Nonlinear Dynamic Analysis of a Rotor Shaft System With Viscoelastically Supported Bearings

2003 ◽  
Vol 125 (3) ◽  
pp. 290-298 ◽  
Author(s):  
Nabeel Shabaneh ◽  
Jean W. Zu
Keyword(s):  
Dynamic Analysis ◽  
Multiple Scales ◽  
Perturbation Expansion ◽  
Nonlinear Dynamic Analysis ◽  
Primary Resonance ◽  
Rotor Shaft ◽  
Model Free ◽  
Shaft System ◽  
Nonlinear Elastic ◽  
Elastic Characteristics

This research investigates the dynamic analysis of a single-rotor shaft system with nonlinear elastic bearings at the ends mounted on viscoelastic suspension. Timoshenko shaft model is utilized to incorporate the flexibility of the shaft; the rotor is considered to be rigid and located at the mid-span of the shaft. A nonlinear bearing pedestal model is assumed which has a cubic nonlinear spring and linear damping characteristics. The viscoelastic supports are modeled using Kelvin-Voigt model. Free and forced vibration is investigated based on the direct multiple scales method of one-to-one frequency-to-amplitude relationship using third order perturbation expansion. The results of the nonlinear analysis show that a limiting value of the internal damping coefficient of the shaft exists where the trend of the frequency-response curve switches. Also, the primary resonance peak shifts to higher frequencies with the increase of the bearing nonlinear elastic characteristics, but with a flattened curve and hence lower peak values. A jump phenomenon takes place for high values of the bearing nonlinear elastic characteristics.

Nonlinear Free Vibration of a Rotor Shaft System With Viscoelastically Supported Bearings

2003 ◽  
Author(s):  
N. Shabaneh ◽  
J. W. Zu
Keyword(s):  
Free Vibration ◽  
Multiple Scales ◽  
Perturbation Expansion ◽  
Third Order ◽  
Rotor Shaft ◽  
Model Free ◽  
Damping Characteristics ◽  
Shaft System ◽  
Linear Damping ◽  
Nonlinear Elastic

This paper investigates the dynamic analysis of a single-rotor shaft system with nonlinear elastic bearings at the ends mounted on viscoelastic suspension. A Timoshenko shaft model is utilized to incorporate the flexibility of the shaft; the rotor is considered to be rigid and located at the mid-span of the shaft. A nonlinear bearing pedestal model is assumed which has a cubic nonlinear spring and linear damping characteristics. The viscoelastic supports are modeled using the Kelvin-Voigt model. Free vibration is investigated based on the direct multiple scales method of one-to-one frequency-to-amplitude relationship using third order perturbation expansion. The results of the nonlinear analysis show that a limiting value of the internal damping coefficient of the shaft exists where the trend of the frequency-response curve switches.

On the Vibration of a Rotor-Shaft System With Viscoelastically Supported Bearings

2003 ◽  
Author(s):  
N. Shabaneh
Keyword(s):  
Nonlinear System ◽  
Linear System ◽  
Vibration Analysis ◽  
Perturbation Expansion ◽  
Free Vibration Analysis ◽  
Rotating Shaft ◽  
Rotor Shaft ◽  
Model Free ◽  
Shaft System ◽  
Nonlinear Elastic

This paper investigates the dynamic behaviour of a single rotor-shaft system with nonlinear elastic bearings at the ends mounted on viscoelastic suspensions. A Timoshenko shaft model is utilized to incororate the flexibility of the shaft; the rotor is considered to be rigig and located at the mid-span of the shaft. A nonlinear bearing pedestal model is assumed which has a cubic nonlinear spring and linear damping characteristics. The viscoelastic supports of the bearings are modeled as Kelvin-Voigt model. Free vibration analysis is performed on the linear system including the damping of the bearings. Forced vibration analysis is performed on the nonlinear system. Equations of motion are derived for the nonlinear system based on the direct multiple scale method of one-to-one frequency-to-amplitude relationship using third order perturbation expansion. The effects of stiffness and loss coefficients of the viscoelastic supports on the complex natural frequencies are identified for the linear system. The results show that optimum values of the viscoelastic stiffness and loss coefficient can be achieved for a specific rotating shaft system to reduce vibrations and increase the operating regions. In addition, the frequency response of the nonlinear system indicates that a jump phenomenon takes place for high values of the bearing nonlinear elastic coefficient.

scholarly journals Nonlinear Dynamic Analysis of the Cutting Process of a Nonextensible Composite Boring Bar

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Bole Ma ◽  
Yongsheng Ren
Keyword(s):  
Differential Equation ◽  
Dynamic Analysis ◽  
Cutting Force ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Analysis ◽  
Primary Resonance ◽  
Cutting Process ◽  
Cutting Depth ◽  
Resonance Curves ◽  
Cutting System

A nonlinear dynamic analysis of the cutting process of a nonextensible composite cutting bar is presented. The cutting bar is simplified as a cantilever with plane bending. The nonlinearity is mainly originated from the nonextensible assumption, and the material of cutting bar is assumed to be viscoelastic composite, which is described by the Kelvin–Voigt equation. The motion equation of nonlinear chatter of the cutting system is derived based on the Hamilton principle. The partial differential equation of motion is discretized using the Galerkin method to obtain a 1-dof nonlinear ordinary differential equation in a generalized coordinate system. The steady forced response of the cutting system under periodically varying cutting force is approximately solved by the multiscale method. Meanwhile, the effects of parameters such as the geometry of the cutting bar (including length and diameter), damping, the cutting coefficient, the cutting depth, the number of the cutting teeth, the amplitude of the cutting force, and the ply angle on nonlinear lobes and primary resonance curves during the cutting process are investigated using numerical calculations. The results demonstrate that the critical cutting depth is inversely proportional to the aspect ratio of the cutting bar and the cutting force coefficient. Meanwhile, the chatter stability in the milling process can be significantly enhanced by increasing the structural damping. The peak of the primary resonance curve is bent toward the right side. Due to the cubic nonlinearity in the cutting system, primary resonance curves show the characteristics of typical Duffing’s vibrator with hard spring, and jump and multivalue regions appear.

A New Approach to the Rigid Finite Element Method in Modeling Spatial Slender Systems

2018 ◽  
Vol 18 (02) ◽  
pp. 1850017 ◽  
Author(s):  
Iwona Adamiec-Wójcik ◽  
Łukasz Drąg ◽  
Stanisław Wojciech
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Nonlinear Dynamic Analysis ◽  
New Approach ◽  
Static And Dynamic Analysis ◽  
Rigid Finite Element Method ◽  
Longitudinal Flexibility ◽  
Element Method

The static and dynamic analysis of slender systems, which in this paper comprise lines and flexible links of manipulators, requires large deformations to be taken into consideration. This paper presents a modification of the rigid finite element method which enables modeling of such systems to include bending, torsional and longitudinal flexibility. In the formulation used, the elements into which the link is divided have seven DOFs. These describe the position of a chosen point, the extension of the element, and its orientation by means of the Euler angles Z[Formula: see text]Y[Formula: see text]X[Formula: see text]. Elements are connected by means of geometrical constraint equations. A compact algorithm for formulating and integrating the equations of motion is given. Models and programs are verified by comparing the results to those obtained by analytical solution and those from the finite element method. Finally, they are used to solve a benchmark problem encountered in nonlinear dynamic analysis of multibody systems.

Modeling and nonlinear dynamic analysis of cable-supported bridge with inclined main cables

2018 ◽  
Vol 156 ◽  
pp. 351-362 ◽  
Author(s):  
Yi Hui ◽  
Hou Jun Kang ◽  
Siu Seong Law ◽  
Zheng Qing Chen
Keyword(s):  
Dynamic Analysis ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Analysis ◽  
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