Coupled-mode Zero-frequency mode or static divergence

Buckling

Before flutter

β ≤ 0, ω > 0

β ≤ 0, ω > 0

β ≤ 0, ω > 0

Flutter state

β1 = β2 = 0, ω1 = ω2 > 0

βi < 0, ωi > 0, i > 2

β1 = β2 = 0, ω1 = ω2 > 0

βi < 0, ωi > 0, i > 2

β1 = 0, βi¹1 < 0

ω1 = 0, ωi¹1 > 0

After flutter

β1 = β2 > 0, ω1 = ω2 > 0

βi < 0, ωi > 0, i > 2

β1 = β2 > 0, ω1 = ω2 > 0

βi < 0, ωi > 0, i > 2

β1 > 0, βi¹1 < 0

ω1 = 0, ωi¹1 > 0

Frequency

Ma?

ω1?

ω i¹1?

Ma?

ω1?

ω i¹1?then?

Ma?

ω?

whenMa a cr

Nx?

ω?

Ma

Macr ≤ Maf

Macr ≤ Maf

Macr = Maf

Boundary conditions

SS, CC, FF, GG,

SC

CF,SF,GF,CG,SG

GC, GS

SS, CC, FF, GG,

SC, SF, CF, GF, GC, GS