摘要
The nonlinear static characteristic of a piezoelectric unimorph cantilever micro actuator driven by a strong applied electric field is studied based on the couple stress theory.The cantilever actuator consists of a piezoelectric layer,a passive（elastic）layer and two electrode layers.First,the nonlinear static characteristic of the actuator caused by the electrostriction of the piezoelectric layer under a strong applied electric field is analyzed using the Rayleigh-Ritz method.Secondly,since the thickness of the cantilever beam is in micro scale and there exists a size effect,the size dependence of the deformation behavior is evaluated using the couple stress theory.The results show that the nonlinearities of the beam deflection increase along with the increase of the applied electric field which means that softening of the micro beam rigidity exists when a strong external electric field is applied.Meanwhile,the optimal value of the thickness ratio for the passive layer and the piezoelectric layer is not around 1.0 which is usually adopted by some previous researchers.Since there exists a size effect of the micro beam deflection,the optimal value of this thickness ratio should be greater than 1.0 in micro scale.
采用偶应力理论对单层压电悬臂梁式微执行器在强外加电场作用下的非线性静态特征进行了研究.悬臂式执行器包括压电层、被动(弹性)层和2个电极层.首先,采用瑞利-里兹方法分析了在强外加电场作用下由于压电层电致伸缩效应引起的执行器非线性静态特性.其次,由于悬臂执行器的厚度在μm量级,存在变形尺度效应,采用偶应力理论对变形的尺度效应进行了分析.分析结果表明:悬臂执行器的非线性随着外加电场强度的增大而增大,当外加电场很大时,出现刚度软化现象;而且,执行器被动层和压电层厚度比的最优值不是通常采用的1.0.在微尺度下,由于微梁变形存在尺度效应,该厚度比的最优值应比1.0大.
基金
The National Natural Science Foundation of China(No.10772086,10772085)
