Vibration suppression of a symmetrically cantilever composite beam using internal resonance under chordwise base excitation

Abstract

Large flexible structures can be modeled as flexible beams with an appendage. Passive, semi-active or active vibration absorber can be used as an appendage in such structures. In this paper, the performance of an oscillator consisting of mass and spring at the tip of a symmetrically cantilever composite beam is investigated under chordwise base excitation. The oscillator is located at the tip of the beam in order to relate first-order uncoupled modes of the composite beam through internal resonance. Natural frequencies which are dependent on the oscillator parameters have been selected such that two-to-one and one-to-one internal resonance can be produced. The motion of the combined system is described by a set of four non-linear coupled partial differential equations, corresponding to the four describing variables of motion. The equations of motion are then solved using the method of multiple-scales in the occurrence of two-to-one and one-to-one internal resonances. Saturation phenomenon is detected in the force modulation response at the one-to-one internal resonance. Reduction of amplitudes is shown in both frequency and force–response curves under primary resonance.