CALCULATION OF NONLINEAR TRANSIENT MOTION OF CABLES

The system of partial differential equations governing the nonlinear transient motion of a cable immersed in a fluid is solved by finite difference methods. This problem may be considered a generalization of the classical vibrating string problem in the following respects: (a) the motion is two dime...

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Bibliographic Details
Main Authors: Walton, Thomas S, Polachek, Harry
Format: Report
Language:English
Subjects:
Machinery and Tools
MECHANICAL CABLES
MOTION
TAYLORS SERIES
VIBRATION
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Summary:The system of partial differential equations governing the nonlinear transient motion of a cable immersed in a fluid is solved by finite difference methods. This problem may be considered a generalization of the classical vibrating string problem in the following respects: (a) the motion is two dimensional, (b) large dis placements are permitted, (c) forces due to the weight of the cable, buoyancy, virtual inertia of the medium and damping or drag are included, and (d) the cable is assumed to be nonuniform. The numerical solution of this system of equations presented a number of interesting mathematical problems related to: (a) the nonlinear nature of the equations, (b) the determination of a stable numerical procedure, and (c) the determination of an effective computational method. The computation is programmed for a high- speed calculator (UNIVAC system). The solution of this problem is of practical significance in the calculation of the transient forces acting on mooring lines due to the bobbing up and down of ships during the period preceding large scale explosion tests, as well as in many other applications involving mooring or towing operations.