Mekhtiev Vibrations of Hollow Elastic Bodies

1. Auflage 2018
ISBN: 978-3-319-74354-7
Verlag: Springer Nature Switzerland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 88, 229 Seiten

Reihe: Advanced Structured Materials

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.

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. 

Autoren/Hrsg.

Mekhtiev, Magomed F.

Inhaltsverzeichnis

1;Preface;6
1.1;References;13
2;About the Book;14
3;Contents;15
4;About the Author;17
5;1 Asymptotic Analysis of Dynamic Elasticity Problems for a Hollow Cylinder of Finite Length;18
5.1;Abstract;18
5.2;1.1 Construction of Homogeneous Solutions;18
5.3;1.2 Analysis of the Roots of the Dispersion Equation;23
5.4;1.3 Construction of Asymptotic Formulas for Displacements and Stresses;36
5.5;1.4 Generalized Orthogonality Condition of Homogeneous Solutions: Satisfaction of Boundary Conditions at the Cylinder Ends;44
5.6;1.5 Construction of Dynamic Refined Applied Theories of a Hollow Cylinder;54
5.7;1.6 Torsional Vibrations of an Isotropic Hollow Cylinder;59
5.8;1.7 Elastic Vibrations of a Hollow Cylinder with a Fixed Side Surface;63
5.9;1.8 Forced Vibrations of a Hollow Cylinder with Mixed Boundary Conditions on the Side Surface;67
5.10;References;74
6;2 Asymptotic Analysis of Dynamic Elasticity Problem for a Hollow Sphere;76
6.1;Abstract;76
6.2;2.1 The General Representation of the Solution to the Equations of Axisymmetric Dynamic Elasticity Theory in Spherical Coordinates;76
6.3;2.2 Inhomogeneous Solutions;78
6.4;2.3 Construction of Homogeneous Solutions;80
6.5;2.4 Asymptotic Analysis of the Dispersion Equation;84
6.6;2.5 Asymptotic Analysis of Homogeneous Solutions for a Spherical Shell;90
6.7;2.6 Dynamical Torsion of a Spherical Layer;99
6.8;2.7 Non-axisymmetric Dynamic Problems of Elasticity Theory for a Hollow Sphere;106
6.9;References;118
7;3 Free Vibrations of Isotropic Hollow Cylinder and Closed Hollow Sphere;120
7.1;Abstract;120
7.2;3.1 Free Vibrations of an Isotropic Hollow Cylinder;121
7.3;3.2 Analysis of the Frequency Equation and Vibration Forms of a Cylinder;123
7.4;3.3 Axisymmetric Free Vibrations of a Hollow Sphere;136
7.5;References;144
8;4 Asymptotic Analysis of Stress-Strain State of a Truncated Hollow Cone;146
8.1;Abstract;146
8.2;4.1 Construction of Homogeneous Solutions;146
8.3;4.2 Analysis of the Roots of the Characteristic Equation;151
8.4;4.3 Analysis of the Stress-Strain State;154
8.5;4.4 Reduction to Infinite Systems;160
8.6;4.5 Construction of Refined Applied Theories for a Conical Shell;164
8.7;4.6 Axisymmetric Problem for a Plate of Variable Thickness;168
8.8;4.7 Analysis of the Characteristic Equation for a Plate of Variable Thickness;169
8.9;4.8 Analysis of Stress-Strain State of a Plate;170
8.10;4.9 Reduction of a Boundary Value Problem for a Plate of Variable Thickness and Infinite Systems at Given Stresses;175
8.11;4.10 Construction of Applied Theories for the Plates of Variable Thickness;178
8.12;4.11 Investigation of Elastic Equilibrium of a Hollow Cone with a Fixed Side Surface and Mixed Boundary Conditions on the Side Surface;182
8.13;4.12 Asymptotic Analysis of the Solutions of Some Axisymmetric Problems for Plates of Variable Thickness;187
8.14;4.13 Asymptotic Analysis of the Characteristic Equation;192
8.15;4.14 Construction of Asymptotic Formulas for Displacements and Stresses;194
8.16;4.15 Kirsch Problem for Plates of Variable Thickness;200
8.17;4.16 Torsional Vibrations of a Conical Shell of Variable Thickness;205
8.18;References;213
9;Appendix;214
10;References;214