Nonlinear vibration with control. For flexible and adaptive structures
This book covers nonlinear vibrations of elastics structures, beams, plates, shells and cables. It provides relevant control techniques for elastic and adaptive structures. The present second edition is updated to include some recent developments in control such as switching and continuous schemes (for the review of the 1st edition see [(2010; Zbl 1180.74004)]). Approximate analytic techniques such as perturbation methods are complemented by adding a normal transformation method for weakly nonlinear vibrations. The book essentially consists of two parts. The first part (Chapters 1--5) deals with basic topics in nonlinear vibrations, control of nonlinear vibrations (Chapters 1--3) and approximate methods such as perturbation methods and normal form transformations. In the second part (Chapters 6--8), small deflection equations and nonlinear equations for beams, cables, plates and shells are presented. A selection of control problems arising from nonlinear vibrations of these structures are studied. Some adaptive structure applications are also presented. Selected examples and problems are inserted at places, however, more exercises could have been added to the reader's benefit. In any case, the present book is a good source of material for a graduate course in this area. It may also serve as a useful reference for researchers working in control theory of nonlinear vibrations.
scientific article; zbMATH DE number 6382714