MATHEMATICAL MODELING FORCE-FREQUENCY CHARACTERISTICS OF THE QUARTZ RESONATORS

S.K. Pidchenko, A.A. Taranchuk, V.I. Stetsyuk

The features of the determination are considered for force-frequency characteristics of the quartz resonators which are based on the calculation of the mechanical stress piezoelectric element (PE) field under influence of the external vibration effects. Correlations, relating the tensor of mechanical tensions and tensor of mechanical deformations and equivalent them matrix expressions for the crystal of quartz, are resulted. Correlations sensitiveness of the modules resiliency of quartz crystal are certain to external mechanical influences. It is got on the basis of method eventual elements in the system of Matlab/Femlab distributing of mechanical tensions of quartz resonators for 2d- and 3d-models QR and different types of fastening of piezoelectric element.

Key words: The quartz resonator, vibrational acceleration, tensor of the mechanical pressure.