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In this paper, the topological optimization problem considering the stability and vibration characteristics of structure is studied. Firstly, the topology optimization model with the minimum structure volume as object is established based on independent, continuous and mapping (ICM) method, which subjects to the critical buckling load and frequencies as constraints. The filter functions with composite exponential function of elemental mass matrix, elemental stiffness matrix and elemental geometric matrix would be introduced, by which the three matrixes are updated in iteration putted into the topology optimization of differential equation to analyse the design sensitivity and optimize the structure. Secondly, the optimal model is conversed into the quadratic programming with the introducing of filter functions, Taylor expansion and sensitivity analysis. And then, the mathematical model is solved by dual sequence quadratic programming (DSQP) algorithm. Finally, the bisection method is applied to reduce searching region of threshold space to find the optimal mapping from “continuous” to “discrete”. Numerical examples are given to illustrate the feasibility and efficiency of the proposed method.