## Hybrid state vector methods for structural dynamic and aeroelastic boundary value problemsLarry Lee Lehman, Langley Research Center, United States. National Aeronautics and Space Administration. Scientific and Technical Information Branch, Stanford University. Dept. of Aeronautics and Astronautics National Aeronautics and Space Administration, Scientific and Technical Information Branch, 1982 - Mathematics - 181 pages |

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### Contents

Summary | 1 |

Hybrid State Vector Equations | 9 |

Integrating and Differentiating Matrices | 27 |

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aeroelastic analysis analytical angle of attack angle-ply laminate appearing in Eq Appendix applied approximation axial modes boundary conditions boundary value problems Chapter collocation intervals collocation points composite materials continuous function convenient convergence corresponding defined deformation derived developed differential equations differentiating matrix discontinuous discretization discussed displacement variables divergence velocities dynamic pressure eigenvalue problem end point nodes exact expressions fiber orientation angle finite element global state vector grid points hybrid state vector integrating matrix approach integrating matrix solutions interpolation isotropic Jacobi integrating matrices Jacobi polynomials Jacobi solutions Laplace Laplace transform lift distribution lifting surfaces linear mixed variational mode shapes Newton integrating matrices Nondimensional frequencies numerical calculations numerical solution obtained orthogonal polynomials partitioned presented procedure quadrature roots loci Section shape functions side of Eq single layer solving static aeroelastic stiffness strip theory structural dynamic structural reference axis subinterval symmetric Table transformation transition matrix unsteady aerodynamic vector equations written zero