8 - Applying Vibration Models

Abstract

This chapter focuses on the simple harmonic oscillator, with and without damping, with and without a forcing function, and in several different guises. These applications include the classical mechanical spring-mass system, inductor-capacitor oscillators, a parallel resistor–inductor–capacitor (RLC) circuit, the vibration of tall buildings, and oscillation in a cyclotron and of a vehicle suspension system. The electrical–mechanical analogy is useful to define the different terms in the various oscillator models. Forced vibration occurs when there is a persistent, repetitive input, such as the kind an air conditioning system imparts to the building it cools. The forced harmonic vibration of an oscillator involves the very important concepts of resonance and impedance. In impedance, the various elements (spring, mass, and damper) provide different response regimes, that is, frequency regimes that are controlled, respectively, by stiffness, mass, and damping. For the development of oscillatory behavior, systems must have elements with stiffness that store potential energy (springs and capacitors), elements with mass that store kinetic energy (masses and inductors), and elements that dissipate energy (dashpots and resistors). Stiffness may take many forms, but there must always be an element that stores potential energy in order for there to be an exchange with an element that stores kinetic energy.