Abstract:  Based on the dynamic simulation of the arch thin shell, an optimal design model for the thickness of the constraint damping layers is proposed for minimizing structural vibration and noise with the weight constraints. The K-S function is adopted to obtain the vibration acceleration level (VAL), which is used as the evaluation parameter to measure the reduction effect of vibration and noise. The response surface methodology (RSM) is used to fit the VAL. The error testing is used to find a better response surface curve fitting, whose fitting is more accurate by narrowing the scope of the variable appropriately to adjust the errors. After using the Quadratic Programming for the optimization model, the
first natual frequency of the structure is increased by 22.97\%, the VAL of the structure is reduced by 12.96\%, and  the whole structure sees a great improvement.