剑杆的弹性振动

剑杆引纬,由于剑杆加速度峰值达几十个 g,不可避免地引起剑杆弹性振动。当剑尾以名义加速度(?)(t)运动时,剑杆纵向振动方程为:ρA[((?)~2u)/((?)t~2)+(?)(t)]=(?)/(?)x(EA((?)u)/((?)x))在现有设计及应用中,(?)(t)均满足展成收敛的傅氏级数条件。从而可应用谐波分析法研究剑杆强迫振动的解。本文假设剑杆为等截面直杆,按梯形加速度规律计算剑杆纵向振动对位移的影响,并给出杆内动态正应力的计算式,为剑杆的强度设计提供了理论依据。

THE ELASTIC VIBRATION OF THE RAPIER IN RAPIER LOOMS

It is impossible to avoid the elastic vibration of the rapier because its accelera-tion reaches a peak value which amounts to dozens of the acceleration of gravity.Asthe tail of the rapier moves with a nominal acceleration (?)(t),the longitudinal vibra-tion equation of the rapier is:(?)In usual designs all conditions under which (?)(t) can be transformed to convergentFourier series are satisfied,thus the solution of forced vibration of the rapier canbe studied by means of harmonic analysis.Assuming that the rapier is a straight bar with uniform cross-section,the ef-fect on displacement by thel ongitudinal vibration of the rapier with trapezoidal ac-celeration has been calculated in this paper.The formula for calculating dynamicstresses of the rapier has also been proposed,and it may serve as the theoretical ba-sis of strength desiffn of the rapier.