Abstract
The Legendre polynomial method has been extended to the modeling of MEMS resonator disc partially covered with electrodes. The disc has been divided into two areas: one with electrodes and the other without electrodes. For each area, The Maxwell equations and the piezoelectric constitutive equations of motion are studied and solved to yield a frequency response and electrical behavior of the MEMS resonator applying a semi analytical method based on a Legendre polynomials series and trigonometric functions. However, the method allows incorporating the boundary conditions directly into the governing equations by assuming position-dependent of elastic constants, mass density and delta functions. The alternating electrical source is described by specific terms which are also introduced into the equation of motion. The formalism has been developed which allows for both harmonic and modal analyses. In order to validate our polynomial approach, numerical results are presented such as resonant and anti-resonant frequencies, electric input admittance, electromechanical coupling coefficient and field profiles of fully and partially metallized PZT5A resonator discs. The results obtained were compared with those obtained by an approximated analytical method. The developed software proves to be very efficient to retrieve the contour modes of all orders.
Highlights
When a piezoelectric material is subjected to a mechanical strain, electrical charges were generated and
This phenomenon was widely exploited in various engineering applications such as Micro-Electro-Mechanical systems (MEMS) technology
The vibration characteristics of piezoelectric materials are extracted from the piezoelectric constitutive equations, linear piezoelectricity and the Maxwell equations [7,8]
Summary
When a piezoelectric material is subjected to a mechanical strain, electrical charges were generated and This phenomenon was widely exploited in various engineering applications such as Micro-Electro-Mechanical systems (MEMS) technology. Kharouf et al [11] studied the vibrational axisymmetric characteristics of hollow cylinders and disks made from piezoelectric materials by using the Rayleigh-Ritz method. These methods give accurate results especially for simple geometries. Legendre polynomial method is one of the most methods used recently to check the electrical response of piezoelectric resonators and gives excellent precision for various structures [14,15,16,17,18,19,20,21]. Centralized area is electroded whereas the annular area is free of electrodes
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call