MATEC Web Conf.
Volume 157, 2018Machine Modelling and Simulations 2017 (MMS 2017)
|Number of page(s)||9|
|Section||Machine dynamics and multibody systems simulations|
|Published online||14 March 2018|
Analysis of transverse vibration and stability issues of discrete-continuous elastic systems with nonlinearly variable parameters
Bialystok University of Technology, Faculty of Engineering Management, Ojca Tarasiuka 2, 16-001 Kleosin, Poland
* Corresponding author: firstname.lastname@example.org
The work is devoted to methods of analysis of vibrations and stability of discrete-continuous, multi-parameter models of beams, shafts, rotors, vanes, converting to homogeneous and one-dimensional. The properties of Cauchy's influence function and the characteristic series method were used to solve the boundary problem. It has been shown that the methods are an effective tool for solving boundary problems described by ordinary fourth-and second-order differential equations with variable parameters. Particular attention should be paid to the solution of the border problem of two-parameter elastic systems with variable distribution of parameters. Universal beam-specific equations with typical support conditions including vertical support, which do not depend on beam shape and axial load type, are recorded. The shape and type of load are considered in the form of an impact function that corresponds to any change in cross-section of the support and continuous axial load, so that the functions describing the stiffness, the mass and the continuous load are complete. As a result of the solution of the boundary vibration problem of freely bent support and any change in its cross-section, loaded with any longitudinal load, arranged on the resilient substrate, strict relations between the own frequency parameters and the load parameters were derived. Using the methods, simple calculations were made, easy to use in engineering practice and conditions of use were given. Experimental studies have confirmed the high accuracy of theoretical calculations using the proposed methods and formulas.
Key words: beams / boundary issues / transverse oscillations / intrinsic frequency stability / critical loads
© The Authors, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (http://creativecommons.org/licenses/by/4.0/).
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