Parameter optimization of fractional Maxwell viscoelastic system based on RSM model

Viscoelastic materials have been successfully used in shock absorbers of engineered vehicles because of their low cost and good cushioning effect. Aiming at the conundrums of excessive computational complexity and difficult parameter optimization of fractional order viscoelastic models, the response surface agent model is introduced to replace the displacement response of the Maxwell fractional order viscoelastic oscillator with fluid characteristics. Firstly, a fractional-order Maxwell viscoelastic model is established by integrating fractional order modeling with a viscoelastic oscillator. Secondly, the Latin hypercube method is used to collect samples, and the natural frequency, damping ratio, and order of the model are selected as design variables to build a secondary response surface proxy model. Finally, the displacement response of the model and the hysteresis area of the constitutive model are taken as the optimization objectives for multi-objective optimization. The results show that the displacement response decreases by approximately 32.6% and the hysteresis area increases by about 25% after the quadratic response surface proxy model is used to proxy the fractional order model and the parameters are optimized.