Nonlinear Dynamics of Continuous Elastic Systems

1 Vibration of Plates and Shells with Added Masses.- 2 Rational Design of Plates and Shells.- 3 Order Reduction by Proper Orthogonal Decomposition (POD) Analysis.- 4 Analytic Modelling of Discreteness Effects in Continuous Systems.- 5 Continuous Systems with Non-smooth Nonlinearities.- References.

From the reviews:
"The authors put together a unique monograph on an interesting array of elastodyamic subjects. … The work is presented in the manner of a series of seminars. Thus it is very appealing to the professional who wishes to focus on the physics and macroscopic mathematics of the subject. An excellent list of references is provided for the interested reader to pursue the mathematical depth of the topic presented. … it is an excellent reference … in the field of elasto-dynamics to have on the shelf." (J. Genin, Zentralblatt MATH, Vol. 1064, 2005)

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.

Novel methodologies with direct applicability to challenging and often encountered problems of continuous mechanic systems New theoretical as well as numerical approaches for continuous elastic systems Special focus on non-homogeneous continua with complicated boundary conditions