On the Internal Resonance in a Nonlinear Two-Degree-of-Freedom System : Forced Vibrations near the Higher Resonance Point When the Natural Frequencies Are in the Ratio 1:2

Abstract

A two-degree-of-freedom vibrating system tuned to internal resonance with the higher natural frequency twice the lower natural frequency, having nonlinear characteristic of second and third order polynomials of the displacements, subjected to harmonic excitation, is taken up. Steady forced vibrations are investigated in the vicinity of the higher resonance point of the system. Through the theoretical analysis it is found that the system has two types of resonances depending on the excitation frequency, namely one in which only harmonic occurs, and the other in which sub-harmonic with the frequency half the excitation frequency occurs strongly in addition to harmonic. Also found is the phenomenon that almost periodic motions occur in a certain range of the excitation frequencies. It is shown that the results of the theoretical analysis agree with those of an analog computer.