 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| S.V. Russkikh and F.N. Shklyarchuk, "Movement of a Heavy Rigid Body Suspended on a Cable of Variable Length with Oscillation Elimination," Mech. Solids. 54 (5), 683-693 (2019) |
| Year |
2019 |
Volume |
54 |
Number |
5 |
Pages |
683-693 |
| DOI |
10.3103/S0025654419050157 |
| Title |
Movement of a Heavy Rigid Body Suspended on a Cable of Variable Length with Oscillation Elimination |
| Author(s) |
S.V. Russkikh (Moscow Aviation Institute, Moscow, 125080 Russia; Institute of Applied Mechanics, Russian Academy of Sciences, Moscow, 125040 Russia, sergey.russkih@rambler.ru)
F.N. Shklyarchuk (Institute of Applied Mechanics, Russian Academy of Sciences, Moscow, 125040 Russia; Moscow Aviation Institute, Moscow, 125080 Russia, shklyarchuk@list.ru) |
| Abstract |
A nonlinear problem of terminal movement of a heavy rigid body suspended on an inextensible inertialess cable of variable length with controlled horizontal movement of the suspension point
is considered. It is required to move the body for a certain time from an initial resting position to a given
final resting position with oscillation elimination in the end of the operation. The law of variation in
the cable length is assumed to be given, and the controlled movement of its suspension point is
unknown. An approximate solution to the problem of kinematic control of the oscillations of a system
described by two nonlinear differential equations with variable coefficients for moderately large angles
of rotation of the strained cable and the body is sought in the form of series with unknown coefficients
by the Bubnov–Galerkin method using given basic functions of time that satisfy some initial and final
conditions. The acceleration of the suspension point of the cable is sought in the form of a finite series
of sines with unknown coefficients. A coupled system of nonlinear algebraic equations for all unknown
coefficients is obtained, which includes the equations of the Bubnov–Galerkin method and initial and
final data that are not fixed when choosing the basis functions. This system of equations is solved by
the method of successive approximations using, in the first approximation, solutions of the linearized
equations. In the examples of a system with a cable of constant and variable length, calculations are
carried out with an analysis of the accuracy of the solutions by comparing them with the numerical
solutions of the nonlinear differential equations of the direct problem by the Adams method with the
control laws found. |
| Keywords |
body on a cable, cable of variable length, nonlinear oscillations, oscillation elimination, terminal control, hoisting-and-transport mechanisms |
| Received |
25 October 2018 | Revised |
23 January 2019 | Accepted |
19 March 2019 |
| Link to Fulltext |
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