Antiresonances

Abstract

In a linear or nonlinear oscillator with a single degree of freedom subjected to an additive periodic driving force with a single frequency a typical frequency-response curve displays a single resonance peak as shown in the introductory chapter. In a linear and undamped system the response amplitude becomes a maximum when the frequency of the driving force matches with the natural frequency of the system. In other oscillators a single resonance peak occurs at a frequency different from their natural frequencies. In a N-coupled linear oscillators with first oscillator alone driven by an additive periodic force, for certain types of interaction (coupling) the frequency-response curve of each oscillator exhibits at most N peaks (maxima) depending upon the values of the parameters of the oscillators [1]. The peaks are the resonance (and the corresponding frequencies are the resonant frequencies). The valleys in the frequency-response curve are the antiresonance frequencies. There are N − 1 antiresonance frequencies. In the absence of damping, for the driving frequency equal to the antiresonance frequencies the response amplitude vanishes. The multiple resonance and antiresonance phenomena occur in nonlinear systems also. Using resonance a dynamical system can be effected to give rise to the most effective signal output. On the other hand, an antiresonance is useful to make the system to deliver the lower signal output. These can be realized in systems subjected to different kinds of external perturbations. Antiresonances can occur in all types of coupled oscillator systems, including mechanical, acoustic, electromagnetic and quantum systems.