# Modeling and analysis of nonlinear rotordynamics due to higher order deformations in bending

Shad, Rizwan and Michon, Guilhem and Berlioz, Alain Modeling and analysis of nonlinear rotordynamics due to higher order deformations in bending. (2011) Applied Mathematical Modelling, 35 (5). 2145-2159 . ISSN 0307-904X

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Official URL: http://dx.doi.org/10.1016/j.apm.2010.11.043

## Abstract

A mathematical model incorporating the higher order deformations in bending is devel- oped and analyzed to investigate the nonlinear dynamics of rotors. The rotor system con- sidered for the present work consists of a flexible shaft and a rigid disk. The shaft is modeled as a beam with a circular cross section and the Euler Bernoulli beam theory is applied with added effects such as rotary inertia, gyroscopic effect, higher order large deformations, rotor mass unbalance and dynamic axial force. The kinetic and strain (defor- mation) energies of the rotor system are derived and the Rayleigh–Ritz method is used to discretize these energy expressions. Hamilton’s principle is then applied to obtain the mathematical model consisting of second order coupled nonlinear differential equations of motion. In order to solve these equations and hence obtain the nonlinear dynamic response of the rotor system, the method of multiple scales is applied. Furthermore, this response is examined for different possible resonant conditions and resonant curves are plotted and discussed. It is concluded that nonlinearity due to higher order deformations significantly affects the dynamic behavior of the rotor system leading to resonant hard spring type curves. It is also observed that variations in the values of different parameters like mass unbalance and shaft diameter greatly influence dynamic response. These influences are also presented graphically and discussed.

Item Type: Article hal-01852902 International peer-reviewed journal Université de Toulouse > Ecole nationale supérieure des Mines d'Albi-Carmaux - IMT Mines Albi (FRANCE)Université de Toulouse > Institut National des Sciences Appliquées de Toulouse - INSA (FRANCE)Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE) Institut Clément Ader - ICA (Toulouse, France) - Modélisation des Systèmes et Microsystèmes Mécaniques - Comportement dynamique des structuresDépartement de Mécanique des Structures et Matériaux - DMSM (Toulouse, France) download Guilhem Michon 25 Aug 2011 11:51

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