Volume 4, Issue 1 (1-2017)                   WJEPAS 2017, 4(1): 1-8 | Back to browse issues page

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Ivanova G, Lilkova-Markova S, Pavlov P. Modular approach in creating the matrix equations, describing the free vibrations of discrete plane systems. WJEPAS. 2017; 4 (1) :1-8
URL: http://europeansp.org/article-15-144-en.html
Universiry of Architecture, Civil Engineering and Geodesy, 1 Hr. Smirnenski Blvd, Sofia 1046, Bulgaria
Abstract:   (261 Views)
A large part of present engineering structures are complex mechanical systems with a large number of degrees of freedom (DOF). Matrix mechanics and mathematical software for engineering calculations are basic tools in studying the dynamic behaviour of such systems. An inductive scientific approach to study the dynamic behavior of complex plane systems are available in the research of this report. The conception of the approach is to examine the modules from simple systems with 2 DOF, composed of bodies performing simple motions (translation, rotation), interconnected by joints and elastic-viscous connections. The dynamic and mathematical models are constructed so, to be easily include into the models of more complex systems, composed of such simple modules. The inertial, elastic, dissipative matrices of the simple modules are composed in a form, that allows easy to form the matrix of the complex systems. The systems are open and can be supplemented with other bodies of the same kind, related to increasing the number of generalized coordinates and respectively the size of modular matrices in matrix equations. The matrices in the matrix differential equations, describing the motion of the systems (inertial, elastic, dissipative, etc.), are sparse matrices derived from the superimposition of modular matrices with a concentration of non-zero elements around the main diagonal. The lasts are very similar to the matrices of stiffness, in static and dynamic analysis of continuous systems with FEM, at an appropriate choice of the numbering of the nodes. © 2016 The Authors. Published by European Science publishing Ltd. Selection and peer-review under responsibility of the Organizing Committee of European Science publishing Ltd.
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Received: 2019/08/8 | Accepted: 2019/08/8 | Published: 2019/08/8

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