A Comparative Study of Parameter Identification Methods for Asymmetric Nonlinear Systems with Quadratic and Cubic Stiffness

Understanding the nonlinear dynamic characteristics of engineering structures is challenging, especially for the systems that exhibit asymmetric nonlinear behavior. This paper compared four parameter identification methods for asymmetric nonlinear systems incorporating quadratic and cubic stiffness nonlinearities. Hilbert transform, zero-crossing, direct quadrature, and wavelet transform were used to obtain the backbone, envelope, and restoring force curves from the free vibration time history. A nonlinear curve-fitting method was then applied to estimate the stiffness parameters of the asymmetric systems, and a linear least square fitting approach was utilized to estimate the damping parameters of the asymmetric systems. We used the Helmholtz–Duffing oscillator as a numerical example and a nonlinear vibration absorber with geometric imperfections to verify the feasibility and accuracy of these methods. The advantages and disadvantages of these methods and the deviations in estimated results are discussed.