Nonlinear stiffness identification of parametrically excited systems based on damping adjustment

This paper presents a method for identifying the nonlinear stiffness of parametrically excited systems based on damping regulation. First, analytical amplitude-frequency response and resonance backbone curve equations are derived using the Harmonic Balance and Alternating Frequency/Time Domain approach for both single-frequency and multi-frequency parametrically excited systems. Second, the effect of system damping on the resonance response mechanism of parametrically excited systems is discussed, and the critical damping for the existence condition of parametric resonance response is calculated. Based on this, a two-step identification strategy for both time-invariant nonlinear stiffness and time-varying stiffness coefficients (i.e., parametric excitation amplitudes) is presented. Specifically, the time-invariant nonlinear stiffness parameters are identified using the resonance backbone curve derived from free decay response, and then the excitation amplitude of the time-varying parameters is estimated using the amplitude-frequency response equations. The results demonstrate that the proposed method, based on nonlinear normal modes and damping adjustment, achieves accurate parameter identification for both single-frequency and multi-frequency parametrically excited systems.