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 SM ISO690:2012BANICHUK, Nikolay, BARSUK, Alexander A., JERONEN, J., TUOVINEN, Tero, NEITTAANMAKI, Pekka. Nonconservative Systems with a Finite Number of Degrees of Freedom. Dusseldorf: 2020, pp. 69-144. ISSN 09250042DOI: 10.1007/978-3-030-23803-2_3 |
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 Solid Mechanics and its Applications | ||||||
| 2020 | ||||||
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| DOI:https://doi.org/10.1007/978-3-030-23803-2_3 | ||||||
| Pag. 69-144 | ||||||
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In this chapter we present some results on the stability and bifurcations of the systems with a finite number of degrees of freedom. We consider damping-induced destabilization in nonconservative systems. We start with a general theoretical treatment of the topic. As the model problem, we consider the double pendulum subject to both a follower force and gravitational loading. A special case of interest is treated with the theoretical framework. The chapter finishes with a thorough presentation and analysis of the model problem including the nonlinear dynamics, quasistatic equilibrium paths and their stability, and special cases of interest. In numerical examples, we show equilibrium paths and trajectory density visualizations of the time evolution of the nonlinear system. Sample-based uncertainty quantification is employed to capture both branches of a bifurcation in the same visualization. |
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