Vibrations of Hollow Elastic Bodies

1. Front Matter

   Pages i-xvii

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2. Asymptotic Analysis of Dynamic Elasticity Problems for a Hollow Cylinder of Finite Length

   • Magomed F. Mekhtiev

   Pages 1-58

3. Asymptotic Analysis of Dynamic Elasticity Problem for a Hollow Sphere

   • Magomed F. Mekhtiev

   Pages 59-102

4. Free Vibrations of Isotropic Hollow Cylinder and Closed Hollow Sphere

   • Magomed F. Mekhtiev

   Pages 103-128

5. Asymptotic Analysis of Stress-Strain State of a Truncated Hollow Cone

   • Magomed F. Mekhtiev

   Pages 129-196

6. Back Matter

   Pages 197-212

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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

• Institute of Mathematics and Mechanics of National Academy of Sciences of Azerbaijan, Baku State University, Baku, Azerbaijan

  Magomed F. Mekhtiev

Honored Science Worker, academician Mekhtiyev Magomed Ferman oghlu graduated from department of Mechanics-Mathematics of Baku State University. He defended his Ph.D. thesis at the chair of elasticity theory of Rostov State University and there. In 1989 he defended his Doctoral thesis in Leningrad (St.Petersburg) State University. In 1966-1991 he occupied various positions in the Institute of Mechanics and Mathematics of National Academy of Sciences of Azerbaijan. He has worked in Baku State University since 1991. In 1994 he became professor. Scientific-research direction of prof. M.F.Mekhtiyev is mathematical methods of Solid Mechanics and Qualitative questions of optimal control. He has published over 120 scientific papers and two monographs in this field. M.F.Mekhtiyev is awarded with Gold medal of Scientific-industrial Chamber of European Union. At present he is Dean of the department of Applied Mathematics and Cybernetics and heads the chair of Mathematical Methods of Applied Analysis. 

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