Theory of Elastic Oscillations

Equations and Methods

  • Vladimir¬†Fridman

Part of the Foundations of Engineering Mechanics book series (FOUNDATIONS)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Equations and Methods

    1. Front Matter
      Pages 1-1
    2. Vladimir Fridman
      Pages 53-77
    3. Vladimir Fridman
      Pages 109-122
    4. Vladimir Fridman
      Pages 179-189
  3. Some Applied Problems

    1. Front Matter
      Pages 191-191
    2. Vladimir Fridman
      Pages 209-228
    3. Vladimir Fridman
      Pages 239-247
  4. Back Matter
    Pages 249-257

About this book

Introduction

This book presents in detail an alternative approach to solving problems involving both linear and nonlinear oscillations of elastic distributed parameter systems. It includes the so-called variational, projection and iterative gradient methods, which, when applied to nonlinear problems, use the procedure of linearization of the original non-linear equations.

These methods are not universal and require a different solution for each problem or class of problems.However, in many cases the combination of the methods shown in this book leads to more efficient algorithms for solving important applied problems.To record these algorithms in a unified form, the first part of the book and its appendix devote considerable attention to compiling the general operator equations, which include (as particular cases) equations for vibrations in rods, plates, shells and three-dimensional bodies. They are mainly considered to be periodic or nearly periodic oscillations, which correspond to stationary or nearly stationary regimes of machinery operation. In turn, the second part of the book presents a number of solutions for selected applications. 

Keywords

Elastic Distributed Parameter Systems Longitudinal Vibrations of a Rod Torsional Vibrations Mixed Boundary Conditions Newton-Kantorovich Method Bending Vibrations Lubrication

Authors and affiliations

  • Vladimir¬†Fridman
    • 1
  1. 1.Los Angeles, CAUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-10-4786-2
  • Copyright Information Springer Nature Singapore Pte Ltd. 2018
  • Publisher Name Springer, Singapore
  • eBook Packages Engineering
  • Print ISBN 978-981-10-4785-5
  • Online ISBN 978-981-10-4786-2
  • Series Print ISSN 1612-1384
  • Series Online ISSN 1860-6237
  • About this book