| Description |
1 online resource (234 pages) |
| Series |
De Gruyter Studies in Mathematical Physics ; v. 25 |
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De Gruyter studies in mathematical physics.
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| Contents |
20.3 Numerical Experiments21 Eigenvalues and eigenfunctions of a biharmonic operator on an arbitrary domain; 21.1 Eigenvalues and eigenfunctions of a biharmonic operator; 21.1.1 Boundary-value problem of the first kind; 21.1.2 Boundary-value problem of the second kind; 21.1.3 Description of the program BIG12AG; 21.2 Program for conformal mapping; 21.3 Numerical experiments; 22 Error estimates for eigenvalue problems; 22.1 Localization theorems; 22.2 A priori error estimate in eigenvalue problems; 22.3 A posteriori error estimate for eigenvalue problems; 22.4 Generalization for operator pencil |
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18.1 The Dirichlet problem18.2 Mixed problem; 18.3 The Neumann problem; 18.4 Numerical experiments; 19 Eigenvalues and eigenfunctions of a biharmonic operator; 19.1 Boundary-value problem of the first kind; 19.2 Boundary-value problem of the second kind; 19.3 Numerical experiments; 20 Eigenvalues and eigenfunctions of the Laplace operator on an arbitrary domain; 20.1 Eigenvalues and eigenvectors of the Laplace operator; 20.1.1 The Dirichlet problem; 20.1.2 Mixed problem; 20.1.3 The Neumann problem; 20.1.4 Description of the program LAP123C; 20.2 Program for conformal mapping |
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16.2 Interpolation formula for a function of two variables on a disk, and its properties16.3 Discretization of the Laplace operator; 16.4 Theorem of h-matrices; 16.5 Construction of h-matrix cells by discretization of Bessel equations; 16.6 Fast multiplication of h-matrices by vectors using the fast Fourier transform; 16.7 Symmetrization of the h-matrix; 17 Discretization of linear equations in mathematical physics with separable variables; 17.1 General form of equations with separable variables; 17.2 Further generalization; 18 Eigenvalues and eigenfunctions of the Laplace operator |
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7.2 Rectangular plates8 Viscoelastic plates; Part II Flutter of shallow shells; 9 General formulation; 10 Determination of aerodynamic pressure; 11 The shallowshell as part of an airfoil; 12 The shallow shell of revolution; 13 The conical shell: external flow; 14 The conical shell: internal flow; 14.1 Statement of the problem; 14.2 Determination of dynamic pressure; 15 Example calculations; Part III Numerical methods for non-self-adjoint eigenvalue problems; 16 Discretization of the Laplace operator; 16.1 The Sturm-Liouville problem |
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Preface; Contents; Introduction; Part I Flutter of plates; 1 Statement of the problem; 2 Determination of aerodynamic pressure; 3 Mathematical statement of problems; 4 Reduction to a problem on a disk; 5 Test problems; 6 Rectangular plate; 6.1 Problem statement and analytical solution; 6.2 Numerical-analytical solution; 6.3 Results; 6.4 Bubnov-Galerkin (B-G) method; 6.5 Dependence of critical flutter velocity on plate thickness; 6.6 Dependence of critical flutter velocity on altitude; 7 Flutter of a rectangular plate of variable stiffness or thickness; 7.1 Strip with variable cross section |
| Summary |
Back-action of wind onto wings causes vibrations, endangering the whole structure. By careful choices of geometry, materials and damping, hazardous effects on wind engines, planes, turbines and cars can be avoided. This book gives an overview of aerodynamics and mechanics behind these problems and describes a range of mechanical effects. Numerical and analytical methods to study and analyse them are developed and supplemented by Fortran code |
| Bibliography |
Includes bibliographical references (pages 189-220) |
| Notes |
Print version record |
| Subject |
Plates (Engineering) -- Vibration.
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Shells (Engineering) -- Vibration.
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Elastic plates and shells -- Mathematical models
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SCIENCE / Mechanics / Aerodynamics.
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Elastic plates and shells -- Mathematical models
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Plates (Engineering) -- Vibration
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Shells (Engineering) -- Vibration
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Flächentragwerk
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Flatterflug
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| Form |
Electronic book
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| Author |
Kijko, Igor A
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| LC no. |
2014034332 |
| ISBN |
9783110338379 |
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3110338378 |
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9781680157703 |
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1680157701 |
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9783110389456 |
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3110389452 |
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