1-Free Vibration 1DOF undamped(单自由度无阻尼振动系统).ppt

Undamped 1DOF Free Vibration 单自由度无阻尼振动系统 Dr. Dong, Mingming 董明明 Lab. of Vibration and Noise Controlling 振动与噪声控制实验室 Main Contents Introduction Free Vibration of an Undamped Translational System Free Vibration of an Undamped Torsional System Free Vibration with Viscous Damping Free Vibration with Coulomb Damping Free Vibration with Hysteretic Damping Conception A system is said to undergo free vibration when it oscillates only under initial disturbance with no external force acting after the initial disturbance. Example Examples Example2 Equation of Motion Using Newton’s Second Law of Motion Select a suitable coordinate to describe the position of the mass or rigid body in the system. Determine the static equilibrium (平衡) configuration Draw the free-body diagram (分离体受力图) Apply Newton’s second law of motion Newton’s second law of motion If mass m is displaced a distance when acted upon by a resultant force (合力) in the same direction, Newton’s second law of motion gives Rotational Motion For a rigid body undergoing rotational motion (回转运动), Newton’s law gives Equation of Motion Using Other Methods D’Alembert’s Principle (达朗贝尔原理) Principle of Virtual Displacements (虚位移原理) Principle of Conservation of Energy (能量守恒定律) D’Alembert’s Principle provided that and are treated as a force and a moment. This fictitious force (虚拟力) (or moment) is known as the inertia force (or inertia moment) Principle of Virtual Displacements If a system is in equilibrium (保持[处于]平衡状态) under the action of a set of forces is subjected to a virtual displacement, and then the total virtual work done by the forces will be zero. Result When the total virtual work done by all the forces is set equal to zero, we obtain Since the virtual displacement can have an arbitrary value (任意值) The equation of motion of the spring-mass system as Principle of Conservation of Energy If no work is done on a conservative system by external forces (other that gravity o