Linear vibrations: A theoretical treatment of multi-degree-of-freedom vibrating systems (Mechanics: Dynamical Systems, 7)

In the last decade the development in vibration analysis was char­ acterized by increasing demands on precision and by the growing use of electronic computers. At present, improvements in precision are obtained by a more accurate modelling of technical systems. Thus, for instance, a system with one degree of freedom is often not accepted, as it used to be, as a model for vibration analysis in mechanical engineering. As a rule, vehicles and machines have to be modelled as systems with many degrees of freedom such as multibody systems, finite element systems or con­ tinua. The mathematical description of multi-degree-of-freedom systems leads to matrix representations of the corresponding equations. These are then conveniently analyzed by means of electronic computers, that is, by the analog computer and especially by the digital machine. Hence there exists a mutually stimulating interaction between the growing require­ ments and the increasing computational facilities. The present book deals with linear vibration analysis of technical systems with many degrees of freedom in a form allowing the use of computers for finding solutions. Part I begins with the classification of vibrating systems. The main characteristics here are the kind of differential equation, the time depen­ dence of the coefficients and the attributes of the exciting process. Next it is shown by giving examples involving mechanical vibrating systems how to set up equations of motion and how to transform these into state equations. Front Matter....Pages I-X Front Matter....Pages 1-1 Classification of vibrations....Pages 3-13 Mechanical vibrating systems....Pages 14-34 State equations of linear vibrating systems....Pages 35-56 Front Matter....Pages 57-57 The general solution of time-invariant vibrating systems....Pages 59-97 Stability and boundedness....Pages 98-130 Free vibrations....Pages 131-167 Forced vibrations....Pages 168-187 Resonance and absorption....Pages 188-233 Random vibrations....Pages 234-256 Front Matter....Pages 257-257 General solution and stability....Pages 259-278 Parametrically excited and forced vibrations....Pages 279-289 Front Matter....Pages 291-291 Controllability and observability....Pages 293-295 Matrix equations....Pages 296-306 Numerical aspects....Pages 307-320 Back Matter....Pages 321-327