Gaetan Kerschen 
Modal Analysis of Nonlinear Mechanical Systems [PDF ebook] 

The book first introduces the concept of nonlinear normal modes (NNMs) and their two main definitions. The fundamental differences between classical linear normal modes (LNMs) and NNMs are explained and illustrated using simple examples. Different methods for computing NNMs from a mathematical model are presented. Both advanced analytical and numerical methods are described. Particular attention is devoted to the invariant manifold and normal form theories. The book also discusses nonlinear system identification.

Table of Content

Definition and fundamental properties of nonlinear normal modes.- Nonlinear normal modes and invariant manifolds.- Nonlinear normal modes and normal form theory.- Nonlinear normal modes in damped-forced systems.- Numerical computation of nonlinear normal modes.- Elements of nonlinear system identification of broad applicability.- Vibration absorption and acoustic mitigation.