Abstract
1/2-order subharmonic oscillations are investigated in the multi-degree-of-freedom system where N nonlinear, identical oscillators with spatially periodic structures are connected by weak linear springs, when the system is subjected to sinusoidal excitation. Van der Pol's method is employed to determine the frequency response curves for the 1/2-order subharmonic oscillations when N=2 and 3. All patterns of vibrations are classified depending on the results of the response curves, and it is determined in which pattern intrinsic localized modes (ILMs) appear. The bifurcation set is also calculated to examine the influence of the connecting spring constants on the response curves and the occurrence of Hopf bifurcations, followed by amplitude modulated motions. Furthermore, The influence of the imperfection of the system on the response curves is investigated by slightly changing the value of the spring constant of the nonlinear oscillator. Numerical simulations are also conducted to confirm the validity of the frequency response curves and the occurrence of amplitude modulated motions.
