Nonlinear Dynamics of Rotors due to Large Deformations and Shear Effects

Abstract:

An analysis of linear and nonlinear dynamics of rotors is presented taking into account the shear effects. The nonlinearity arises due to the consideration of large deformations in bending. The rotor system studied is composed of a rigid disk and a circular shaft. In order to study the combined effect of rotary inertia and shear effects the shaft is modeled as a Timoshenko beam of circular cross section. A mathematical model is developed consisting of 4th order coupled nonlinear differential equations of motion. Method of multiple scales is used to solve these nonlinear equations. Linear and nonlinear dynamic behavior is studied numerically for different values of slenderness ratio r. Resonant curves are plotted for the nonlinear analysis. Due to nonlinearity these curves are of hard spring type. This spring hardening effect is more visible for lower values of r. Also the nonlinear response amplitude is higher when shear deformations are taken into account.

• Periodical: Applied Mechanics and Materials (Volumes 110-116)
• Pages: 3593-3599
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.110-116.3593
• Online since: October 2011
• Authors: Muhammad Rizwan Shad, Guilhem Michon, Alain Berlioz
• Keywords: Large Deformations, Method of Multiple Scales, Nonlinear Dynamics, Rotors, Shear Effects, Timoshenko Beam

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