Kerschen G. Modal Analysis of Nonlinear Mechanical Systems 2014

Textbook in PDF format

This book contains lecture material from CISM course on Modal Analysis of Nonlinear Mechanical Systems, delivered in June 25-29, 2012.
The concept of normal modes is central in the theory of linear vibrating systems. Besides their obvious physical interpretation, the linear normal modes (LNMs) have interesting mathematical properties.
LNMs are therefore exploited routinely for various purposes including experimental modal analysis, model reduction and structural health monitoring. Clearly, nonlinearity is a frequent occurrence in engineering applications and can take its origin from different sources including contact, friction and large displacements. This is why the concept of nonlinear normal modes (NNMs) was introduced in the 1960s by Rosenberg. The course gives a complete and thorough overview of NNMs, going from their definition and fundamental properties to their applications in structural dynamics, which include model reduction, system identification and acoustic and vibration mitigation.
Definition and fundamental properties of nonlinear normal modes
Invariant manifold representations of nonlinear modes of vibrations
Normal form theory and nonlinear normal modes: theoretical settings and applications
Nonlinear normal modes in damped - forced systems
Computation of nonlinear normal modes through shooting and pseudo-arclength continuation
Numerical computation of nonlinear normal modes using HBM and ANM
Elements of nonlinear system identification of broad applicability
Acoustic mitigation