An extended polynomial approach for modeling the effect of electrode thickness in piezoelectric sandwich plates

Abstract In this work, we introduce a semi-analytical modeling framework that extends the polynomial approach to investigate the vibrational behavior of circular MEMS resonators with axisymmetric sandwich configurations. By explicitly accounting for the finite thickness of metallic electrodes, the structure is partitioned into three separate regions. Each region’s mechanical displacement fields are expanded using tailored polynomial series, assisted by window functions that ensure proper continuity and physical representation across interfaces. This method enables accurate tracking of wave propagation phenomena and captures the distinct characteristics introduced by each region. The developed model is validated through comparison with benchmark results from existing literature using both modal and harmonic analyses. To explore its relevance, the influence of electrode thickness ratio on key performance metrics, such as resonance frequencies (RFs), antiresonance frequencies (AFs), and the dynamic electromechanical coupling factor k , is systematically examined. The analysis reveals a noticeable sensitivity of k to electrode thickness, with possible enhancements as the metal layer becomes more substantial. Additional studies on impedance spectra and displacement distributions confirm these observations, offering valuable insights into the design optimization of circular piezoelectric resonators for enhanced MEMS device performance.