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© 1985

Linear vibrations

A theoretical treatment of multi-degree-of-freedom vibrating systems

Book

Part of the Mechanics: Dynamical Systems book series (MDYS, volume 7)

Table of contents

  1. Front Matter
    Pages I-X
  2. Mathematical description of vibrating systems

    1. Front Matter
      Pages 1-1
    2. P. C. Müller, W. O. Schiehlen
      Pages 3-13
    3. P. C. Müller, W. O. Schiehlen
      Pages 14-34
    4. P. C. Müller, W. O. Schiehlen
      Pages 35-56
  3. Time-invariant vibrating systems

    1. Front Matter
      Pages 57-57
    2. P. C. Müller, W. O. Schiehlen
      Pages 59-97
    3. P. C. Müller, W. O. Schiehlen
      Pages 98-130
    4. P. C. Müller, W. O. Schiehlen
      Pages 131-167
    5. P. C. Müller, W. O. Schiehlen
      Pages 168-187
    6. P. C. Müller, W. O. Schiehlen
      Pages 188-233
    7. P. C. Müller, W. O. Schiehlen
      Pages 234-256
  4. Time-variant vibrating systems

    1. Front Matter
      Pages 257-257
    2. P. C. Müller, W. O. Schiehlen
      Pages 259-278
    3. P. C. Müller, W. O. Schiehlen
      Pages 279-289
  5. Mathematical background

    1. Front Matter
      Pages 291-291
    2. P. C. Müller, W. O. Schiehlen
      Pages 293-295
    3. P. C. Müller, W. O. Schiehlen
      Pages 296-306
    4. P. C. Müller, W. O. Schiehlen
      Pages 307-320
  6. Back Matter
    Pages 321-327

About this book

Introduction

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.

Keywords

kinematics multibody system resonance stability vibration

Authors and affiliations

  1. 1.Sicherheitstechnische Regelungs- und MesstechnikBergische Universität Gesamthochschule WuppertalWuppertal 1Germany
  2. 2.Institut B für MechanikUniversität StuttgartStuttgart 80Germany

Bibliographic information

  • Book Title Linear vibrations
  • Book Subtitle A theoretical treatment of multi-degree-of-freedom vibrating systems
  • Authors P.C. Müller
    Werner Schiehlen
  • Series Title Mechanics: Dynamical Systems
  • DOI https://doi.org/10.1007/978-94-009-5047-4
  • Copyright Information Springer Science+Business Media B.V. 1985
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-90-247-2983-8
  • Softcover ISBN 978-94-010-8735-3
  • eBook ISBN 978-94-009-5047-4
  • Series ISSN 0169-667X
  • Edition Number 1
  • Number of Pages X, 327
  • Number of Illustrations 89 b/w illustrations, 0 illustrations in colour
  • Additional Information Originally published in German
  • Topics Vibration, Dynamical Systems, Control
    Classical Mechanics
  • Buy this book on publisher's site

Reviews

`This excellently written and easily readable book is highly recommended to every scientist, engineer and student interested in vibration theory and its mathematical justification.'
Acta Scientiarum Mathematicarum
`The contents are well presented, and the introduction of topics not readily to be found in many textbooks on vibration makes this book a worthwhile addition to a dynamicist's library.'
The Aeronautical Journal, February 1986
`It is written in the form of a textbook useful for senior and graduate level students in mechanics or mechanical engineering. Practicing engineers faced with complex vibration problems will also find this book to be of value. The material is well organized into four parts.'
Applied Mechanics Review, 39:6 (1986)