Investigation of mathematical models for vibrations of one dimensional environments with considering nonlinear resistance forces
No Thumbnail Available
Date
2016
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Commission of Motorization and Energetics in Agriculture
Abstract
In this paper we consider important classes of one dimensional environments, bending stiffness of which can be neglected. It is impossible to apply approximate analytical method of solution of mathematical models of dynamic processes. So justification of existence and uniqueness of solutions, carried out a qualitative their evaluation, based on numerical analysis are considering in this paper. Also the features of dynamic processes of some of examined class of systems are analyzed. Methods of qualitative study of oscillations for restricted and unrestricted bodies under the influence of the resistance forces, described in this paper are based on the general principles of the theory of nonlinear boundary value problems – Galerkin method and the method of monotonicity. Scientific novelty consists in generalization these methods of studying for nonlinear problems at new classes of oscillating systems, justification of solution correctness for specified mathematical models that have practical application in real engineering vibration systems.
Description
Keywords
mathematical model, nonlinear vibrations, nonlinear boundary value problem, Galerkin method, nonlinear elastic properties
Citation
Pukach P. Investigation of mathematical models for vibrations of one dimensional environments with considering nonlinear resistance forces / P. Pukach, P. Sokhan, R. Stolyarchuk // Econtechmod : an international quarterly journal on economics in technology, new technologies and modelling processes. – Lublin ; Rzeszow, 2016. – Volum 5, number 1. – P. 97–102. – Bibliography: 22 titles.