Vibration Concepts: Linear Systems

Abstract

The intention in this chapter is to first enunciate the equation of motion of a single degree-of-freedom (SDOF) oscillator vibrating in simple harmonic motion. This theoretical base is then extended to encompass undamped free vibrations, followed by damped free vibrations. Thereafter, a structure’s response to an impulse is evaluated, and it is shown how this technique can be used to determine the response to earthquake excitation. This leads up to the well-known Duhamel’s integral. This basic approach is then systematically expanded to arrive at equations of motion to determine the response of two degree-of-freedom and multi-degree-of-freedom (MDOF) systems. Subsequently, torsional and rocking vibrations are also addressed. The response equations developed herein are later utilised in Chaps. 4 and 6 to demonstrate how they can be applied to analyse building frameworks under seismic excitation.