Stochastic Structural Dynamics




Preface

Stochastic structural dynamics is concerned with the studies of dynamics of

structures and structural systems that are subjected to complex excitations treated

as random processes. In engineering practice, many structures and structural

systems cannot be dealt with analytically and therefore the versatile numerical

analysis techniques, the finite element methods (FEM) are employed.

The parallel developments of the FEM in the 1950's and the engineering

applications of stochastic processes in the 1940's 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 chapter(s) dealing

with random response analysis. However, a systematic treatment of stochastic

structural dynamics applying the FEM seems to be lacking. The present book is

believed to be the first relatively in-depth and systematic treatment on the subject.

It is aimed at advanced and specialist level. It is suitable for classes taken by

master’s degree level post-graduate students and specialists.


The present book has seven chapters and ten appendices. Chapter 1

introduces the displacement-based FEM, element equations of motion for

temporally and spatially stochastic systems, hybrid stress-based element equations

of motion, incremental variational principle and mixed formulation-based

nonlinear element matrices, constitutive relations and updating of configurations

and stresses.

Chapter 2 is concerned with the spectral analysis and response statistics of

linear structural systems. It includes evolutionary spectral analysis, evolutionary

spectra of engineering structures, modal analysis and time-dependent response

statistics, and response statistics of engineering structures.


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