FREE DYNAMICS OF FINITE CHAINS OF WEAKLY NONLINEAR OSCILLATORS
Infinite and finite chains of mono-coupled nonlinear oscillators are considered.
The dynamics of these one dimensional chains is studied relying upon discrete nonlinear periodic models governed by second order nonlinear difference equations. At first, amplitude dependent frequency thresholds bounding nonlinear propagation and attenuation zones are determined for infinite chains through a nonlinear map approach. Next, finite chains with homogenous boundary conditions are tackled through the multiple scales perturbation approach by assuming weak nonlinearities.
Free vibrations frequency-amplitude curves as well as nonlinear modes are determined. Furthermore, their connection with the amplitude dependent frequency thresholds of the nonlinear propagation zone is discussed.