Vibration and Damping in Distributed Systems, Volume I provides a comprehensive account of the mathematical study and self-contained analysis of vibration and damping in systems governed by partial differential equations. The book presents partial differential equations techniques for the mathematical study of this subject. A special objective of establishing the stability theory to treat many distributed vibration models containing damping is discussed. It presents the theory and methods of functional analysis, energy identities, and strongly continuous and holomorphic semigroups. Many mechanical designs are illustrated to provide concrete examples of damping devices. Numerical examples are also included to confirm the strong agreements between the theoretical estimates and numerical computations of damping rates of eigenmodes.
Table of Contents
Volume 1, Vibration, Wave Propagation and Damping in one Space Dimension; Functional Analysis' Distributions, Sobolev Spaces and Boundary Value Problems; Strongly Continuous Semigroups of Evolution; Asyptotic Stability and Exponential Decay of Energy; The Method of Energy Identities, Holomorphic Semigroups Corresponding to Structures with Strong Damping. Volume 2, WKB and Wave Methods, Visualization and Experimentation; The WKB Method for Eigenvalue Problems I, II; Miscellaneous Methods; Visualization; Remarks on experimental Determination of Modal Damping Rates in Elastic Beams.
Goong Chen (Texas A&M University, College Station, USA) (Author) , Jianxin Zhou (Texas A & M University, College Station, Texas, USA) (Author)