A novel approach to quantitative predictions of high-frequency coupled vibrations in layered piezoelectric plates

Abstract

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.