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Research Papers

Propagation of Longitudinal Deformation Wave Along a Hoisting Rope Carrying an Intermediate Concentrated Load

[+] Author and Article Information
A. G. Razdolsky

Independent Research Scientist,
Ein Gedi St. 2/16,
Holon 58506, Israel

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received December 6, 2012; final manuscript received April 21, 2014; published online August 8, 2014. Assoc. Editor: Gregory Shaver.

J. Dyn. Sys., Meas., Control 136(6), 061002 (Aug 08, 2014) (12 pages) Paper No: DS-12-1411; doi: 10.1115/1.4027540 History: Received December 06, 2012; Revised April 21, 2014

Motion of the hoisting rope carrying an intermediate concentrated load is described by the one-dimensional wave equation in the region consisting of two sections separated by a moving boundary condition. The system is moved by the driving force acting at the upper cross section of the rope. Position of the intermediate load and consequently the lengths of the rope sections vary in the time depending on the magnitude of driving force. Solution of the wave equation is represented as a sum of integrals with variable limits of integration. The problem is reduced to solving the sequence of ordinary differential equations which describe a motion of the load in the fixed coordinate system and the paths of the rope ends in the moving coordinate system connected with the load. The argument of functions involved in the right-hand side of these equations lag behind the argument of the derivatives in the left-hand side of equations by a short time interval. A description of the unknown functions in a parametric form makes possible to eliminate retarded arguments from the equations. The problem is solved by using a technique of the sequential continuation of solution for time intervals corresponding to propagation of the deformation wave in the opposite directions. A computer program has been developed for solving the problem. Results of the numerical solution are presented in the case that the driving force is a piecewise linear function of time and is discontinuous at the peak point.

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Copyright © 2014 by ASME
Topics: Stress , Ropes
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Figures

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Fig. 1

Scheme of the hoisting device component

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Fig. 2

Mapping a state of the cross section of the main rope on the phase plane

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Fig. 3

Mapping a state of the cross section of the compensate rope on the phase plane

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Fig. 4

Propagation of the deformation wave from the rope top to the load and to the rope bottom

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Fig. 5

Propagation of the deformation wave from the rope bottom to the load and to the rope top

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Fig. 6

Schematic representation of the process of sequential continuation of solution

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Fig. 7

Driving force as function of time

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Fig. 8

Variation of motion velocity of the load during the rope motion

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Fig. 9

Variation of longitudinal deformation of the main rope during the rope motion

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