Aeroelastic Vibrations and Stability of Plates and Shells

Sergey D. Algazin; Igor A. Kijko

Published by De Gruyter 2015

Aeroelastic Vibrations and Stability of Plates and Shells

Sergey D. Algazin and Igor A. Kijko

Volume 25 in the series De Gruyter Studies in Mathematical Physics

https://doi.org/10.1515/9783110338379

Overview
Contents

About this book

Back-action of aerodynamics onto structures such as wings cause vibrations and may resonantly couple to them, thus causing instabilities (flutter) and endangering the whole structure. By careful choices of geometry, materials and damping mechanisms, hazardous effects on wind engines, planes, turbines and cars can be avoided.

Besides an introduction into the problem of flutter, new formulations of flutter problems are given as well as a treatise of supersonic flutter and of a whole range of mechanical effects. Numerical and analytical methods to study them are developed and applied to the analysis of new classes of flutter problems for plates and shallow shells of arbitrary plane form. Specific problems discussed in the book in the context of numerical simulations are supplemented by Fortran code examples (available on the website).

Accompanying simulation code written in Fortran is available from the website.

Author / Editor information

Sergey D. Algazin, Ishlinsky Institute of Problems of Mechanics, Russia.
Igor A. Kijko, Moscow State University, Russia.

Supplementary Materials

Fortran

Topics

Frontmatter Publicly Available Download PDF	i
Preface Requires Authentication Unlicensed Licensed Download PDF	vii
Contents Publicly Available Download PDF	ix
Introduction Requires Authentication Unlicensed Licensed Download PDF	1
Part I: Flutter of plates
1. Statement of the problem Requires Authentication Unlicensed Licensed Download PDF	5
2. Determination of aerodynamic pressure Requires Authentication Unlicensed Licensed Download PDF	6
3. Mathematical statement of problems Requires Authentication Unlicensed Licensed Download PDF	11
4. Reduction to a problem on a disk Requires Authentication Unlicensed Licensed Download PDF	14
5. Test problems Requires Authentication Unlicensed Licensed Download PDF	20
6. Rectangular plate Requires Authentication Unlicensed Licensed Download PDF	36
7. Flutter of a rectangular plate of variable stiffness or thickness Requires Authentication Unlicensed Licensed Download PDF	48
8. Viscoelastic plates Requires Authentication Unlicensed Licensed Download PDF	57
Part II: Flutter of shallow shells
9. General formulation Requires Authentication Unlicensed Licensed Download PDF	63
10. Determination of aerodynamic pressure Requires Authentication Unlicensed Licensed Download PDF	66
11. The shallow shell as part of an airfoil Requires Authentication Unlicensed Licensed Download PDF	71
12. The shallow shell of revolution Requires Authentication Unlicensed Licensed Download PDF	74
13. The conical shell: external flow Requires Authentication Unlicensed Licensed Download PDF	78
14. The conical shell: internal flow Requires Authentication Unlicensed Licensed Download PDF	82
15. Example calculations Requires Authentication Unlicensed Licensed Download PDF	91
Part III: Numerical methods for non-self-adjoint eigenvalue problems
16. Discretization of the Laplace operator Requires Authentication Unlicensed Licensed Download PDF	99
17. Discretization of linear equations in mathematical physics with separable variables Requires Authentication Unlicensed Licensed Download PDF	118
18. Eigenvalues and eigenfunctions of the Laplace operator Requires Authentication Unlicensed Licensed Download PDF	122
19. Eigenvalues and eigenfunctions of a biharmonic operator Requires Authentication Unlicensed Licensed Download PDF	142
20. Eigenvalues and eigenfunctions of the Laplace operator on an arbitrary domain Requires Authentication Unlicensed Licensed Download PDF	151
21. Eigenvalues and eigenfunctions of a biharmonic operator on an arbitrary domain Requires Authentication Unlicensed Licensed Download PDF	168
22. Error estimates for eigenvalue problems Requires Authentication Unlicensed Licensed Download PDF	180
Conclusion Requires Authentication Unlicensed Licensed Download PDF	187
Bibliography Requires Authentication Unlicensed Licensed Download PDF	189

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Physicists, mathematicians and engineers in aerodynamics, aerospace and wind engine industry; graduate students; libraries.
Pages
- Front matter: 11
- Main content: 220
Illustrations
- Illustrations: 35
- Tables: 25

eBook

Published: December 11, 2014
ISBN: 9783110338379

Hardcover

Published: November 17, 2014
ISBN: 9783110338362