Damping treatments have been extensively used as a powerful means to damp out structural resonant vibrations[1-3].Usually, damping materials are fully or partially covered on the surface of structure[4-6].The target of parametric design for damping structure is to determine the types such as unconstrained layer damping or constrained layer damping, the number of layers, thickness of each layer and position of CLD (constrained laver damping) patches, so that vibration energy dissipation of the damping structure is maximized[7-8].They are referred to as sizing and shape optimization.However.conventional sizing or shape optimization is not always economical and effective due to a fixed topology.In order to overcome this deficiency, the topology optimization must be considered.