Vibration and Coupling of Continuous Systems Asymptotic Methods [Paperback]

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.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.I Classical Theory of Vibration for Systems with Infinitely Many Degrees of Freedom.- 1. Introduction.- 2. Elements of Vibration Theory for Systems with n Degrees of Freedom.- 3. Infinite-Dimensional Separable Hilbert Spaces.- 4. A Class of Compact Self-Adjoint Operators.- 5. Introduction of the Spaces V and H Associated with the Elastic and Kinetic Energies.- 6. The Standard Vibration Problem for a System with Discrete Spectrum.- 7. Variational Properties of Eigenvalues. Rayleigh Principle. Minimax Principle and Comparison Theorem.- II Some Classical Vibration Problems.- 1. IntroduclÁ