单自由度体系；的体系称作单自由度体系；自由度大于自由度大于1 1的体系称作多（有限）自由度体系的体系称作多（有限）自由度体系; ;自由度无限多的体系为无限自由度体系自由度无限多的体系为无限自由度体系2个自由度个自由度y2y12个自由度个自由度mm>>m梁m+αm梁II2Im+αm柱厂房排架水平振厂房排架水平振时的计算简图时的计算简图单自由度体系单自由度体系水平振动时的计算体系水平振动时的计算体系多自由度体系多自由度体系构架式基础顶板简化成刚性块构架式基础顶板简化成刚性块θ(t)v(t)u(t)4个自由度个自由度m1m2m32个自由度个自由度⑵ Generalized Displacementy(x,t)x无限自由度体系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，其中称它是几个自由度体系，其中: : —— 是根据边界约束条件选取是根据边界约束条件选取的函数，称为形状函数。

的函数，称为形状函数 ak(t) ——称广义座标，为一组待定称广义座标，为一组待定参数，其个数即为自由度数参数，其个数即为自由度数x yxa1， a2，…….. any(x,t)(3) The finite-Element Method1) Direct Equilibration Using d‘Alembert Principle 直接平衡法——d‘Alembert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 d‘Alembert PrincipleThe applied force vectorThe position vector of the mass m For most problems in structural dynamics it may be Assumed that the mass does not vary with time : The Inertia force resisting the accelerationelastic constraints, viscous forces, independently defined external loads. d’Alembert 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) 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 system‘s constraints, the total work done by the set of forces will be zero.3) Hamilton Principle make use of scalar quantities in a variational form (变分)known as Hamilton's principle.思思 考考★动力荷载的特点？与静力荷载的区别？动力荷载的特点？与静力荷载的区别？★结构的动力计算与静力计算的主要区别？结构的动力计算与静力计算的主要区别？★结构动力计算中的自由度概念与结构的几结构动力计算中的自由度概念与结构的几何组成分析中的自由度概念有何异同？何组成分析中的自由度概念有何异同？。