This work constitutes an excellent textbook which not only reveals and conveys an interesting and complex subject to eager students and demanding researchers but is also a valuable source of information for practitioners in industry. It emanates from the last volume of the three-volume work of the authors, under the general title 'Die Methode der finiten Elemente in der elementaren Strukturmechanik' [l-3] which was first published in 1986688. The first two volumes of the series comprise the linear and nonlinear theory of structures, respectively, while the third volume is dedicated to the field of computational structural dynamics. The present volume is an upgraded version of Volume III of the series where its contents are presented with a fresh perspective and in a more elaborate way. It includes a great number of significant clarifications, corrections, modifications and extensions.
This book contains an overview of the relevant activities pursued for more than 35 years in the Department of Aeronautics at Imperial College and in the former ISD and its successor ICA institute at the University of Stuttgart. The authors have succeeded in giving a systematic description of the analysis of the dynamic process in complex structures on the basis of their computer-oriented research and their experience in the solution of engineering problems. The theoretical principles have been revisited and universalized decisively in a form ideally suited for computer implementation and have been presented in a physically attractive form avoiding unnecessary theoretical abstractions.
The book has a length of 800 pages and consists of 13 chapters, starting from number 14 since they are considered to be continuation to the chapters of the previous two volumes of the series [1,2]. Chapter 14 gives an elementary account to single-degree-of-freedom linear oscillators and is intended to act as an introduction to subsequent extensive discussions of computational techniques in the dynamics of deformable solid bodies. In Chapter 15 some important basic equations and the principle of virtual work are re-examined in view of the additional temporal dimension arising in dynamics. The principle of virtual displacements is extended to dynamics starting from Newton's law and the system of ordinary differential equations is obtained by applying a partial discretization restricted to space. Chapter 16 discusses linear dynamics using the finite element theory to produce mass matrices for some element types. A general method for the computation of kinematically equivalent mass matrices is presented and exemplified on truss, beam, triangular membrane and tetrahedron elements.
Chapter 17 focuses on the calculation of eigenvalue and eigenvectors of symmetric eigenproblems including the special cases of singular mass matrices. A number of eigensolution methods, like classic vector iteration, simultaneous vector iteration, Jacobi, Givens, Housholder and Eberlein methods, as well as Lanczos method are presented and documented with illustrative examples. Chapter 18 deals with freely oscillating restrained and free-free systems using the modal reduction approach. Forced vibrations of undamped systems subject to external excitations, either due to forces or prescribed displacements, are considered in Chapter 19. The response of the system is treated as an assembly of single-degree-of-freedom responses using the spectral information of the freely oscillating system. Chapter 20 presents the damping models commonly adopted in dynamics. Viscous, Coulomb, structural or hysteretic damping models are discussed and explained in a number of examples, while particular emphasis is given to the modal type of damping and its decoupling derivation to single-degree-offreedom systems.
Chapter 21 gives a comprehensive overview to random vibrations of modally damped systems. It starts with a