CONFERENCE PROCEEDINGS
4th INTERNATIONAL CONFERENCE
CONTEMPORARY ACHIEVEMENTS IN CIVIL ENGINEERING 2016 , 2016.y., pp. 249-258
MODEL OF FORCED OSCILLATIONS OF CONSTRUCTION WITH INTERNAL ASYMMETRY| |
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| DOI: 10.14415/konferencijaGFS 2016.024 |
| UDC: 534.01 : 517.9 |
| CC-BY-SA 4.0 license |
| Author : Rakarić, Zvonko |
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| | Summary: |
| | In addition to well-developed and well-known linear theory of oscillations of
structures, there is an increasing need for taking into account the non-linearity in the studied system. This is imposed due to modern requirements in design. Causes of nonlinearities can be different in its nature. The emphasis in this paper will be the cases that take into account the asymmetry. It is taken into account those asymmetry which is
coused by different structural elements stiffness in compression or tension, as well as the
geometric asymmetry. The appropriate mechanical and mathematical model is formed
using quadratic nonlinearities in the restoring force. It has been shown the exact
analytical solutions of nonlinear forced oscillations by using Jacobi elliptic functions, which is a new result in this field. Also it has be given the appropriate relationship with the linear theory. This work has an educational character too, as it aims to contribute to the greater application of elliptic functions in engineering. Today, the application of these functions greatly facilitated using a symbolic software. |
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| | Keywords: |
| | Non-linear oscillations, quadratic nonlinearities, forced oscillations, Jacobi elliptic function, transcritical bifurcation |
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