scholarly journals Nonlinear Vibration Analysis of Moving Strip with Inertial Boundary Condition

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Chong-yi Gao ◽  
Guo-jun Du ◽  
Yan Feng ◽  
Jian-xiong Li
Keyword(s):  
Nonlinear Vibration ◽  
Rolling Process ◽  
Vertical Vibration ◽  
Rotational Inertia ◽  
Longitudinal Motion ◽  
Euler Beam ◽  
Motion Equations ◽  
Moving Strip ◽  
Movement Mechanism ◽  
Axially Moving

According to the movement mechanism of strip and rollers in tandem mill, the strip between two stands was simplified to axially moving Euler beam and the rollers were simplified to the inertial component on the fixed axis rotation, namely, inertial boundary. Nonlinear vibration mechanical model of Euler beam with inertial boundary conditions was established. The transverse and longitudinal motion equations were derived based on Hamilton’s principle. Kantorovich averaging method was employed to discretize the motion equations and the inertial boundary equations, and the solutions were obtained using the modified iteration method. Depending on numerical calculation, the amplitude-frequency responses of Euler beam were determined. The axial velocity, tension, and rotational inertia have strong influences on the vibration characteristics. The results would provide an important theoretical reference to control and analyze the vertical vibration of moving strip in continuous rolling process.

Free, Periodic, Nonlinear Oscillation of an Axially Moving Strip

1969 ◽  
Vol 36 (1) ◽  
pp. 83-91 ◽  
Author(s):  
A. L. Thurman ◽  
C. D. Mote
Keyword(s):  
Equations Of Motion ◽  
Nonlinear Partial Differential Equations ◽  
Practical Interest ◽  
Limited Range ◽  
Fundamental Period ◽  
Transverse Motion ◽  
Longitudinal Motion ◽  
Moving Strip ◽  
Axially Moving ◽  
Linear Period

The free, nonlinear, fundamental period of transverse oscillation of axially moving strips (e.g., tapes, fibers, belts, and band saws) is determined by the approximate solution of two, coupled, nonlinear, partial differential equations. One equation describes longitudinal motion and the other transverse motion. A solution method is developed that permits accurate and efficient period calculations. The results indicate that the existence of the axial transport velocity reduces the fundamental period of oscillation and increases the relative importance of the nonlinear terms in the equations of motion. In many cases of practical interest the linear analysis is shown to be seriously in error and one may be led to erroneous conclusions because of its limited range of applicability. Curves are presented that assist one to estimate the accuracy of the linear period calculation.

Stability and vibration analysis of an axially moving thin walled conical shell

2021 ◽  
pp. 107754632199760
Author(s):  
Hossein Abolhassanpour ◽  
Faramarz Ashenai Ghasemi ◽  
Majid Shahgholi ◽  
Arash Mohamadi
Keyword(s):  
Natural Frequency ◽  
Conical Shell ◽  
Shell Theory ◽  
Cone Angle ◽  
Theory Of Elasticity ◽  
Lower Velocity ◽  
Motion Equations ◽  
Conical Shells ◽  
Divergence Instability ◽  
Axially Moving

This article deals with the analysis of free vibration of an axially moving truncated conical shell. Based on the classical linear theory of elasticity, Donnell shell theory assumptions, Hamilton principle, and Galerkin method, the motion equations of axially moving truncated conical shells are derived. Then, the perturbation method is used to obtain the natural frequency of the system. One of the most important and controversial results in studies of axially moving structures is the velocity detection of critical points. Therefore, the effect of velocity on the creation of divergence instability is investigated. The other important goal in this study is to investigate the effect of the cone angle. As a novelty, our study found that increasing or decreasing the cone angle also affects the critical velocity of the structure in addition to changing the natural frequency, meaning that with increasing the cone angle, the instability occurs at a lower velocity. Also, the effect of other parameters such as aspect ratio and mechanical properties on the frequency and instability points is investigated.

scholarly journals Nonlinear Vibration Analysis of Rotor considering Cogging and Harmonic Effects

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Shanle Li ◽  
Feng Liu ◽  
Hongyan Wang ◽  
Haijun Song ◽  
Kuilong Yu
Keyword(s):  
Nonlinear Vibration ◽  
Vibration Analysis ◽  
Magnetic Force ◽  
Rotor System ◽  
Kutta Method ◽  
Rotor Vibration ◽  
Motion Equations ◽  
Runge Kutta Method ◽  
Static Eccentricity ◽  
New Formula

This paper aims to investigate nonlinear vibration characteristics of rotor system considering cogging and harmonic effects. Firstly, relative permeance with eccentric was established and then corrected by correction factor caused by the cogging effect. Based on the new formula of relative permeance, the expression of unbalanced magnetic force was obtained, and the coefficient of cogging effect was defined. Motion equations of rotor system were established, and Runge–Kutta method was used to solve the equations. Results showed that errors between finite and analytical results were smaller considering cogging and harmonic effects. When the harmonics were taken into consideration, the vibration of rotor increases sharply. When the cogging and harmonics were taken into consideration simultaneously, the vibration of rotor decreased instead, which means that stator slots have the effect of reducing vibration in rotor system. Rotor vibration was axis symmetry with static eccentricity rather than central symmetry with no eccentricity, and double, four times, and six times supply frequency always existed in the components of main frequency with eccentric.

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