Linear vibrations - A theoretical treatment of multi-degree-of-freedom vibrating systems
Von P. C. Müller & W. O. Schiehlen
"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."