Theoretical-experimental investigation of a three-degree-of-freedom structure

A theoretical-experimental investigation is conducted into the response of a three-degree-of-freedom structure having an autoparametric combination resonance of the additive type to a primary resonance of the higher mode. The structure consists of two light-weight beams and three concentrated masses arranged in a T-shape. The theoretically predicted natural frequencies are in good agreement with those obtained experimentally. The method of multiple scales is used to determine six first-order differential equations describing the modulation of the amplitudes and phases of the three modes with nonlinearity, damping, and resonances. Some of the predicted nonlinear phenomena include the saturation phenomenon, coexistence of stable solutions, jumps, and periodic, two-period quasiperiodic, and phase-locked or synchronized motions. The experiment confirms these predictions and shows other phenomena that are not yet explained by the theory.