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Linear vibrations

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

  • Book
  • © 1985

Overview

Authors:
  1. P. C. Müller

    1. Sicherheitstechnische Regelungs- und Messtechnik, Bergische Universität Gesamthochschule Wuppertal, Wuppertal 1, Germany

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    You can also search for this author in PubMed   Google Scholar

  2. W. O. Schiehlen

    1. Institut B für Mechanik, Universität Stuttgart, Stuttgart 80, Germany

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    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (14 chapters)

  1. Front Matter

    Pages I-X
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  2. Mathematical description of vibrating systems

    1. Front Matter

      Pages 1-1
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    2. Classification of vibrations

      • P. C. Müller, W. O. Schiehlen
      Pages 3-13

    3. Mechanical vibrating systems

      • P. C. Müller, W. O. Schiehlen
      Pages 14-34

    4. State equations of linear vibrating systems

      • P. C. Müller, W. O. Schiehlen
      Pages 35-56

  3. Time-invariant vibrating systems

    1. Front Matter

      Pages 57-57
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    2. The general solution of time-invariant vibrating systems

      • P. C. Müller, W. O. Schiehlen
      Pages 59-97

    3. Stability and boundedness

      • P. C. Müller, W. O. Schiehlen
      Pages 98-130

    4. Free vibrations

      • P. C. Müller, W. O. Schiehlen
      Pages 131-167

    5. Forced vibrations

      • P. C. Müller, W. O. Schiehlen
      Pages 168-187

    6. Resonance and absorption

      • P. C. Müller, W. O. Schiehlen
      Pages 188-233

    7. Random vibrations

      • P. C. Müller, W. O. Schiehlen
      Pages 234-256

  4. Time-variant vibrating systems

    1. Front Matter

      Pages 257-257
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    2. General solution and stability

      • P. C. Müller, W. O. Schiehlen
      Pages 259-278

    3. Parametrically excited and forced vibrations

      • P. C. Müller, W. O. Schiehlen
      Pages 279-289

  5. Mathematical background

    1. Front Matter

      Pages 291-291
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    2. Controllability and observability

      • P. C. Müller, W. O. Schiehlen
      Pages 293-295

    3. Matrix equations

      • P. C. Müller, W. O. Schiehlen
      Pages 296-306

    4. Numerical aspects

      • P. C. Müller, W. O. Schiehlen
      Pages 307-320

  6. Back Matter

    Pages 321-327
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Keywords

About this book

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.

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)

Authors and Affiliations

  • Sicherheitstechnische Regelungs- und Messtechnik, Bergische Universität Gesamthochschule Wuppertal, Wuppertal 1, Germany

    P. C. Müller

  • Institut B für Mechanik, Universität Stuttgart, Stuttgart 80, Germany

    W. O. Schiehlen

Bibliographic Information

  • Book Title: Linear vibrations

  • Book Subtitle: A theoretical treatment of multi-degree-of-freedom vibrating systems

  • Authors: P. C. Müller, W. O. Schiehlen

  • Series Title: Mechanics: Dynamical Systems

  • DOI: https://doi.org/10.1007/978-94-009-5047-4

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 1985

  • Hardcover ISBN: 978-90-247-2983-8Due: 31 July 1985

  • Softcover ISBN: 978-94-010-8735-3Published: 13 November 2013

  • eBook ISBN: 978-94-009-5047-4Published: 06 December 2012

  • Series ISSN: 0169-667X

  • Edition Number: 1

  • Number of Pages: X, 327

  • Number of Illustrations: 89 b/w illustrations

  • Additional Information: Originally published in German

  • Topics: Vibration, Dynamical Systems, Control, Classical Mechanics

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