Based on the idea of the ICM method (Independent, Continuous and Mapping) and the SIMP method, topology optimization problem with the smallest structural weight and only dynamic response constraints on the specified locations is investigated under white-noise force excitation.In order to control the change quantity of topologic design variables, new dynamic response constraints limits are formed and introduced into the optimization model at the beginning step of each sub-loop iterations.At the same time, this paper introduces a reasonable model of the rational approximation of material properties (RAMP) in the pseudo-density method and removes the approximate zero density elements to avoid the occurrence of localized modes.Moreover, the element deletion and adding criterion and a set of structural optimization strategies are given.Some elements with artificial material property are inserted around the cavities and boundaries of the structure optimized to get a non singular structure and realize the function of element restoring.At last, the dual programming method is used to solve the optimization problem.The two topology optimization examples are solved to demonstrate the method is correct and effective.