Forced vibration analysis for damped periodic systems with one nonlinear disorder

The steady-state responses of damped periodic systems with finite or infinite degrees-of-freedom and one nonlinear disorder to harmonic excitation are investigated by using the Lindstedt-Poincare method and the U-transformation technique. The perturbation solutions with zero-order and first-order approximations, which involve a parameter n, i.e., the total number of subsystems, as well as the other structural parameters, are derived. When n approaches infinity, the limiting solutions are applicable to the system with infinite number of subsystems. For the zero-order approximation, there is an attenuation constant which denotes the ratio of amplitudes between any two adjacent subsystems. The attenuation constant is derived in an explicit form and calculated for several values of the damping coefficient and the ratio of the driving frequency to the lower limit of the pass band.