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Advances in Aircraft and Spacecraft Science
  Volume 1, Number 3, July 2014, pages 291-310

Flutter analysis by refined 1D dynamic stiffness elements and doublet lattice method
Alfonso Pagani, Marco Petrolo and Erasmo Carrera

    An advanced model for the linear flutter analysis is introduced in this paper. Higher-order beam structural models are developed by using the Carrera Unified Formulation, which allows for the straightforward implementation of arbitrarily rich displacement fields without the need of a-priori kinematic assumptions. The strong form of the principle of virtual displacements is used to obtain the equations of motion and the natural boundary conditions for beams in free vibration. An exact dynamic stiffness matrix is then developed by relating the amplitudes of harmonically varying loads to those of the responses. The resulting dynamic stiffness matrix is used with particular reference to the Wittrick-Williams algorithm to carry out free vibration analyses. According to the doublet lattice method, the natural mode shapes are subsequently used as generalized motions for the generation of the unsteady aerodynamic generalized forces. Finally, the g-method is used to conduct flutter analyses of both isotropic and laminated composite lifting surfaces. The obtained results perfectly match those from 1D and 2D finite elements and those from experimental analyses. It can be stated that refined beam models are compulsory to deal with the flutter analysis of wing models whereas classical and lower-order models (up to the second-order) are not able to detect those flutter conditions that are characterized by bending-torsion couplings.
Key Words
    flutter; higher-order models; unified formulation; beams; doublet lattice method; dynamic stiffness method
(1) Alfonso Pagani:
Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy;
(2) Marco Petrolo:
School of Aerospace, Mechanical and Manufacturing Engineering RMIT University, Bundoora VIC 3083, Australia;
(3) Erasmo Carrera:
Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy (Currently at SAMME, RMIT University, Melbourne, Australia).

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