scholarly journals Nonlinear dynamics of the ion Weibel-filamentation instability: An analytical model for the evolution of the plasma and spectral properties

2015 ◽  
Vol 22 (3) ◽  
pp. 032102 ◽  
Author(s):  
C. Ruyer ◽  
L. Gremillet ◽  
A. Debayle ◽  
G. Bonnaud
Keyword(s):  
Nonlinear Dynamics ◽  
Analytical Model ◽  
Spectral Properties ◽  
Filamentation Instability

Nonlinear Dynamics Behaviors of Ball Screws with Preload Considered

2012 ◽  
Vol 510 ◽  
pp. 304-309 ◽  
Author(s):  
Yong Jiang Chen ◽  
Wen Cheng Tang ◽  
Shi Gen Zhang
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Behavior ◽  
Analytical Model ◽  
Rotational Speed ◽  
Nonlinear Dynamic ◽  
Hertzian Contact ◽  
Ball Screw ◽  
Contact Deformation ◽  
Rolling Element ◽  
Equations Of Motions

In order to improve the vibration problem arise when rotational speed of a ball screw is increased, an analytical model is proposed to study the nonlinear dynamic behavior of the ball screw with preload considered. The contact force of each rolling element described according to nonlinear Hertzian contact deformation and the re-circulating mechanism has been taken in to account. A end-type ball screw is selected as an example, the methods of Runge-Kutta-fehlberg is used to solve the equations of motions numerically. It was found that the preload can be useful in controlling the vibration of the system,but the inhibit effect is not proportional to it,in the light of different type of ball screw, corresponding prevention preload is recommended.

Analysis of Reversal Behavior for an Automobile Wiper Blade

2007 ◽  
Author(s):  
Yuki Takebe ◽  
Masatsugu Yoshizawa ◽  
Tuneo Akuto ◽  
Takeshi Yoda ◽  
Katuya Kamiyama
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Simulation ◽  
Dynamic Behavior ◽  
Analytical Model ◽  
Nonlinear Equations ◽  
Degree Of Freedom ◽  
Mass System ◽  
The Real ◽  
Dynamic Motion

The development of a numerical simulation has been demanded for improving the automobile wiper systems from the industrial viewpoints. It is widely known that, however, vibrations caused by the wiping motion cause a trouble of wiping. Several studies have been carried out to investigate the dynamic behavior of the wiper systems. However, the phenomena have not yet been theoretically analyzed. The purpose of this research is to develop a numerical simulation of the reversal behavior of a wiper blade. To begin with, the experiment was conducted with the real wiper systems to observe the reversal behavior of the wiper blade. After observing its motion, an analytical model was developed to essentially characterize the wiper systems. The model is composed of a multi-degree-of-freedom spring-mass system with restraint conditions to ensure the contact between a blade and a wind-shield at all time. The dynamic motion and the mechanism of the reversal behavior of the wiper blade were investigated by using nonlinear equations. Furthermore, the above phenomena were discussed using the nonlinear equations of the vibration of the wiper blade from the viewpoint of the nonlinear dynamics.

scholarly journals Spectral Properties of Circular Piezoelectric Unimorphs

2017 ◽  
Vol 42 (4) ◽  
pp. 743-751
Author(s):  
Martin Pustka ◽  
Ladislav Půst
Keyword(s):  
Analytical Model ◽  
Spectral Properties ◽  
Closed Form Solution ◽  
Wide Frequency Range ◽  
Calculation Model ◽  
Form Solution ◽  
Mode Shapes ◽  
Vibration Velocity ◽  
Design Work ◽  
Resonant Frequencies

Abstract The piezoelectric unimorphs are essential resonant components of many oscillating systems including electroacoustic devices. The unimorph spectral properties are namely dependent on geometric dimensions, applied materials and mounting. Preliminary dimensioning and optimization of unimorph shape are usually carried out prior to comprehensive design work mostly based on finite element method. Simple analytical model is a suitable tool for initial design phase. This paper presents a derivation of calculation model describing natural vibrations of a circular unimorph with the piezoelectric layer diameter smaller than the elastic layer diameter. The system of equations with closed-form solution is instrumental to calculation of resonant frequencies and mode shapes for unimorphs with clamped, simply supported and free circumference. The theoretical results are compared with vibration velocity measurement of clamped unimorph sample in a wide frequency range. Analytical model derived in this paper is used to assess the effect of the thickness tolerance on unimorph resonant frequencies.

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