Lagrange's formalism for modeling of a triaxial microaccelerometer with piezoelectric thin-film sensing

Lagrange's equation has been used to construct a dynamic model of a triaxial microaccelerometer with piezoelectric thin-film sensing. A practical and representative structure is used throughout instead of the more usual spring-mass type simplified model. The elastic properties of both the silicon substrate and the PZT thin film are included by use of the laminated plate theory. The three out-of-plane bending motions of the accelerometer, symmetric, antisymmetric, and torsional, are analyzed. The accuracy of the dynamic model is confirmed by finite element analysis. The dependence of structural parameters on the characteristics of the accelerometer for two-end supported structures is discussed. The results show that the model gives close insight into the structural design of the triaxial microaccelerometer and will be a useful tool for the design, analysis, optimization, and characterization of a range of microaccelerometer devices, especially with regard to parameter optimization, and a tradeoff between sensitivity and resonant frequency.