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El. knyga: Aeroelastic Vibrations and Stability of Plates and Shells [De Gruyter E-books]

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  • De Gruyter E-books
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Aeroelastic Vibrations and Stability of Plates and ShellsDidesnis paveikslėlis
Kitos knygos pagal šią temą:
Wiley OnlineMore info about De Gruyter e-books
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).
Preface vii
Introduction 1(4)
Part I Flutter of plates
1 Statement of the problem
5(1)
2 Determination of aerodynamic pressure
6(5)
3 Mathematical statement of problems
11(3)
4 Reduction to a problem on a disk
14(6)
5 Test problems
20(16)
6 Rectangular plate
36(12)
6.1 Problem statement and analytical solution
36(2)
6.2 Numerical--analytical solution
38(3)
6.3 Results
41(1)
6.4 Bubnov--Galerkin (B--G) method
42(4)
6.5 Dependence of critical flutter velocity on plate thickness
46(1)
6.6 Dependence of critical flutter velocity on altitude
46(2)
7 Flutter of a rectangular plate of variable stiffness or thickness
48(9)
7.1 Strip with variable cross section
48(4)
7.2 Rectangular plates
52(5)
8 Viscoelastic plates
57(6)
Part II Flutter of shallow shells
9 General formulation
63(3)
10 Determination of aerodynamic pressure
66(5)
11 The shallow shell as part of an airfoil
71(3)
12 The shallow shell of revolution
74(4)
13 The conical shell: external flow
78(4)
14 The conical shell: internal flow
82(9)
14.1 Statement of the problem
82(5)
14.2 Determination of dynamic pressure
87(4)
15 Example calculations
91(8)
Part III Numerical methods for non-self-adjoint eigenvalue problems
16 Discretization of the Laplace operator
99(19)
16.1 The Sturm-Liouville problem
99(5)
16.2 Interpolation formula for a function of two variables on a disk, and its properties
104(4)
16.3 Discretization of the Laplace operator
108(1)
16.4 Theorem of h-matrices
109(3)
16.5 Construction of h-matrix cells by discretization of Bessel equations
112(2)
16.6 Fast multiplication of h-matrices by vectors using the fast Fourier transform
114(2)
16.7 Symmetrization of the h-matrix
116(2)
17 Discretization of linear equations in mathematical physics with separable variables
118(4)
17.1 General form of equations with separable variables
118(1)
17.2 Further generalization
119(3)
18 Eigenvalues and eigenfunctions of the Laplace operator
122(20)
18.1 The Dirichlet problem
123(12)
18.2 Mixed problem
135(1)
18.3 The Neumann problem
136(4)
18.4 Numerical experiments
140(2)
19 Eigenvalues and eigenfunctions of a biharmonic operator
142(9)
19.1 Boundary-value problem of the first kind
145(1)
19.2 Boundary-value problem of the second kind
145(3)
19.3 Numerical experiments
148(3)
20 Eigenvalues and eigenfunctions of the Laplace operator on an arbitrary domain
151(17)
20.1 Eigenvalues and eigenvectors of the Laplace operator
151(13)
20.1.1 The Dirichlet problem
158(1)
20.1.2 Mixed problem
158(1)
20.1.3 The Neumann problem
159(1)
20.1.4 Description of the program LAP123C
159(5)
20.2 Program for conformal mapping
164(2)
20.3 Numerical Experiments
166(2)
21 Eigenvalues and eigenfunctions of a biharmonic operator on an arbitrary domain
168(12)
21.1 Eigenvalues and eigenfunctions of a biharmonic operator
168(9)
21.1.1 Boundary-value problem of the first kind
173(1)
21.1.2 Boundary-value problem of the second kind
173(1)
21.1.3 Description of the program BIG12AG
173(4)
21.2 Program for conformal mapping
177(2)
21.3 Numerical experiments
179(1)
22 Error estimates for eigenvalue problems
180(7)
22.1 Localization theorems
180(3)
22.2 A priori error estimate in eigenvalue problems
183(2)
22.3 A posteriori error estimate for eigenvalue problems
185(1)
22.4 Generalization for operator pencil
185(2)
Conclusion 187(2)
Bibliography 189
Sergey D. Algazin, Ishlinsky Institute of Problems of Mechanics, Russia. Igor A. Kijko, Moscow State University, Russia.
Pastovi nuoroda: https://www.kriso.lt/db/9783110338379_pe.html