Steady-state dynamic behavior of an on-board rotor under combined base motions

Abstract

To cite this version:M. Zaki Dakel, Sébastien Baguet, Régis Dufour. Steady-state dynamic behavior of an on-board rotor under combined base motions.. Journal of Vibration and Control, SAGE Publications, 2014, 20 (15) AbstractIn the transportation domain, on-board rotors in bending are subjected not only to rotating mass unbalance but also to several movements of their base. The main objective of this article is to predict the dynamic behavior of a rotor in the presence of base excitations. The proposed on-board rotor model is based on the Timoshenko beam finite element. It takes into account the effects corresponding to the rotary inertia, the gyroscopic inertia, the shear deformation of shaft as well as the geometric asymmetry of disk and/or shaft and considers six types of deterministic motions (rotations and translations) of the rotor rigid base. The use of Lagrange's equations associated with the finite element method yields the linear second-order differential equations of vibratory motion of the rotating rotor in bending relative to the moving rigid base which forms a non-inertial frame of reference. The linear equations of motion highlight periodic parametric terms due to the geometric asymmetry of the rotor components and time-varying parametric terms due to the rotational motions of the rotor rigid base. These parametric terms are considered as sources of internal excitation and can lead to lateral dynamic instability. In the presented applications, the rotor is excited by a rotating mass unbalance combined with constant rotation and sinusoidal translation of the base. Quasi-analytical and numerical solutions for two different rotor configurations (symmetric and asymmetric) are analyzed by means of stability charts, Campbell diagrams, steady-state responses as well as orbits of the rotor.

Nonlinear Dynamics of Marine Rotor System Coupled with Air Bag-Floating Raft Subjected to the Basement Excitations in Lateral Directions

“…Equation 10belongs to high-dimensional, strong constrained, and nonlinear nonautonomous problems with various parameters; generally, in order to facilitate calculation and solution for convenience. Equation (10) could be discussed on the state space, and hence the four second-order equations can be easily converted into eight first-order ones and the equation of motion governing the behavior of the mechanical isolation system can be written as equation (12).…”

“…For the strongly nonlinear differential equation (12), no analytical method exists, which is solved by applying the Runge-Kutta integration routine with a variable step in the present work. e calculation parameters of the system are as follows [24,25]: Table 1: e dimensionless expressions of the parameters.…”

“…Han and Chu acquired the parametric instability regions induced by the periodic base angular motions based on the discrete state transition matrix method [10,11]. Dakel et al investigated the dynamics of two different rotor configurations under various support motion through the numerical method [12]. Saeed and Kamel investigated the vibration control of a horizontally suspended Jeffcott-rotor system.…”

Preface

“…It is worth mentioning that there is a small number of contributions related to the analysis of rotors subjected to base excitations in the literature (Dakel;Baguet;Dufour, 2014).…”

Parametric resonance of shaft with variable slenderness ratio

“…In parametric instability analysis the instability chart or the so called the Strut-Ince diagram such as shown in Figure 1 [1] is sought to give the stable and unstable operating regions of the shaft for several modes of instability. Finite element method (FEM) has been used greatly in modelling the parametric instability behavior of shaft [2][3][4]. Beam theories have been applied to represent shaft as the effects of the lateral displacement, transverse shear displacement and gyroscopic are included in the formulation.…”