An amplitude equation for the nonlinear vibration of viscoelastically damped sandwich beams
Abstract
An elementary theory for nonlinear vibrations of viscoelastic sandwich beams is presented. The harmonic balance method is coupled with a one mode Galerkin analysis. This results in a scalar complex frequencyresponse relationship. So the nonlinear free vibration response is governed by only two complex numbers. This permits one to recover first the concept of linear loss factor, second a parabolic approximation of the backbone curve that accounts for the amplitude dependence of the frequency. A new amplitudeloss factor relationship is also established in this way. The forced vibration analysis leads to resonance curves that are classical within nonlinear vibration theory. They are extended here to any viscoelastic constitutive behaviour. This elementary approach could be extended to a large class of structures and in a finite element framework. The amplitude equation is obtained in closed form for a class of sandwich beams. The effects of the boundary conditions and of the temperature on the response are discussed.
 Publication:

Journal of Sound Vibration
 Pub Date:
 April 2004
 DOI:
 10.1016/S0022460X(03)007545
 Bibcode:
 2004JSV...271..789D