A novel analysis method for calculating nonlinear Frequency Response Functions

The paper asserts that nonlinear drive frequencies are unique solutions obtained by cutting a synthesized nonlinear frequency-response surface with a constant-force plane, but it does not provide a rigorous uniqueness proof; it relies on numerical solution of a quartic and demonstrations (Eq. (12)–(15), (38)–(39)) without formal conditions ensuring single-valuedness along the resonant branch . The candidate model supplies a correct uniqueness argument under standard SISO, single-mode, amplitude-dependent FRF assumptions by showing the level-set equation reduces to a strictly unimodal function of frequency and is strictly monotone on each side of its minimum; it also offers a clean SDOF quartic-in-ω anchor consistent with the paper’s setup. The only mismatch is that the model places the imaginary modal-constant B(X) as an additive term in the denominator shift Δ, whereas in the paper B(X) belongs to the numerator (modal constant), not the denominator; this does not undermine the core monotonicity/uniqueness argument but should be corrected for notational fidelity (cf. Eqs. (22), (28), (36)–(39) ).