Vibration and Coupling of Continuous Systems : Asymptotic Methods

Real Problems Concerning Vibrations Of Elastic Structures Are Among The Most Fascinating Topics In Mathematical And Physical Research As Well As In Applications In The Engineering Sciences. This Book Addresses The Student Familiar With The Elementary Mechanics Of Continua Along With Specialists. The Authors Start With An Outline Of The Basic Methods And Lead The Reader To Research Problems Of Current Interest. An Exposition Of The Method Of Spectra, Asymptotic Methods And Perturbation Is Followed By Applications To Linear Problems Where Elastic Structures Are Coupled To Fluids In Bounded And Unbounded Domains, To Radiation Of Immersed Bodies, To Local Vibrations, To Thermal Effects And Many More. Contents: Classical Theory Of Vibration For Systems With Infinitely Many Degrees Of Freedom -- Some Classical Vibration Problems -- Elements Of Operator Theory -- Examples Of Nonstandard Vibrations And Coupling -- Spectral Perturbation -- Formal Perturbation Methods -- Perturbation Of Vibrating Systems -- The Helmholtz Equation In Unbounded Domains -- Scattering Problems Depending On A Parameter. Elastic Structure-fluid Interaction In Unbounded Domains -- References -- Index. Edited By J. Sanchez Hubert, E. Sanchez Palencia. Front Matter....Pages i-xv Classical Theory of Vibration for Systems with Infinitely Many Degrees of Freedom....Pages 1-26 Some Classical Vibration Problems....Pages 27-69 Elements of Operator Theory....Pages 70-126 Examples of Nonstandard Vibrations and Coupling....Pages 127-169 Spectral Perturbation....Pages 170-220 Formal Perturbation Methods....Pages 221-253 Perturbation of Vibrating Systems....Pages 254-321 The Helmholtz Equation in Unbounded Domains....Pages 322-375 Scattering Problems Depending on a Parameter. Elastic Structure-Fluid Interaction in Unbounded Domains....Pages 376-402 Back Matter....Pages 403-421