中文摘要：

压电叠层复合梁是一种三叠片对称结构。这里以压电陶瓷一金属一压电陶瓷复合结构为研究对象，给出了悬臂式对称压电复合结构的压电振子弯曲振动共振频率表达式，并建立了相应的有限元模型；计算分析了压电陶瓷一金属复合梁弯曲振动的固有频率值与几何尺寸之间的关系，并与相应的有限元模态分析结果进行了比较。结果表明，两种分析方法得到的压电振子的固有频率值基本符合，计算公式和模型是精确有效的；压电叠层复合梁愈细长则表达式的计算结果愈准确。

英文摘要：

Piezoelectric laminated composite cantilever beam is a structure wtth three symmetrtcat laminate. With piezoelectric ceramic -metal -piezoelectric ceramic composite structure as research object, the bending vibration frequency expression of the piezoelectric ceramic-metal composite structure can- tilever piezoelectric vibrator is derived and its finite-element model is established.The relationship be- tween the natural frequency values and different dimension of piezoelectric ceramic-metal composite struc- ture beams are calculated and analyzed, which are compared with the results from FEM analysis.The results show that the computing value of the peizoelectric vibrator obLained from two methods are fits.The results show that calculation formula and FEM model are accurate and effective.The longer piezoelectric laminated composite beam is the more accurate calculation results of expression is.