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1 ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes

1 2013

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Qualitative methods for research of transversal vibrations of semi-infinite cable under the action of nonlinear resistance forces

Pukach P., Kuzio I., Sokil M.

ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes

2013

Vol. 2, No 1

43--48

The aim of paper is to study the solution of the problem of nonlinear transverse vibrations of elastic elongated body under the force of resistance in unbounded domain. Such problems have applications in various technical systems - vibration of pipelines, railways, long bridges, electric lines, optical fibers. Unboundedness of the area creates more fundamental difficulties in the study of the problem. For the considered models of nonlinear oscillations have no general analytical techniques for determining the dynamic characteristics of the oscillatory process. Therefore it is sugges ted to use qualitative methods of the theory of nonlinear boundary value problems to obtain correct problem solution conditions (existence and uniqueness of the solution). In the paper conditions of the correctness of the solution of mathematical model for these nonlinear systems (sufficient conditions of the existence and uniqueness in the class of locally integrable functions) are obtained. Methods of qualitative study of semi-infinite cable vibrations under the forces of resistance based on general principles of the theory of nonlinear boundary value problems - method of monotony and Galerkin method. Scientific novelty of the work lies in particular in the generalization of methods of studying nonlinear problems on a new class of oscillatory systems In unbounded domains, justifying the correctness of the solution with specified mathematical model, which has practical applications in real engineering oscillatory systems. The technique allows not only for proving the correctness of the model solution, but also has an opportunity in its study to apply various approximate methods.