Vibration wave characteristics of Timoshenko beam with eccentric mass

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Journal of Vibration and Shock ›› 2022, Vol. 41 ›› Issue (1) : 265-270.

WANG Jian1,2, YUAN Xiufeng2, HU Yongbiao1

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Abstract

The main bodies can usually be simplified as beams in the study of low-frequency vibrations of ships, submarines, and other engineering structures. While the couplings between bending and longitudinal vibrations will arise because of the non-uniform mass distribution in the cross-section. Analytical expression of cut-off frequency for the bending-longitudinal coupled eccentric Timoshenko beam was derived. Influences of eccentricity on the longitudinal waves, propagating bending waves, and decaying bending waves were discussed. Variations of longitudinal/bending displacement ratio with frequency and eccentricity under three sets of wavenumbers were studied. Analysis results show that eccentricity reduces the cut-off frequency of beam. The greater the eccentricity, the more obvious the reduction. The decaying bending wave transforms into propagating one at the cut-off frequency. Eccentricity induces the transition of longitudinal wave from non-dispersive one to dispersive one. If the eccentricity or frequency increases, or both, the bending-longitudinal coupling will be further strengthened.

Key words

vibration waves / mass eccentricity / Timoshenko beam / bending-longitudinal coupling

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WANG Jian1,2, YUAN Xiufeng2, HU Yongbiao1. Vibration wave characteristics of Timoshenko beam with eccentric mass[J]. Journal of Vibration and Shock, 2022, 41(1): 265-270

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