Supersonic/Hypersonic Flutter and Postflutter of Geometrically Imperfect Circular Cylindrical Panels

A parametric study on supersonic/hypersonic flutter behavior of aero-thermo-elastic geometrically imperfect curved skin panel

“…These are the harmonic balance technique [48], perturbation method [49], finite element method [28,29,38,39,50], direct numerical integration technique (DNIT) [26,40,47,[51][52][53][54][55][56][57][58], pseudo-arc length continuation method that complements the DNIT [32,59] and recently the Lyapunov first quantity (LFQ) [8,31,60]. Galerkin's method [72] and DNIT will be considered to solve the integro-differential equation (Eq.…”

“…(7) and (g sm ∂ j+1 w/∂t∂ x j ) to the membrane terms of Eq. (8). Herein, g s is a structural damping coefficient, and it is constant for viscous damping.…”

“…where σ x_total = σ x + σ T x is the total in-plane stress, in the x-direction, evaluated using the average end-shortening x [8,46] in the case of immovable edges, x = (0, a), i.e. x = 0,…”

“…The strain ε x of the mid-plane surface in the x-direction, based on the Von Kármán assumption, is given by [8] …”

“…Thus, to study the behavior of aeroelastic systems near the flutter instability boundary, or even in the post-instability region, the inherent non-linearities of structural and aerodynamic nature must be accounted for. It was recognized that geometrical non-linearities due to moderate plate deflection (mainly mid-plane stretching forces) represented following the Von Kármán large deflection plate theory combined with the linear piston theory, one of the popular unsteady aerodynamic theories used, can play an important role in panel flutter [8]. This led to a number of studies [9][10][11][12][13][14][15][16] which showed that, when geometrically nonlinearities are included in the model, the linear stability boundary can be exceeded, thereby inducing stable LCO with finite amplitudes, having an order of magnitude equal to the thickness of the panel.…”