การหาพารามิเตอร์ของระบบระดับความเสรีขั้นเดียวไม่เชิงเส้นที่ถูกเหนี่ยวนำให้เกิดการสั่นสะเทือนด้วยกระแสหมุนวนของกระแสลม

Abstract

This study presents a method for identifying the nonlinear parameters of a structure subjected to wind-induced vibrations caused by vortex shedding. It highlights the differences in natural frequencies between systems modeled using linear and nonlinear mathematical approaches. In this research, the Scanlan model, a nonlinear aerodynamic model, was selected due to its ability to provide more accurate results than linear models.  To estimate the nonlinear parameters of the system, the Volterra series was applied as a theoretical framework to design for a target natural frequency. Partial results based on the Scanlan model showed that this parameter estimation method produced accurate outcomes. Furthermore, the aerodynamic stiffness parameter, which was additionally considered in the nonlinear model, was determined using the damped natural frequency method in conjunction with the Volterra series, also yielding precise results.  Using assumed parameter values, the natural frequency of the system based on the linear model was found to be 84.01 rad/sec, while the nonlinear model produced a natural frequency of 85.18 rad/sec, reflecting a 1.37% difference. This discrepancy arises from the inclusion of aerodynamic stiffness during structural vibration in the nonlinear model, which increases the system’s natural frequency compared to the linear model that only accounts for structural stiffness. This principle can be applied to avoid structural damage caused by resonance when the structure vibrates at its natural frequency due to wind excitation. Alternatively, it can be used constructively—for example, in bladeless wind turbines where controlled vibrations are used to generate electricity with high precision in determining the output frequency.