ДИСПЕРСІЙНИЙ АНАЛІЗ ПОЗДОВЖНІХ ІМПУЛЬСІВ ДЕФОРМАЦІЙ У КАНАТАХ МІНІМАЛЬНОЇ МАСИ ВАНТАЖОПІДЙОМНИХ МЕХАНІЗМІВ КРАНІВ

Abstract

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).