Introduction to Dynamics and Control in Mechanical Engineering Systems [Hardcover]

One of the first books to provide in-depth and systematic application of finite element methods to the field of stochastic structural dynamics
The parallel developments of the Finite Element Methods in the 1950s and the engineering applications of stochastic processes in the 1940s provided a combined numerical analysis tool for the studies of dynamics of structures and structural systems under random loadings. In the open literature, there are books on statistical dynamics of structures and books on structural dynamics with chapters dealing with random response analysis. However, a systematic treatment of stochastic structural dynamics applying the finite element methods seems to be lacking. Aimed at advanced and specialist levels, the author presents and illustrates analytical and direct integration methods for analyzing the statistics of the response of structures to stochastic loads. The analysis methods are based on structural models represented via the Finite Element Method. In addition to linear problems the text also addresses nonlinear problems and non-stationary random excitation with systems having large spatially stochastic property variations.

Series Preface xiii

Preface xv

Acknowledgments xvii

1 Introduction 1

1.1 Important Difference between Static and Dynamic Responses 1

1.2 Classification of Dynamic Systems 2

1.3 Applications of Control Theory 3

1.4 Organization of Presentation 4

References 5

2 Review of Laplace Transforms 7

2.1 Definition 8

2.2 First and Second Shifting Theorems 10

2.3 Dirac Delta Function (Unit Impulse Function) 10

2.4 Laplace Transforms of Derivatives and Integrals 11

2.5 Colk