Vibrations of Hollow Elastic Bodies

  • Magomed F.¬†Mekhtiev

Part of the Advanced Structured Materials book series (STRUCTMAT, volume 88)

Table of contents

About this book


This book focuses on the justification and refinement of highly diverse approximate dynamic models for engineering structures arising in modern technology, including high-tech domains involving nano- and meta-materials. It proposes a classification for vibration spectra over a broad frequency domain and evaluates the range of validity of various existing 2D theories for thin-walled shells by comparing them with 3D benchmark solutions. The dynamic equations in 3D elasticity are applied to the analysis of harmonic vibrations in hollow bodies with canonical shapes. New exact homogeneous and inhomogeneous solutions are derived for cylinders, spheres and cones (including spherical and conical layers), as well as for plates of variable thickness. The book includes a wealth of numerical examples, as well as refined versions of 2D dynamic formulations. Boundary value problems for hollow bodies are also addressed.


hollow bodies solutions for cylinders solutions for spheres solutions for cones spherical layers conical layers thin-walled shells Boundary value problems

Authors and affiliations

  • Magomed F.¬†Mekhtiev
    • 1
  1. 1.Institute of Mathematics and Mechanics of National Academy of Sciences of AzerbaijanBaku State UniversityBakuAzerbaijan

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-74353-0
  • Online ISBN 978-3-319-74354-7
  • Series Print ISSN 1869-8433
  • Series Online ISSN 1869-8441
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