Nonlinear dynamic analysis of the response to the excitation forces of a symmetrical on-board rotor mounted on hydrodynamic bearings using h-p finite elements method

Abstract

This work aims to study the nonlinear dynamic analysis response of the external excitation forces of an on-board rotor with a mobile non-deformable supports, mounted on hydrodynamic bearings. The modeling of the structure is achieved by the hierarchical polynomial (h-p) version of the finite element method. A theoretical study based on the Euler–Bernoulli beam model made for the establishment of the kinetic energy and the strain energy of the shaft. The Reynolds equation used to determine the hydrodynamic forces of the plain bearings. The motion equations of rotor system are determined by the Lagrange method. Linear results are obtained using the implicit time-step integration scheme of Newmark, and nonlinear results obtained with a complex resolution algorithm combining Newton–Raphson's iterative incremental procedure with the Newmark temporal integration scheme. The calculation steps for the nonlinear analysis of the onboard rotor system dynamic behavior are grouped together in an application created using the MATLAB programming language, and validated with work done previously by the classical version of the finite element method. In this article, we make some examples to study the influence of the excitations of the mobile support on the behavior of the rotor and the hydrodynamic bearings.

Keywords:

• Rotor’s dynamics
• h-p finite element version
• on-board rotor
• finite element methods
• hydrodynamic bearings
• support excitation
• nonlinear analysis

Acknowledgments

We acknowledge with grateful thanks the support by the Laboratory of Mechanical and Material Systems Engineering, as well as the General Directorate of Scientific Research and Technological Development of the Ministry of Higher Education of Algeria. We also want to thank the effort made by the Mechanics Based Design of Structures and Machines journal team, and the reviewers.