Abstract The two-dimensional elastic wave propagation in an infinite layered structure with nonlinear interlayer interfaces is analyzed theoretically to investigate the second-harmonic generation due to interfacial nonlinearity. The structure consists of identical isotropic linear elastic layers that are bonded to each other by spring-type interfaces possessing identical linear normal and shear stiffnesses but different quadratic nonlinearity parameters. Explicit analytical expressions are derived for the second-harmonic amplitudes when a single monochromatic Bloch mode propagates in the structure in arbitrary directions by applying the transfer-matrix approach and the Bloch theorem to the governing equations linearized by a perturbation method. The second-harmonic generation by a single nonlinear interface and by multiple consecutive nonlinear interfaces are shown to be profoundly influenced by the band structure of the layered structure, the fundamental Bloch wave mode, and its propagation direction. In particular, the second harmonics generated at multiple consecutive interfaces are found to grow cumulatively with the propagation distance when the phase matching occurs between the Bloch modes at the fundamental and double frequencies.

中文翻译：

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具有非线性弹簧型界面的无限分层结构中二维弹性波传播的二次谐波产生

摘要 从理论上分析了具有非线性层间界面的无限层状结构中二维弹性波的传播，以研究界面非线性引起的二次谐波的产生。该结构由相同的各向同性线性弹性层组成，这些层通过具有相同线性法向刚度和剪切刚度但二次非线性参数不同的弹簧型界面相互结合。当单个单色布洛赫模式在结构中以任意方向传播时，通过将传递矩阵方法和布洛赫定理应用于由微扰方法线性化的控制方程，可以推导出二次谐波幅度的显式解析表达式。由单个非线性界面和多个连续非线性界面产生的二次谐波被证明受到层状结构的能带结构、基本布洛赫波模式及其传播方向的深刻影响。特别是，当在基频和双频布洛赫模式之间发生相位匹配时，发现在多个连续界面上产生的二次谐波随着传播距离的增加而累积增长。