Analytical approach to dynamic and vibration analysis of a spherical ball under contact stress

Aram, A ; Sharif University of Technology | 2011

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  1. Type of Document: Article
  2. DOI: 10.1016/j.scient.2011.11.022
  3. Publisher: 2011
  4. Abstract:
  5. This paper presents a nonlinear model to illustrate the effect of contact stress in the vibration behavior of mechanical components, especially rotating systems. The problem is considered in the case of the vertical vibration of a sphere on a plate. The Hertzian contact theory is used to obtain the relationship between contact force and the deflection of the mass center of the sphere. Modeling the system by a mass and a nonlinear spring, the vibration equation of the mass center of the sphere is derived. The method of LindstedtPoincar is implemented to solve the equation of motion, and obtain vibration characteristics under a compressive preload. The dependency of frequency on several parameters, such as initial applied force, initial amplitude of oscillation and the diameter of the sphere, is distinguished. Results show that increasing the initial applied force or the diameter of the ball raises the frequency, while increasing oscillation amplitude has an inverse effect. Finally, the accuracy and convergence of the solution are illustrated by comparison between different orders of approximation. Also, results are in good agreement with those extracted from numerical modeling
  6. Keywords:
  7. Nonlinear vibration ; The LindstedtPoincar method ; Amplitude of oscillation ; Analytical approach ; Contact Stress ; Different order ; Equation of motion ; Hertzian-contact theory ; Mass centers ; Mechanical components ; Non-linear model ; Non-linear vibrations ; Nonlinear springs ; Numerical modeling ; Oscillation amplitude ; Preloads ; Rotating systems ; Vertical vibrations ; Vibration behavior ; Vibration characteristics ; Vibration equations ; Dynamic mechanical analysis ; Equations of motion ; Mathematical models ; Nonlinear equations ; Spheres ; Stresses ; Vibration analysis ; Accuracy assessment ; Continuum mechanics ; Diameter ; Dynamic analysis ; Mathematical theory ; numerical model ; Parameterization ; Perturbation ; Preloading ; Rotation ; Sphere ; Stress analysis ; Vibration
  8. Source: Scientia Iranica ; Volume 18, Issue 6 , 2011 , Pages 1306-1312 ; 10263098 (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S1026309811002276