Professor for post graduation, department of mechanical engineering, bangalore institute of technology, bangalore introduction a two degree of freedom system is one that requires two coordinates to completely describe its equation of motion. This document describes free and forced dynamic responses of simple oscillators somtimes called single degree of freedom sdof systems. The mathematical models that govern the free vibration of single degree of freedom systems can be described in terms of homogeneous secondorder ordinary differential equations that contain displacement, velocity, and acceleration terms. The simplest vibratory system can be described by a single mass connected to a spring and possibly a dashpot. Unit 6 vibrations of two degree of freedom systems. Structural dynamics of linear elastic singledegreeoffreedom. This particular trilogarithmic format of the response spectrum displays the frequency. This last expression is the equation of motion of a single degree of freedom system and is a linear, secondorder, ordinary differential equation with constant coefficients. The relevance of the current topic to the asce 705 document is provided here. Free vibration of single degree of freedom systems springerlink. Single degree of freedom systems request pdf researchgate. The velocity coefficients define the damping constants and. Single degree of freedom sdof system m k ft ut figure 1. The displacement coefficients describe the stiffness of the elastic members or the restoring forces.
The easiest example to describe a vibrating system is a singledegreeoffreedom system sdof system. Vibrations of single degree of freedom systems cee 541. Gavin fall, 2016 this document describes free and forced dynamic responses of single degree of freedom sdof systems. Unit 6 vibrations of two degree of freedom systems dr. Free vibration of single degree of freedom systems. Vibrations of single degree of freedom systems 5 1. Exact solutions for free vibration of singledegreeoffreedom. Dynamics of simple oscillators single degree of freedom. This document describes free and forced dynamic responses of single degree of freedom sdof systems. Instructional material complementing fema 451, design examples. Free vibration of single degree of freedom sdof chapter 2 introduction a. Equation 2 can be solved to yield the time history of the position of the mass m, given the initial position and velocity of the mass. Only one degree of freedom is applied and usually only the vertical movement is considered.
The prototype single degree of freedom system is a. Lecture notes, vibrations of single degree of freedom systems. This very simple equation describes the phase lines in terms of the horizontal position x of. Structural dynamics department of civil and environmental engineering duke university henri p. Dynamics of simple oscillators single degree of freedom systems. A single degree of freedom sdof system is one for which the behavior of interest can. Singledegreeoffreedom linear oscillator sdof for many dynamic systems the relationship between restoring force and deflection is approximately linear for small deviations about some reference. Undamped sdof system its acceleration and opposing its motion.
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