Perturbation Methods and Nonlinear Phenomena: Synthesis Lectures on Engineering, Science, and Technology

Introduction.- Conservative static systems.- Non-autonomous dynamical systems.- Autonomous nonconservative dynamical systems.- Nonlinear continuum models.- Perturbation methods for a continuum metamodel.- Solved Problems.- Summary.

Dr. Angelo Luongo is Professor of Solid and Structural Mechanics - Department of Civil, Construction-Architectural and Environmental Engineering – Univ. of L’Aquila, Italy.
Dr. Daniele Zulli is Professor of Solid and Structural Mechanics - Department of Civil, Construction-Architectural and Environmental Engineering – Univ. of L’Aquila, Italy.
Dr. Manuel Ferretti is Associate Professor of Solid and Structural Mechanics - Department of Civil, Construction-Architectural and Environmental Engineering – Univ. of L’Aquila, Italy.
Dr. Francesco D’Annibale is Professor of Solid and Structural Mechanics - Department of Civil, Construction-Architectural and Environmental Engineering – Univ. of L’Aquila, Italy.

This concise text introduces the reader to the use of perturbation methods, able to investigate nonlinear phenomena in continuous (not only discrete) mechanical systems. Distinct from the classic books on perturbation methods, the algorithms are directly illustrated for continuous systems, referring to a very simple case-study as well as to a metamodel, for which Statics, Buckling, Dynamics and Bifurcation behavior are quickly analyzed. Moreover, fundamental mechanical aspects are discussed in dealing with applications. Concepts herein are reinforced with worked examples at the end the book, relevant to several continuous systems.

Illustrates perturbation analysis with straightforward simple examples, able to reveal nonlinear mechanical phenomena Emphasizes computations and concepts of bifurcation analysis and nonlinear dynamics, giving insights on the phenomena Discusses perturbation methods as a straightforward expansion, strained parameter method, and the multiple scale method