Vibro-Impact Dynamics: Modeling, Mapping and Applications

By Raouf A. Ibrahim

Book Overview

Vibro-impact dynamics has occupied a wide spectrum of studies by dyn- icists, physicists, and mathematicians. These studies may be classi'ed into three main categories: modeling, mapping and applications. The main te- niques used in modeling of vibro-impact systems include phenomenological modelings, Hertzian models, and non-smooth coordinate transformations- velopedbyZhuravlevandIvanov. Oneofthemostcriticalsituationsimpeded invibro-impactsystemsisthegrazingbifurcation. Grazingbifurcationisu- ally studied through discontinuity mapping techniques, which are very useful to uncover the rich dynamics in the process of impact interaction. Note the availablemappings arevalidonly intheabsenceofnon-impactnonlinearities. Complex dynamic phenomena of vibro-impact systems include subharmonic oscillations, chaotic motion, and coexistence of di'erent attractors for the sameexcitationand systemparametersbut under di'erent initial conditions. Selectedapplicationsofvibro-impactdynamics. Theseincludelumpedand continuous systems. Lumped systems cover a bouncing ball on an oscillating barrier, mass-spring-dashpot systems, normal and inverted pendulums, the spherical pendulum, the ship roll motion against icebergs, joints with fr- play, rotor-stator rubbing in rotating machinery, vocal folds, microactuators, strings, beams, pipes conveying ?uids with end-restraints, nuclear reactors and heat exchangers, and plates. These applications are discussed within the framework of the deterministic theory. Under random excitation the tre- ment requires special tools. The techniques of equivalent linearization and stochastic averaging have been applied to limited number of problems. One of the most bene'cial outcomesof vibro-impact dynamics is the development of impact dampers, which have witnessed signi'cant activities over the last four decades and have been used in several applications. On the other hand, vibro-impacthas detrimental e'ects on the operationsof mechanicalsystems and damage of pipes and rods in nuclear reactors.

• Format: Paperback
• Language: English
• ISBN: 364210133X
• ISBN13: 9783642101335
• Release Date: October 2010
• Publisher: Springer
• Length: 298 Pages
• Weight: 0.97 lbs.
• Dimensions: 0.7" x 6.1" x 9.2"