Dynamic behavior of a sandwich beam with internal resonators

Jung-San Chen, Purdue University

Abstract

Wave propagation in a sandwich beam with internal resonators was investigated. Two continuum Timoshenko beam models were presented and used to interpret the dispersion characteristics of the original sandwich beam. One model treats the resonators as continuously distributed mass and the other with an effective mass density. It was found that the range of frequencies that yield negative mass densities in the continuum Timoshenko beam actually correspond to a bandgap in which no harmonic waves can propagate in the sandwich structure without attenuation in amplitude. Also, the bandgap can be tailored by altering the local resonance frequency of the resonator. The resonator can give rise to a significant wave attenuation effect near the local resonance frequency, and hence can be used to block disturbances with certain frequencies from entering the structure. Besides resonators, periodic structural assemblies are also capable of filtering waves with certain frequencies. A sandwich beam with periodic cores were presented and its dynamic behavior was investigated. It was found that the bandgap can be adjusted by altering the material properties of the core. Also, in order to block disturbances in the low frequency range, the dimension of the structure has to be large. By comparing the beam with resonators and the beam with periodic cores, it was concluded that the resonators have a better effect on wave attenuation and vibration reduction. If a uniform harmonic pressure was applied to the top surface of a supported sandwich beam containing spring-mass resonators, the local resonance frequency of the resonator becomes the antiresonant frequency of the whole structure. A simple two-degree-of-freedom system consisting of an absorbing mass connected by springs to a drive mass was introduced and employed to interpret the vibration characteristics of the sandwich structure. It was found that the sandwich structure with resonators could be effective in mitigating vibration induced by wave slamming impact which produces dynamic motion with a dominant frequency.

Degree

Ph.D.

Advisors

Sun, Purdue University.

Subject Area

Aerospace engineering

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