3.Dynamic Model and Equilibrium Equation 3.1.1 Dynamic Model and Equilibrium Equation .How to determine theDegreeof-freedom .How to determine theDegree-of-freedomfor such eteha .How to determine the"Degree-of-freedom"for such 3.1.1 Dynamic Model and Equilibrium Equation kinds of system Newton's 2nd Law 而 e8 my· sheouc of thebody mass 路四培贩回 3.1 Dynamic Model and Equilibrium Equation 3.1.2 Undamped Free Vibration D'Alambert Principle Inertial force Based on D'Alambert's principle: F-ma=0 成+x=0 2015/1012  How to determine the “Degree-of-freedom” In mechanics, the degree of freedom (DOF) of a mechanical system is the number of independent parameters that define its configuration. It is the number of parameters that determine the state of a physical system. Degree of freedom is a fundamental concept central to the analysis of systems of bodies in mechanical engineering, aeronautical engineering, robotics, and structural engineering. 2015/10/13 熊海贝，同济大学土木工程学院 xionghaibei@tongji.edu.cn 7 3.1.1 Dynamic Model and Equilibrium Equation  How to determine the “Degree-of-freedom” for such kinds of system 2015/10/13 熊海贝，同济大学土木工程学院 xionghaibei@tongji.edu.cn 8 3.1.1 Dynamic Model and Equilibrium Equation  How to determine the “Degree-of-freedom” for such kinds of system Adjustable Slippage Element 2015/10/13 熊海贝，同济大学土木工程学院 xionghaibei@tongji.edu.cn 9 Newton’s 2nd Law “The force acting on a body and causing its movement, is equal to the rate of change of momentum in the body.” • Momentum Q, is equal to the product of the body mass by its velocity. mx dt dx Q  mv  m   3.1.1 Dynamic Model and Equilibrium Equation mx ma dt dx m dt dv m dt d( mv ) dt dQ F         D’Alambert suggested that Newton’s Law can be written in a similar way that principle of equilibrium in statics (F=0): Inertial force D’Alambert Principle F ma  0 3.1.1 Dynamic Model and Equilibrium Equation 2015/10/13 熊海贝，同济大学土木工程学院 xionghaibei@tongji.edu.cn 11 x m k 0 mx kx Based on D’Alambert’s principle: m  x   kx  0 3.1.2 Undamped Free Vibration Ordinate that describes the mass movement stiffness mass This is Dynamic Equilibrium Equation of undamped free vibration of SDOF mass