Awrejcewicz J., Krys’ko V., Vakakis A.F. Nonlinear Dynamics of Continuous Elastic Systems

Springer, 2004. — 341 p. — ISBN: 978-3-642-05810-3.This monograph is devoted to recent advances in nonlinear dynamics of continuous elastic systems. A major part of the book is dedicated to the analysis of non-homogeneous continua, e.g. plates and shells characterized by sudden changes in their thickness, possessing holes in their bodies or/and edges, made from different materials with diverse dynamical characteristics and complicated boundary conditions. New theoretical and numerical approaches for analyzing the dynamics of such continua are presented, such as the method of added masses and the method of proper orthogonal decomposition. The presented hybrid approach leads to results that cannot be obtained by other standard theories in the field. The demonstrated methods are illustrated by numerous examples of application.Vibration of Plates and Shells with Added Masses
Rational Design of Plates and Shells
Order Reduction by Proper Orthogonal Decomposition (POD) Analysis
Analytic Modelling of Discreteness Effects in Continuous Systems
Continuous Systems with Non-smooth Nonlinearities