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.

Angelo Luongo is a professor (retired) of Solid and Structural Mechanics at L'Aquila University, Italy. He currently serves as an editor-in-chief of MDPI journal "CivilEng" and associate editor of Springer Journal "Nonlinear Dynamics." His research interests include linear and nonlinear dynamics, buckling and postbuckling, aeroelasticity, dynamic instability, perturbation methods, structural modeling. With Springer, he published the textbooks Stability and Bifurcation of Structures (2023) and Perturbation Methods and Nonlinear Phenomena (2024). Achille Paolone is a professor of Structural Mechanics at Sapienza University of Rome, Italy. His research interests include structural dynamics, computational mechanics, structural identification and monitoring, seismic engineering, structural stability, and earthquake resistant structures. His extensive practical experience in structural engineering informs his teaching approach, connecting theoretical concepts to real-world applications. Simona Di Nino holds a Ph.D. in Mathematics and Modeling and is currently an assistant professor of Solid and Structural Mechanics at the University of L'Aquila, Italy. Her research interests encompass linear and nonlinear dynamics, aeroelasticity, dynamic instability, perturbation methods, homogenization methods, masonry, and damage constitutive models. In 2023, she published the textbook Stability and Bifurcation of Structures with Springer.

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