<p>In this paper, we propose a new structural dynamic topology optimization method based on the solid isotropic material with a penalization model for the viscoelastic material considering the viscoelastic material degradation. In our research scheme, the material degradation constraint is derived to be handled as the dissipation energy upper limit constraint under two assumptions based on entropy-degradation. The finite element method is employed to obtain the structural displacement and velocity fields. Then, the adjoint variable method is brought up to derive the sensitivities of the structural dynamic compliance and the overall dissipation energy with respect to the design variables. Finally, the pseudo density design variables are optimized with the method of moving asymptotes to yield the minima of dynamic compliance. Three numerical examples with different load-cases are carried out to illustrate the validity and the stability of the proposed method, and the obtained structural topology patterns, together with the structural performance functions, are compared with those yielded without the dissipation energy constraints. In the discussion part, the influences of the volume fraction and the dissipation energy constraint values on both of the final structural topology patterns and the objective function are numerically investigated and discussed.</p>