The frequency variation of vibration responses of nonlinear vibration systems is closely related to the displacement, velocity and amplitude of the vibration, which is the main feature of the nonlinear vibration systems. In this paper, a new method for identifying the stiffness of Duffing nonlinear systems is presented based on this feature. First of all, the relation between instantaneous frequency and instantaneous amplitude of the Duffing nonlinear systems is established by means of Lindestedt- Poincaré method. Then, the maximum gradient method and Hilbert transform are employed respectively to extract the instantaneous frequency and the instantaneous amplitude from the nonlinear response signals. On this basis, the least square optimization algorithm is employed to identify the linear and cubic stiffness of the Duffing nonlinear systems. The effectiveness of the proposed new method is validated via a numerical example of a nonlinear Duffing system. The results demonstrate that the new method can identify the stiffness effectively even if the response signals are contaminated by Gauss white noise.%振动响应的频率变化与位移、速度、振幅息息相关,基于非线性振动系统的这一主要特征提出一种新的识别Duffing非线性系统刚度的方法.该方法首先通过Lindestedt-Poincaré法建立Duffing非线性系统瞬时幅值与瞬时频率的关系式,然后分别采用Hilbert变换和最大坡度法提取非线性系统响应的瞬时幅值和瞬时频率.在此基础上,应用最小二乘优化算法识别非线性系统的线性和立方体刚度.通过一个Duffing非线性系统数值算例对所提出的新方法进行验证,结果表明:即使在信号被噪声干扰的情况下,该方法仍然能够有效识别Duffing非线性系统的刚度.
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