Finite element method applied to the supersonic flutter of circular cylindrical shells

Bismarck-Nasr, Maher N.

doi:10.1002/nme.1620100212

Cited by 34 publications

(8 citation statements)

References 18 publications

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“…Therefore, in many recent investigations the subject of extensive discussion is the finite element method as applied to the problems of panel flutter. In contrast to differential approaches, most of the FEM-based developments for panel flutter problems (e.g., Bismarck-Nasr, 1976;Bismarck-Nasr and Costa Savio, 1979;Sunder, Ramakrishnan, and Sengupta, 1983) do not completely allow for a variety of factors affecting the boundary of aerodynamic stability. In an effort to compensate for this deficiency, we have attempted to develop a more effective finite element algorithm to determine the aerodynamic stability boundary for revolution shells of different geometry under the action of internal or external supersonic gas flow.…”

Section: Introductionmentioning

confidence: 96%

Numerical Analysis of Panel Flutter in Shells of Revolution

Бочкарев

Matveyenko

Шардаков

1997

Journal of Vibration and Control

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A mathematical model is proposed to investigate panel flutter of revolution shells subject to external or internal supersonic gas flow. The mathematical formulation of the problem is constructed in terms of the virtual displacement principle, which is treated numerically by the finite element method. Consideration is given to the two alternatives of the shell relations based either on the Kirchhoff-Love hypothesis or on the generalized theory of shells by Timoshenko. A series of numerical experiments were performed to estimate the computational efficiency of the model and to compare its performance in the context of some problems in recently published solutions. A numerical analysis is performed to assess the effect of some factors (laminated structure, the stress-strain state due to preloading) on the boundary of aeroelastic stability and to allow comparison with the results obtained on the basis of considered shell theories.

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Section: Introductionmentioning

confidence: 96%

Numerical Analysis of Panel Flutter in Shells of Revolution

Бочкарев

Matveyenko

Шардаков

1997

Journal of Vibration and Control

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“…Axial load reduced the flutter boundary until the shell buckled, later reproduced by Barr and Stearman 9 and Bismarck-Nasr. 10 After buckling, the new corrugated shape was stable. Internal pressure was shown to initially have a destabilizing effect, reducing the flutter boundary, but stabilized the shell at sufficiently high pressures.…”

Section: Introductionmentioning

confidence: 98%

Aeroelastic Stability of High-Speed Cylindrical Vehicles

Klock

Cesnik

2017

58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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Different levels of structural modeling fidelity are evaluated against experimental results for the aeroelastic stability boundaries of an internally pressurized circular cylindrical shell. A modal approach is taken to model the structural dynamics while third-order piston theory is used to model the external and internal surfaces' unsteady aerodynamic pressures. Results are used to inform model improvements of freeflight aero-thermo-elastic simulation in order to accurately predict aeroelastic instabilities in a representative supersonic vehicle. The stability of a finite-element model when inclined to the flow is also considered in an unpressurized condition to inform future work where a cylindrical high-speed vehicle is required to perform maneuvers.

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“…Aeroelastic governing equations were formulated by applying the classical shell theory coupled with the piston theory for evaluation of aerodynamic forces. For example, Bismarck-Nasr [11] developed a FEM applied to the supersonic flutter of a circular shell subjected to internal pressure and axial loading. Ganapathi et al [12] modeled an orthotropic and laminated anisotropic cylindrical shell in supersonic flow using the FEM and analyzed the effect of different shell geometries on the flutter boundaries.…”

Section: Introductionmentioning

confidence: 99%

Numerical Investigation of the Flutter of a Spherical Shell

Menaa

Lakis

2013

Journal of Vibration and Acoustics

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In this study, aeroelastic analysis of a spherical shell subjected to external supersonic airflow is carried out. The structural model is based on a combination of the linear spherical shell theory and the classic finite element method (FEM). In this hybrid method, the nodal displacements are found from the exact solution of shell governing equations rather than approximated by polynomial functions. Therefore, the number of elements chosen is a function of the complexity of the structure. Convergence is rapid. It is not necessary to choose a large number of elements to obtain good results. Linearized first-order potential (piston) theory with the curvature correction term is coupled with the structural model to account for pressure loading. The linear mass, stiffness, and damping matrices are found using the hybrid finite element formulation. Aeroelastic equations are numerically derived and solved. The results are validated using the numerical and theoretical data available in literature. The analysis is accomplished for spherical shells with different boundary conditions, geometries, flow parameters, and radius to thickness ratios. the results show that the spherical shell loses its stability through coupled-mode flutter. This proposed hybrid FEM can be used efficiently for the design and analysis of spherical shells employed in high speed aircraft structures.

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Finite element method applied to the supersonic flutter of circular cylindrical shells

Cited by 34 publications

References 18 publications

Numerical Analysis of Panel Flutter in Shells of Revolution

Numerical Analysis of Panel Flutter in Shells of Revolution

Aeroelastic Stability of High-Speed Cylindrical Vehicles

Numerical Investigation of the Flutter of a Spherical Shell

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