Flutter Boundary Identification from Time-Domain Simulations Using the Matrix Pencil Method

ck Complex amplitude in a Prony series m Mass per unit span Iα Sectional moment of inertia L Matrix pencil parameter M Model order N Number of interpolated samples Sα Static unbalance sk Complex exponent in a Prony series Vs Flutter speed index M Prony series extraction matrix Y = UΣVT Singular value decomposition of the matrix Y ŷ Aeroelastic modal amplitude samples y Interpolated samples Y Matrix of interpolated sample values αk Damping of mode k in the Prony series Λ Diagonal matrix of eigenvalues/exponential terms M = ΨΛΦ Eigenvalue decomposition of the matrix M ρ Aggregation parameter ωk Frequency of mode k in the Prony series (·)+ Moore–Penrose inverse ◦ Hadamard component-wise product