Aeroelastic Vibrations and Stability of Plates and Shells.

Intro -- 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 -- 7.2 Rectangular plates -- 8 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 -- 16.2 Interpolation formula for a function of two variables on a disk, and its properties -- 16.3 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 -- 18.1 The Dirichlet problem -- 18.2 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 -- 20.3 Numerical Experiments -- 21 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 -- Conclusion -- Bibliography.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.