The interface/interphase is modeled by distributed springs, and the degree of interface damage is characterized by the flexibility coefficient of the springs. Considering different degrees of damage at different interfaces, a general dispersion equation by the transfer matrix method was obtained. For the purpose of application, the transmission coefficient of finite-period phononic crystals is also derived. Additionally, the band structures and the transmission coefficients are calculated for different degrees of damage to confirm the interface effect on band gaps. A numerical simulation of the transmission coefficient is performed using the commercial FEM software Comsol Multiphysics. The numerical results obtained agree well with the analytical solution. Finally, based on a monotonic decreasing relationship between the degree of interface damage and the central frequency of band gaps and a monotonic relationship between the degree of interface damage and the amplitude of transmission coefficients, a new method how to evaluate the degree of interface damage theoretically is proposed.

中文翻译：

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界面损伤对周期性多层板能带结构的影响

界面/相间由分布弹簧建模，界面损坏程度由弹簧的柔韧性系数表征。考虑不同界面处不同程度的损伤，通过传递矩阵法得到了一般的色散方程。为便于应用，还推导出有限周期声子晶体的透射系数。此外，还计算了不同损伤程度的能带结构和传输系数，以确认界面对带隙的影响。使用商用 FEM 软件 Comsol Multiphysics 进行传输系数的数值模拟。得到的数值结果与解析解非常吻合。最后，