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Vibrations of Elastic Systems

With Applications to MEMS and NEMS

  • Edward B. Magrab

Part of the Solid Mechanics and Its Applications book series (SMIA, volume 184)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Edward B. Magrab
    Pages 1-6
  3. Edward B. Magrab
    Pages 7-82
  4. Edward B. Magrab
    Pages 83-220
  5. Edward B. Magrab
    Pages 221-271
  6. Edward B. Magrab
    Pages 273-339
  7. Edward B. Magrab
    Pages 341-399
  8. Back Matter
    Pages 439-489

About this book

Introduction

This work presents a unified approach to the vibrations of elastic systems as applied to MEMS devices, mechanical components, and civil structures.

Applications include atomic force microscopes, energy harvesters, and carbon nanotubes and consider such complicating effects as squeeze film damping, viscous fluid loading, in-plane forces, and proof mass interactions with their elastic supports. These effects are analyzed as single degree-of-freedom models and as more realistic elastic structures. The governing equations and boundary conditions for beams, plates, and shells with interior and boundary attachments are derived by applying variational calculus to an expression describing the energy of the system. The advantages of this approach regarding the generation of orthogonal functions and the Rayleigh-Ritz method are demonstrated.

A large number of graphs and tables are given to show the impact of various factors on the systems’ natural frequencies, mode shapes, and responses.

Keywords

Elastic systems Elastic systems Elastic systems Elastic systems Elastic systems Elastic systems MEMS MEMS MEMS MEMS MEMS MEMS Mode shapes Mode shapes Mode shapes Mode shapes Mode shapes Mode shapes Natural frequencies Natural frequencies Natural frequencies Natural frequencies Natural frequencies Natural frequencies Vibrations Vibrations Vibrations Vibrations Vibrations Vibrations

Authors and affiliations

  • Edward B. Magrab
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of MarylandCollege ParkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-007-2672-7
  • Copyright Information Springer Science+Business Media B.V. 2012
  • Publisher Name Springer, Dordrecht
  • eBook Packages Engineering
  • Print ISBN 978-94-007-2671-0
  • Online ISBN 978-94-007-2672-7
  • Series Print ISSN 0925-0042
  • Buy this book on publisher's site