Dynamics of Large Structures and Inverse Problems [Hardcover]

This book deals with the various aspects of stochastic dynamics, the resolution of large mechanical systems, and inverse problems. It integrates the most recent ideas from research and industry in the field of stochastic dynamics and optimization in structural mechanics over 11 chapters. These chapters provide an update on the various tools for dealing with uncertainties, stochastic dynamics, reliability and optimization of systems. The optimizationreliability coupling in structures dynamics is approached in order to take into account the uncertainties in the modeling and the resolution of the problems encountered.

Accompanied by detailed examples of uncertainties, optimization, reliability, and model reduction, this book presents the newest design tools. It is intended for students and engineers and is a valuable support for practicing engineers and teacher-researchers.

Preface xi

Chapter 1 Introduction to Inverse Methods 1

1.1 Introduction 1

1.2 Identification methods 3

1.3 Identification of the strain hardening law 6

1.3.1 Example of an application 8

1.3.2 Validation test 9

1.3.3 Hydroforming a welded tube 11

Chapter 2 Linear Differential Equation Systems of the First Order with Constant Coefficients: Application in Mechanical Engineering 15

2.1 Introduction 15

2.2 Modeling dissipative systems 15

2.2.1 Intrinsic solutions of autonomous systems 17

2.2.2 Intrinsic solutions 17

2.2.3 Intrinsic solutions of the adjoining system 19

2.2.4 Relation between the intrinsic solutions of s and s* 19

2.2.5 Relation between modal matrices X and X* 20

2.3 Autonomous system general solution 21