Abstract
A numerical model was developed to investigate the flutter instability of truncated conical shells subjected to supersonic flows. The exact solution of Sanders’ best firstorder approximation was used to develop the finite elements model of the shell. Nonlinear kinematics of Donnell’s, Sanders’ and Nemeth’s theories, in conjunction with the generalized coordinates method, were used to formulate the nonlinear strain energy of the shell. A pressure field was formulated using the piston theory with the correction term for the curvature. Lagrangian equations of motion based on Hamilton’s principle were obtained. A variation of the harmonic balance method was used for developing the amplitude equations of the shell, and a numerical method was used for solving these equations. Results of linear and nonlinear flutter of truncated conical shells were validated against the existing data in the literature. It was observed that geometrical nonlinearities have a softening effect on the stability of the shell in supersonic flows.
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Abbreviations
- [AQ]:
-
Characteristic polynomial matrix
- cNLc1, c2, c3 :
-
Flag parameters to define different shell theories
- [C̄C̄°]:
-
Symmetric constitutive matrix for conical element
- e11°, e12°, e23° :
-
Linear deformation parameters defined by Eq. (3)
- M∞, MI :
-
Free stream Mach number and local flow Mach number (after the conical shock)
- [N]:
-
Displacement field matrix of a finite element defined by Eq. (15)
- n c :
-
Circumferential mode number
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Mehrdad Bakhtiari received his first master’s degree in propulsion (KNTU- 2009) and a second master’s in industrial systems engineering (UofR-2014). He is currently a Ph.D. candidate in mechanical engineering at Polytechnique Montréal. His research interests are fluid structure interactions in thin shells.
Aouni. A. Lakis, is Full Professor at Department of Mechanical Engineering of Polytechnique de Montréal. He received his Ph.D. from McGill University. His research interest concerns are Aeroelasticity, dynamic stability, fluid-structure, numerical methods, plates and shells, Health monitoring.
Kerboua Youcef is research associate at Department of Mechanical Engineering
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Bakhtiari, M., Lakis, A.A. & Kerboua, Y. Nonlinear supersonic flutter of truncated conical shells. J Mech Sci Technol 34, 1375–1388 (2020). https://doi.org/10.1007/s12206-020-0301-6
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DOI: https://doi.org/10.1007/s12206-020-0301-6