The thickness-extensional mode in layered piezoelectric plates can be inevitably interfered by some undesirable eigen-modes due to the lateral edge effect. A reported theoretical method to predict high-frequency coupled vibrations is the 2D high-order plate theory derived based on approximate dispersion relations. In this paper, based on accurate dispersion relations a novel approach called Frequency Spectrum Quantitative Prediction (FSQP) is developed to quantitatively investigate coupled vibration behaviors in piezoelectric multilayered plates operating at ultra-high frequency. Two significant sub-goals need to be achieved: one is the accurate dispersion relations of the layered structure; the other is the variational formulation for the layered plates with piezoelectric and/or elastic phases. Lastly, the objective equation, i.e., frequency spectra, describing coupling strengths between the thickness-extensional mode and unwanted eigen-modes, is derived. A reported numerical example of a piezoelectric thin-film resonator is considered to demonstrate the correctness and superiority of the proposed methodology. Mode shapes of mechanical displacements are investigated in detail to illustrate the application of frequency spectra to suppress the undesirable eigen-modes. Numerical results show that the proposed approach FSQP is efficient and more accurate than the existing 2D high-order plate theory in quantitative predictions of high-frequency coupled vibrations in layered piezoelectric plates.

由于侧边缘效应，层状压电板中的厚度扩展模式不可避免地会受到一些不希望有的本征模式的干扰。预测高频耦合振动的一种理论方法是基于近似色散关系得出的二维高阶板理论。在本文中，基于精确的色散关系，开发了一种称为“频谱定量预测”（FSQP）的新方法，以定量研究在超高频下工作的压电多层板的耦合振动行为。需要实现两个重要的子目标：一个是层状结构的精确色散关系；另一个是分层结构的精确色散关系。另一类是具有压电和/或弹性相的层状板的变形配方。最后，客观方程，即 得出描述厚度扩展模式和有害本征模式之间耦合强度的频谱。压电薄膜谐振器的报道数值示例被认为可以证明所提出方法的正确性和优越性。详细研究了机械位移的模式形状，以说明频谱抑制不想要的本征模式的应用。数值结果表明，在分层压电板高频耦合振动的定量预测中，所提出的方法FSQP比现有的二维高阶板理论更有效，更准确。压电薄膜谐振器的报道数值示例被认为可以证明所提出方法的正确性和优越性。详细研究了机械位移的模式形状，以说明频谱抑制不想要的本征模式的应用。数值结果表明，在分层压电板高频耦合振动的定量预测中，所提出的方法FSQP比现有的二维高阶板理论更有效，更准确。压电薄膜谐振器的报道数值示例被认为可以证明所提出方法的正确性和优越性。详细研究了机械位移的模式形状，以说明频谱抑制不想要的本征模式的应用。数值结果表明，所提出的方法FSQP在定量预测层状压电板中高频耦合振动方面比现有的2D高阶板理论更为有效和准确。