Fig. 1 Schematic of a nonlinear cantilever beam with an intermediate concentrated mass deflecting due to distributed pressure from an axial supersonic flow More

Fig. 2 Discontinuous rise in flutter Mach number as a concentrated mass ratio η is varied for s η = 0.9 (solid line). If the mass ratio was instead increased in a homogeneous fashion (increasing thickness, dashed line), an abrupt flutter mode switch does not occur. More

Fig. 3 Eigenvalue behavior two different concentrated mass ratios: one prior to the discontinuous jump in flutter Mach number (a,b; η = 0.2), and one after (c,d; η = 0.3). For both cases, s η = 0.9 . More

Fig. 4 Flutter Mach number behavior as a mass ( η = 0.5) is varied along the length of the plate. From left to right in ( a ), we see in ( b ) that traditional modes 1 and 2 merging drives flutter. At about s η = 0.35 flutter is due to merging of modes 2 and 3 ( c ). Between the dash... More

Fig. 5 Purely structural nonlinear behavior when base excited: ( a ) Effect of various nonlinearities on the response of a cantilever plate with no concentrated mass and forcing amplitude F a = 0.075 and ( b ) Effect of several different masses on the nonlinear inertial response with stiffnes... More

Fig. 6 LCO properties as dynamic pressure is varied: ( a ) LCO amplitudes as various nonlinear forces are included and ( b ) Corresponding LCO frequencies. Results are for M ∞ = 4 and no point mass. In ( b ), the dotted “Flutter” line indicates the linear flutter frequency. More

Fig. 7 LCO amplitudes: ( a ) and LCO frequencies ( b ) as dynamic pressure (Λ) is varied for η = 0.1 and s η = 0.9 More

Fig. 8 LCO amplitudes: ( a ) and LCO frequencies ( b ) as mass ratio η is varied (modes 1:2 merging, s η = 0.9 , Λ = 120 ) More

Fig. 9 LCO amplitudes: ( a ) and corresponding LCO frequencies and ( b ) for several different mass ratios (modes 1:2 merging, M ∞ = 3, s η = 1 ) More

Fig. 10 LCO amplitude hump mode and the effect of varying Mach number (modes 1:2 merging, η = 0.1, s η = 1 ) More

Fig. 11 Flutter mode shapes when the flutter mechanism is due to modes 1:2 merging (blue line), modes 2:3 merging (red line), and modes 3:4 merging (green line) (Color version online.) More

Fig. 12 LCO amplitudes: ( a ) and LCO frequencies and ( b ) as dynamic pressure Λ is varied when flutter mechanism is due to modes 2:3 merging ( η = 0.5, s η = 0.7 , 6 modes). FOPT stands for First-Order Piston Theory aerodynamics only. More