Passive free-layer damping is an effective means in vibration control,especially in the vibration suppression of automotive and commercial airplane.Damping performance of the passive layer damping structure mainly depends on the layout and physical properties of the viscoelastic damping material.In addition,the damping material is heavy and the additional mass results in higher fuel consumption and pollution.Therefore,the layout optimization of the layer damping material is necessary for the structures to obtain an optimal balance of vibration performance,the total mass of the structure and the economic efficiency.Most of the works concerning layer damping material topology optimization has concentrated on either the macro or the micro scale,while concurrent design optimization on both macro and micro scales is still limit.