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

Area of Science:

• Mechanical Engineering
• Nonlinear Dynamics
• Structural Analysis

Background:

• Engineering structures often exhibit asymmetric nonlinear behavior, posing challenges for dynamic characteristic analysis.
• Accurate parameter identification is crucial for understanding and predicting the response of these systems.

Purpose of the Study:

• To compare the effectiveness of four parameter identification methods for asymmetric nonlinear systems.
• To evaluate the accuracy of Hilbert transform, zero-crossing, direct quadrature, and wavelet transform methods.

Main Methods:

• Obtained backbone, envelope, and restoring force curves using Hilbert transform, zero-crossing, direct quadrature, and wavelet transform from free vibration data.
• Estimated stiffness parameters using nonlinear curve fitting and damping parameters using linear least square fitting.
• Validated methods with the Helmholtz-Duffing oscillator and a nonlinear vibration absorber with geometric imperfections.

Main Results:

• All four methods successfully extracted dynamic characteristics from free vibration time history.
• Parameter estimation accuracy varied among the methods, with detailed discussion on advantages, disadvantages, and deviations.
• The Helmholtz-Duffing oscillator and imperfect nonlinear vibration absorber served as effective validation models.

Conclusions:

• The study provides a comparative analysis of parameter identification techniques for asymmetric nonlinear systems.
• The findings aid in selecting appropriate methods for analyzing complex structural dynamics.
• Understanding method-specific deviations is key for reliable parameter estimation in engineering applications.