武汉理工大学结构力学课件5.ppt

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 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 ⑴ Lumped-Mass 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 思 考 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？ 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 Principle The applied force vector The 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 acceleration elastic 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) 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