Free Vibration of Single Degree of Freedom Systems

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The term free vibration is used to indicate that there is no external force causing the motion, and that the motion is primarily the result of initial conditions, such as an initial displacement of the mass element of the system from an equilibrium position and/or an initial velocity. The free vibration is said to be undamped free vibration if there is no loss of energy throughout the motion of the system. This is the case of the simplest vibratory system, which consists of an inertia element and an elastic member which produces a restoring force which tends to restore the inertia element to its equilibrium position. Dissipation of energy may be caused by friction or if the system contains elements such as dampers which remove energy from the system. In such cases, the oscillation is said to be free damped vibration. The mathematical models that govern the free vibration of single degree of freedom systems can be described in terms of homogeneous second-order ordinary differential equations that contain displacement, velocity, and acceleration terms. The displacement coefficients describe the stiffness of the elastic members or the restoring forces. The velocity coefficients define the damping constants and determine the amount of energy dissipated, and the acceleration coefficients define the inertia of the system.KeywordsFree VibrationStiffness CoefficientSingle DegreeInitial DisplacementLogarithmic DecrementThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.