在研究船舶、潜艇等工程结构的低频振动时，通常可以将其简化为质量在截面内分布非均匀的梁结构，此质量偏心会引起弯-纵耦合。本文针对弯-纵耦合的质量偏心Timoshenko梁，推导了其截止频率的解析表达式；探讨了质量偏心对其纵振波、传播弯曲波及衰减弯曲波波数的影响规律；研究了三组波数下纵向/弯曲位移比随频率及质量偏心的变化。分析结果表明，质量偏心会降低梁的截止频率，偏心率越大，降低越明显；弯曲衰减波会在截止频率处转变为弯曲传播波；质量偏心使得非频散的纵向振动波转变为频散波；纵向振动与弯曲振动的耦合在质量偏心率或频率增大时，会进一步加强。
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.
关键词
振动波 /
质量偏心 /
Timoshenko梁 /
弯-纵耦合
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Key words
vibration waves /
mass eccentricity /
Timoshenko beam /
bending-longitudinal coupling
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