2. Nonlinearities are considered in some system identification techniques.

There are many good standard textbooks on nonlinear vibrations. For the purpose of understanding and modeling
nonlinearities in structural dynamics, a few most recent books are introduced as follows: 

This is a very comprehensive and popular book reflecting the-state-of-the-art techniques and aimed at handling
nonlinearities in structural dynamics. Many practical issues are covered.
Nonlinearity in Structural Dynamics: Detection, Identification and Modelling
by K. Worden, G. R. Tomlinson
680 pages
Institute of Physics Pub, 2001
ISBN: 0750303565

This book is an intensive and extensive coverage on nonlinear system identification.
Nonlinear System Identification: From Classical Approaches to Neural Networks and Fuzzy Models
by Oliver Nelles
785 pages
Springer Verlag, 2000
ISBN: 3540673695

Nonlinear Ordinary Differential Equations: An Introduction to Dynamical Systems
(Oxford Applied and Engineering Mathematics) (3rd Edition)
by D.W. Jordan (Editor), Peter Smith
330 pages
Oxford University Press, 1999
ISBN: 0198565623

Nonlinear System Techniques and Applications  (2nd Edition)
by Julius S. Bendat
474 pages
Wiley-Interscience, 1998
ISBN: 047116576X

2.2. Journals –

Some key technical journals are listed below where you can find research on nonlinear vibrations, modeling
anelasticity and plasticity and identification of nonlinear including nonlinear hysteretic systems.

 ASCE Journal of Engineering Mechanics
There is a special issue on structural health monitoring:
Journal of Engineering Mechanics--July 2000, Volume 126, Issue 7, pp. 665-777
Special Topics Issue on Structural Health Monitoring

ASME Journal of Applied Mechanics
International Journal of Non-Linear Mechanics

2.3. Research Groups and Labs –

Dynamics Research Group at the University of Sheffield
Earthquake Engineering Research Laboratory, California Institute of Technology
Earthquake Engineering-Strong Motion Group, USC
LANL Structural Health Monitoring
Structural Dynamics Research Lab (UC-SDRL), University of Cincinnati
Smart Structures Technology Laboratory, UIUC

 2.4. Class Notes –

Classnotes 20-263-781: Non-Linear Vibrations
Structural Dynamics Research Laboratory, University of Cincinnati

2.5. People –

Some researchers whose work is related to identification and modeling of inelasticity and nonlinearities of systems
(especially structural systems) are listed below.

Douglas E. Adams
Joel P. Conte
Wilfred D. Iwan
Nicos Makris
Sami Masri
A.M. Reinhorn
Andrew Smyth
G R Tomlinson
Keith Worden