Vibro-Impact Dynamics Modeling, Mapping and Applications

Studies of vibro-impact dynamics falls into three main categories: modeling, mapping and applications. This text covers the latest in those studies plus selected deterministic and stochastic applications. It includes a bibliography exceeding 1,100 references.

Vibro-impact dynamics has occupied a wide spectrum of studies by dynamicists, physicists, and mathematicians. These studies may be classified into three main categories: modeling, mapping and applications. The main techniques used in modeling of vibro-impact systems such as phenomenological modelings, Hertzian models, and non-smooth coordinate transformations developed by Zhuravlev and Ivanov are outlined. One of the most critical situations impeded in vibro-impact systems is the grazing bifurcation. Grazing bifurcation is usually studied through discontinuity mapping techniques, which are very useful to uncover the rich dynamics in the process of impact interaction. This book also considers selected deterministic and stochastic applications of vibro-impact dynamics which cover lumped and continuous systems. One of the most beneficial outcomes of vibro-impact dynamics is the development of impact dampers, which have witnessed significant activities over the last four decades and have been used in several applications. The book is supported by an extensive bibliography which exceeds 1,100 references.

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.