Nonlinear Flutter of Composite Panels Under Yawed Supersonic Flow Using Finite Elements

Application of aeroelastic modes on nonlinear supersonic panel flutter at elevated temperatures

“…With the use of von Kármán plate theory, the maximum deflection is of order of plate thickness. The finite element system equations of motion for nonlinear flutter of a laminated composite panel at an arbitrary yawed supersonic flow angle K and temperature distribution DT can be expressed in the matrix form [2,[4][5][6][8][9][10][11][12][13] as The parameters k, C a and K are the non-dimensional dynamic pressure, non-dimensional aerodynamic damping, and flow yaw angle, respectively, with k and C a defined as [4,10] k ¼ 2q a a 3 bD 110…”

“…The selection of the dominant modes, either AEMs or NMs, to the LCO response, is based on their participation values. For the rth mode, its modal participation (MP) value is defined [4,7,14] as…”

“…It is known that a minimum of six (or 6 · 1) NMs is needed for converged LCO of isotropic rectangular plates at zero yaw angle [1,3]. For isotropic or orthotropic rectangular plates under an arbitrary non-zero yawed supersonic flow, 36 or 6 · 6 NMs are needed [4]; for laminated anisotropic rectangular plates even at zero yaw angle, 36 or fewer NMs are needed [4]. The large number of NMs or coupled nonlinear modal equations is not only computationally costly for flutter analysis, but also causes certain complexity and difficulty in controller design for flutter suppression [5,6].…”

Parametric study on supersonic flutter of angle-ply laminated plates using shear deformable finite element method

“…The effects of lay-up schedule, fiber orientation, flow direction, skew angle etc. on the flutter characteristics of laminated panels are investigated by many authors [2][3][4][5][6][7][8][9][10][11][12][13][16][17][18][19][20][21][22]. However, most of the studies are conducted for thin panels, to the authors' knowledge, the flutter analysis of thick or moderately thick laminated panels has not been reported in any major international journal.…”

“…They adopted Reissner-Mindlin theory which assumes that the normals to the middle surface after deformation remain straight but rotate around the middle surface, and introduced an element-appropriate shear correction factor to calculate the constant transverse shear stresses through the thickness and avoid the problem of shear locking. The Mindlin plate elements are used extensively to study the thermal buckling, nonlinear flutter response and flutter suppression of laminated plates [15][16][17]. Besides the Reissner-Mindlin theory, various shear deformation laminate theories, such as the first-order shear deformation theory (FSDT) considering the variation of the membrane displacement with the thickness, and the high-order shear deformation theories (HSDT) allowing for the warping in the ply are extended to panel flutter analysis in recent years [18][19][20][21][22].…”