Finite element model to investigate the dynamic instability of rectangular plates subjected to supersonic airflow

Abbas, 2011, Panel flutter analysis of plate element based on the absolute nodal coordinate formulation, J. Multibody Syst. Dyn., 135 Aravinth, D., et al., 2018. Dynamic aeroelasticity of a trapezoidal wing using enhanced piston theory. In: AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Ashley, Holt, Zartarian, Garabed, 1956. Piston theory-A new aerodynamic tool for the aeroelastician. In: Presented at the Aeroelasticity Session, Twenty-Fourth Annual Meeting, IAS, New York, January 1956, 23–26. Bismarck-Nasr, 1977, Finite element method applied to the flutter of two parallel elastically coupled flat plates, Int. J. Numer. Methods Eng., 11, 1188, 10.1002/nme.1620110713 Bismarck-Nasr, 1992, Finite element analysis of aeroelasticity of plates and shells, Appl. Mech. Rev., 45, 10.1115/1.3119783 Bloomhardt, Elizabeth M., Dowell, Earl H., 2011. A study of the aeroelastic behavior of flat plates and membranes with mixed boundary conditions in axial subsonic flow. In: 52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference <BR> 19th 4-7 2011, Denver, Colorado. Chen, 1985, Flutter analysis of thin cracked panels using the finite element method, AIAA J., 23, 795, 10.2514/3.8986 Cook, 2002 Dixon, 1969, Flutter boundary for simply supported unstiffened cylinders, AIAA J., 7, 1390, 10.2514/3.5363 Dowell, 1966, Nonlinear oscillations of a fluttering plate I, AIAA J., 4, 1267, 10.2514/3.3658 Dowell, 1967, Nonlinear oscillations of a fluttering plate II, AIAA J., 5, 1856, 10.2514/3.4316 Dowell, 1969, Theoretical-experimental correlation of plate flutter boundaries at low supersonic speeds, AIAA J., 6, 1810, 10.2514/3.4881 Dowell, 2016, Investigation of higher order effects in linear piston theory, Math. Eng. Sci. Aerosp. (MESA), 7 Dowell, 1965, Experimental and theoretical panel flutter studies in the mach number range 1.0 to 5.0, TDR 63-449, Dec. 1963, aeronautical systems division, AIAA J., 3, 2292, 10.2514/3.3359 Dowell, 1991, Limit cycle oscillation of a fluttering cantilever plate, AIAA J., 29, 1929, 10.2514/3.10821 Erickson, 1971 Ganji, 2016, Panel flutter prediction in two-dimensional flow with enhanced piston theory, J. Fluids Struct., 63, 97, 10.1016/j.jfluidstructs.2016.03.003 Gibbs, 2015, Stability of rectangular plates in subsonic flow with various boundary conditions, J. Aircr., 52, 10.2514/1.C032738 Grover, 2016, An inverse trigonometric shear deformation theory for supersonic flutter characteristics of multilayered composite plates, Aerosp. Sci. Technol., 52, 41, 10.1016/j.ast.2016.02.017 Hess, 1962 Katsikadelis, 2009, Nonlinear flutter instability of thin damped plates: A solution by the analog equation method, J. Mech. Mater. Struct., 4, 1395, 10.2140/jomms.2009.4.1395 Kerboua, 2007, Marcouiller hybrid method for vibration analysis of rectangular plates, J. Nucl. Eng. Des., 237, 791, 10.1016/j.nucengdes.2006.09.025 Kerboua, 2008, Vibration analysis of rectangular plates coupled with fluid, Appl. Math. Model., 32, 2570, 10.1016/j.apm.2007.09.004 Lakis, 1972, Dynamic analysis of axially non-uniform thin cylindrical shells, J. Mech. Eng. Sci., 14, 49, 10.1243/JMES_JOUR_1972_014_009_02 Leissa, 1973 Librescu, 1968, Supersonic flutter of circular cylindrical heterogeneous orthotropic thin panels of finite length, J. Sound Vib., 8, 494, 10.1016/0022-460X(68)90253-8 Lin, 1989, Flutter analysis of composite panels using high-precision finite elements, Int. J. Comput. Struct., 33, 561, 10.1016/0045-7949(89)90030-8 Lin, 2018, Studies for aeroelastic characteristics and nonlinear response of FG-CNT reinforced composite panel considering the transient heat conduction, J. Compos. Struct., 188, 470, 10.1016/j.compstruct.2018.01.028 Lock, 1961 Mahran, 2015, Aero-elastic characteristics of tapered plate wings, Finite Elem. Anal. Des., 94, 24, 10.1016/j.finel.2014.09.009 Muhlstein, 1968 Olson, 1967, Finite elements applied to panel flutter, AIAA J., 5, 2267, 10.2514/3.4422 Olson, 1970, Some flutter solutions using finite elements, AIAA J., 8, 747, 10.2514/3.5751 Sabri, 2010, Finite element method applied to supersonic flutter of circular cylindrical shells, AIAA J., 48, 73, 10.2514/1.39580 Sanders, 1959 Sarma, 1988, Nonlinear panel flutter by finite-element method, AIAA, 126, 566, 10.2514/3.9935 Selmane, 1997, Non-linear dynamic analysis of orthotropic open cylindrical shells subjected to a flowing fluid, J. Sound Vib., 202, 67, 10.1006/jsvi.1996.0794 Shideler, 1966 Singa Rao, 1983, Nonlinear supersonic flutter of panels considering shear deformation and rotary inertia, Int. J. Comput. Str’ll.et, 17, 361, 10.1016/0045-7949(83)90127-X Song, 2014, Investigations on the flutter properties of supersonic panels with different boundary conditions, Int. J. Dyn. Control, 2, 346, 10.1007/s40435-013-0038-5 Stroud, 1963 Tian, 2017, Analysis of nonlinear aeroelastic characteristics of a trapezoidal wing in hypersonic flow, J. Nonlinear Dyn., 89, 1205, 10.1007/s11071-017-3511-4 Vlasov, 1951 Xie, 2015, A comparison of numerical and semi-analytical proper orthogonal decomposition methods for a fluttering plate, J. Nonlinear Dyn., 79, 1971, 10.1007/s11071-014-1787-1 Xie, 2014, Projection-free proper orthogonal decomposition method for a cantilever plate in supersonic flow, J. Sound Vib., 333, 6190, 10.1016/j.jsv.2014.06.039 Xie, 2014, Observation and evolution of chaos for a cantilever plate in supersonic flow, J. Fluids Struct., 50, 271, 10.1016/j.jfluidstructs.2014.05.015