Supersonic flutter of a compressed elongated plate in the presence of concentrated inertial masses and moments

Supersonic divergence of a panel with a free edge initially loaded in two directions tensile and compressive forces

“…[1,11,16] and the compressive stresses σ y are small as compared to the critical stresses (σ y ) cr. that can produce buckling of the plate in the absence of the gas flow (V = 0) [1,2,8,10,11,15,[17][18][19]. The values of (σ x ) pr.…”

“…is the critical stresses, leading to buckling of the plate in the absence of flow (V = 0) and tensile forces (σ x = 0). Its values are found in [15][16][17][18][19]. Thus, analysis of the stability of the "plate-flow" system (1)-( 4) is reduced to the study of the differential equation (1) with the corresponding boundary conditions (2)-( 4) for the deflection w = w(x, y) under the assumption ( 5) and (6).…”

“…Thus, γ * = γ * (ν, β 2 x , β 2 y ) is the limiting value of the parameter γ = ab −1 delimiting the domains of panel divergence (γ < γ * ) and localized divergence (γ ≥ γ * ) in the space of "essential" parameters of the stability problem ( 1)-( 4) [13,[14][15][16][17][18][19].…”

“…Substituting the general solution (21) of the differential equation (1) into the boundary conditions ( 2) and (3), we obtain a homogeneous system of second-order algebraic equations with respect to constants C nk , k = 1, 2. The determinant of this system equated to zero leads to the dispersion equation of the localized divergence in the form [15][16][17][18][19]:…”

“…An analytical solution to the problem was obtained using a method whose algorithm is described in detail in work [14]. This method is used to obtain an analytical solution to a number of problems of aero elastic stability [15][16][17][18][19].…”