中文摘要：

针对一维三振子周期结构,导出了系统无量纲色散方程.利用奇异性理论证明,色散曲线的拓扑结构不随刚度参数和质量参数的变化而变化,并由此给出带隙起止频率的计算公式.以此为基础提出带隙设计方法,并用等刚度和等质量两类例子进行了验证.本文方法也可用于声子晶体和光子晶体的带隙设计.

英文摘要：

Dimensionless dispersion curve equation of one-dimensional periodic structure with three oscillators is deduced. It is proved by singularity theory that the topology of the dispersion curves does not change with mass and stiffness parameter. Then the equations of initial and final frequencies of the bands are presented. The method of band gap design is gained consequently. Two examples i.e., the system with the same stiffness and the system with the same mass, are given to verify it. The method may provide the reference for designing the band gap of the photonic and phononic crystals.