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Modal Analysis of Nonlinear Mechanical Systems is written by Gaetan Kerschen and published by Springer. It's available with International Standard Book Number or ISBN identification 3709117917 (ISBN 10) and 9783709117910 (ISBN 13).
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.