起重机起重机构最小质量绳索纵向变形脉冲的频散分析

Y. Chovnyuk, P.P. Cherednichenko, O. Ostapuschenko
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摘要

本文对满足各特定截面强度相等条件的起重机起重机构最小质量绳索纵向变形脉冲进行了频散分析。确定了在这种类型的绳索中发生的相位和群波形速度。用固定相位法研究了“用拾取器”/“从基座”(“从地面”)提起负载时的脉冲频散。本文采用的方法有:1)数学物理的经典方法;2)复傅里叶变换随时间的变化;3)用定相法计算表征远场渐近过程中变形的积分。结果表明,该渐近调度将钢丝绳中产生的应力和变形波场的分析简化为使用复参数的Airy函数。这个论证的符号是由上述波的群速度稳定点附近的波矢量对频率的三阶导数的符号决定的(听着,二阶导数等于零)。证实了Airy函数负责再现波前在绳系内部运动前后的扰动性质。确定了指数乘法器的恒相平面在绳中携带时的相速度。这个乘法器描述了新兴波形的时空依赖性。在脉冲前沿(绳索的载荷/变形)附近,其持续时间增加,但振幅与到观测点距离的立方根成比例地减小。建立了该公式,根据该公式,在波形在绳索中传播群速度曲线极值的情况下,建立了该问题解的渐近解。类似的方法提供了探索在起重机起重机构绳索中产生的非平稳波场的主要模式的可能性。所得结果可用于建立起重机索系在瞬态状态下的载荷和变形量估计。当使用不同类型的起重机(特别是桥式、龙门式、门式)在操作模式(实际操作模式)下提升或降低负载时,这种负载/变形通常会导致上述系统过度应变,并可能导致紧急情况(例如绳索系统断裂)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
DISPERSION ANALYSIS OF LONGITUDINAL DEFORMATION PULSES IN MINIMUM MASS ROPES OF CRANES LOAD LIFTING MECHANISMS
Dispersion analysis of longitudinal deformation pulses in minimum mass ropes of cranes load lifting mechanisms (which satisfy the conditions of equal strength in each specific cross section) is carried out in the article. The phase and group waveform velocities occurring in the ropes of this type are determined. The impulse dispersion by the method of lifting the load "with the pickup"/"from the base" ("from the ground") was investigated using the stationary phase method. Such methods are used in this work as: 1) classic methods of mathematical physics; 2) complex Fourier transform over time; 3) stationary phase method for the calculation of the integral which characterizes the deformations in the remote field during its asymptotic schedule. It is shown that the asymptotic schedule reduces the analysis of stress and deformation wave fields arising in the rope to the using of the Airy function with a complex argument. The sign of this argument is determined by the sign of the third derivative of the frequency by the wave vector for mentioned above fields near stationary points of the group velocity of wave formations (hear, in accordance, the second derivative is equal to zero). It is substantiated that Airy function is responsible for reproducing the nature of perturbations before and after the wave front moving inside the rope system. The phase velocity with which the constant phase plane of the exponential multiplier is carried in the rope is determined. This multiplier the spatial-temporal dependence of the emerging waveform describes. Near the pulse front (load/deformation of the rope), its duration increases, but the amplitude decreases in proportion to the cubic root of the distance to the observation point. The formula is established, according to which the asymptotic of this problem solution should be built, in the case of the curve extreme of waveform propagation group velocity in the rope. A similar approach gives the possibility to explore the main patterns of no stationary wave fields generated in the ropes of cranes load lifting mechanisms. The results obtained in the work can be used for establishing cranes rope systems loads and deformations quantities estimates under the condition of their transience. Such loads/deformations usually cause of the above systems overstrain when lifting or lowering loads with different types cranes (particularly, bridge, gantry, portal), which work in operation modes (real operation mode) and can lead to emergencies (for example, breaks in rope systems).
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