The optimal design is studied for a type of one-dimensional dissipative metamaterial to achieve broadband wave attenuation at low-frequency ranges. The complex dispersion analysis is made on a super-cell consisting of multiple mass-in-mass unit cells. An optimization algorithm based on the sequential quadratic programming method is used to design the wave suppression of target frequencies by coupling multiple separate narrow bandgaps into a broad bandgap. A new objective function is proposed in the optimization process for a continuous bandgap. Then, the continuous frequency range with low-wave transmissibility is optimized to achieve the maximal width of bandgap. The stiffness optimization of super-cell gives the broad bandgap from 10 Hz to 22.9 Hz at low-frequency ranges. In addition, numerical simulations are conducted for a type of dissipative metamaterial composed of a finite number of periodicities. The level of vibration isolation can be tuned by adjusting a critical value in the optimization scheme. The wave suppression in the numerical simulation well coincides with the obtained bandgaps and verifies the optimization results.

研究了一种一维耗散超材料的优化设计，以在低频范围内实现宽带波衰减。复杂色散分析是在由多个质量质量单位单元组成的超级单元上进行的。一种基于序列二次规划方法的优化算法通过将多个分离的窄带隙耦合成一个宽带隙来设计目标频率的波抑制。在连续带隙的优化过程中提出了一个新的目标函数。然后，优化具有低波透射率的连续频率范围，以实现带隙的最大宽度。超级电池的刚度优化在低频范围内提供了从 10 Hz 到 22.9 Hz 的宽带隙。此外，对一种由有限数量的周期性组成的耗散超材料进行了数值模拟。可以通过调整优化方案中的临界值来调整隔振水平。数值模拟井中的波浪抑制与得到的带隙相吻合，验证了优化结果。