Abstract
A mathematical model incorporating higher order deformation in bending is developed to investigate the nonlinear behavior of rotor. Transverse harmonic base excitation is imparted to rotor system and Euler-Bernoulli beam theorem is applied with effects such as rotary inertia, gyroscopic effect, higher order large deformations, rotor mass unbalance and dynamic axial force. Discretization of the kinetic and strain (deformation) energies of the rotor system is done using the Rayleigh–Ritz method. Second order coupled nonlinear differential equations of motion are obtained using Hamilton’s principle. Nonlinear dynamic response of the rotor system is obtained by solving above equations using the method of multiple scales. This response is examined for resonant condition. It is concluded that nonlinearity due to higher order deformations and variations in the values of different parameters like mass unbalance and shaft diameter significantly affects the dynamic behavior of the rotor system. It is also observed that the external harmonic excitation greatly affects the dynamic response.
Highlights
Rotating machinery [1,2,3] such as steam turbines, gas turbines, internal combustion engines, and electric motors, are the most widely used elements in mechanical systems
The prediction and analysis of the dynamic behavior of rotor system are crucial because their rotating components possess unlimited amounts of energy that can be transformed into vibrations
Nonlinear dynamic response of the rotor system is obtained by solving above equations using the method of multiple scales
Summary
Rotating machinery [1,2,3] such as steam turbines, gas turbines, internal combustion engines, and electric motors, are the most widely used elements in mechanical systems. The analysis of the nonlinear effects in rotorbearing systems is extremely difficult and there are a few analytical procedures that will generate valid results over a wide range of parameters. The perturbation methods [5] are a collection of techniques that can be used to simplify, and to solve, a wide variety of mathematical problems, involving small or large parameters. The method of multiple scales [5] is applied is used to solve this model including nonlinear terms. The results of perturbation method are validated with numerical simulations
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