Fractional Equivalent Linearization Method For Hysteretic Nonlinear Random Vibrations

In civil engineering,due to the randomness of excitation and structural characteristics,there are a large number of random vibration phenomena in actual engineering.The structure is generally exposed to various uncertain loads,such as vehicle loads,wind loads,earthquakes,etc.Due to external load uncertainty and nonlinearity of the structural materials,it is difficult to accurately predict safety in actual engineering.problem.The traditional stochastic equivalent linearization simplified model often has problems such as large error,low precision and complicated calculation in explaining the structural hysteresis system.Simplicity is important.Based on stochastic vibration theory and fractional calculus theory,considering the complexity of stochastic uncertainty and hysteresis nonlinearity,a fractional order equivalent linearity is proposed by combining fractional order theory with equivalent linearization theory.The method simplifies the numerical calculation steps.It is provided in the field of civil engineering to solve the structural hysteresis nonlinear problem.A useful reference.The specific research contents are summarized as follows:(1)A fractional-order equivalent linearization method is proposed to improve the computational accuracy of the random vibration response of the structure,which makes the calculation result more accurate and the error is smaller.A fractional-order equivalent linearization method for Duffing oscillator is proposed.The formula of the displacement response variance of Duffing oscillator under Gaussian white noise is derived,which greatly improves the accuracy of the calculation results.(2)The fractional-order equivalent linearization method of bilinear hysteresis model is proposed.The equivalent linear equations of rigid plastic hysteresis model and slip rigid plastic hysteresis model are established by this method,and the random equivalent linearity is solved.The method has a large error,for the bouc-wen hysteresis model,the fractional-order equivalent linearization method of the smooth hysteresis model is established by introducing the description function and the fractional calculus theory.The method has better accuracy and higher computational efficiency.