Anti-resonance in a one-dimensional chain of driven coupled oscillators

Abstract

We investigate a driven system of N one-dimensional coupled oscillators with identical masses. The first mass is connected to a sinusoidal driving force of frequency ω. In the steady state, when all the masses perform simple harmonic motion, we analytically obtain the dependence of their amplitudes on ω and show that there are resonance and anti-resonance frequencies. At an anti-resonance frequency, the amplitude of one of the masses becomes exactly zero. The mass directly connected to the driving force has the largest number of anti-resonance frequencies, N – 1. The phase of each mass's motion is either 0 or π with respect to the driving force. The case where damping forces are present is also considered, and the amplitude dependence on driving frequency is analytically obtained. In the presence of damping, there is no anti-resonance.