Modular methodology applied to the nonlinear modeling of a pipe conveying fluid
- 89 Downloads
This paper proposes an extension of a modular modeling approach, originally developed for lumped parameter systems, to the derivation of FEM-discretized equations of motion of one-dimensional distributed parameter systems. This methodology is characterized by the use of a recursive algorithm based on projection operators that allows any constraint condition to be enforced a posteriori. This leads to a modular approach in which a system can be conceived as the top member of a hierarchy in which the increase of complexity from one level to the parent one is associated to the enforcement of constraints. For lumped parameter systems this allows the implementation of modeling procedures starting from already known mathematical models of subsystems. In the case of distributed parameter systems, such a novel methodology not only allows to explore subsystem-based modeling strategies, but also makes it possible to propose formulations in which compatibility and boundary conditions can be enforced a posteriori. The benchmark chosen to explore these further possibilities is the classical problem of a cantilevered pipe conveying fluid. Taking a pipe made of a linear-elastic material, allowing geometric nonlinearities and assuming an internal plug-flow, a Hamiltonian derivation of FEM-discretized equations of motion is performed according to this novel approach. Numerical simulations are carried out to address the nonlinear model obtained.
KeywordsAnalytical mechanics Mathematical modeling Finite element method Modular modeling Pipe conveying fluid
Authors thank Dr. Guilherme Rosa Franzini and Prof. Luiz Bevilacqua for encouraging discussions. First author acknowledges the post-doctoral Grant #2016/09730-0, São Paulo Research Foundation (FAPESP). Second author acknowledges CNPq research Grant no. 308990/2014-5.
- 9.Kheiri M, Païdoussis MP (2014) On the use of generalized Hamiltons principle for the derivation of the equation of motion of a pipe conveying fluid. J Fluids Struct 50:18–24. https://doi.org/10.1016/j.jfluidstructs.2014.06.007 CrossRefGoogle Scholar
- 11.Orsino RMM (2016) A contribution on modeling methodologies for multibody systems. Ph.D. thesis, Universidade de São PauloGoogle Scholar
- 14.Orsino RMM, Pesce CP (2017a) Modular approach for the modeling and dynamic analysis of a pipe conveying fluid. In: 9th European nonlinear dynamics conference, ENOC 2017, Budapest, HungaryGoogle Scholar
- 15.Orsino RMM, Pesce CP (2017b) Novel modular modeling methodology applied to the problem of a pipe conveying fluid. In: XVII international symposium on dynamic problems of mechanics, DINAME 2017, São Sebastião, São Paulo, BrazilGoogle Scholar
- 16.Orsino RMM, Coutinho AG, Hess-Coelho TA (2016) Dynamic balancing of mechanisms and synthesizing of parallel robots SE-16. In: Zhang D, Wei B (eds) Dynamic modelling and control of balanced parallel mechanisms. Springer International Publishing, Switzerland. https://doi.org/10.1007/978-3-319-17683-3
- 17.Païdoussis MP (2014) Fluid–structure interactions: slender structures and axial flow, vol 1. Academic Press, Elsevier Science, LondonGoogle Scholar