ANALYSIS OF THE LOWER MODES OF FREE VIBRATION OF A PIEZOELECTRIC CERAMIC DISK POLARIZED IN THE THICKNESS DIRECTION

By means of the adjoints method of solving the differential equations of two-point boundaryvalue problems,the equations of motion of a boundary stress-free ceramic disk vibrator polarizedin the thickness direction are solved by numerical integration.The resonance frequencies of the lowermodes of radial vibration under the influence of motion in the thickness direction and the particledisplacement distribution patterns are obtained for disks whose thickness-diameter ratios are less than0.45.Correction curves for thickness effect on fundamental frequencies are given.Curves showing.the effect of Poisson ratio on the relation between the second harmonic-fundamental ratio and thethickness-diameter ratio are also given. In the numerical calculations,piezoelectric ptoperties of the ceramic disks are fully taken intoconsideration and no restrictions are set for the dimensions of the disks.Experimental results agreewell with those obtained by calculation.     

轴向极化压电陶瓷圆片的自由振动低阶振动方式分析

本文利用解微分方程二点边值问题的伴随法,对应力自由边界条件下的轴向极化压电陶瓷圆片振子的压电运动方程进行了数值积分。求出了厚度与直径比小于0.45的振子在厚度方向运动影响下的低阶径向模的谐振频率及质点位移分布图象。给出了基频的厚度影响修正曲线及与泊松比有关的泛音比曲线。 本文的数值计算全面考虑了压电性的作用,未对振子尺度作任何限制.实验结果与计算结果很好相符。