【作者】 陈明；

【导师】 郑世杰；

【作者基本信息】 南京航空航天大学 ， 工程力学， 2017， 博士

【摘要】 在微机电系统(MEMS)中,当构件的尺寸达到微米、亚微米量级,将出现尺寸效应,此时构件的力学行为用宏观的连续介质理论不能够准确解释。本文运用修正偶应力理论结合经典的欧拉-伯努利梁理论和层合梁理论,分析了均质、非均质PZT双晶片,均质、非均质0-1极化PLZT双晶片,0-3极化PLZT单晶片、非均质双晶片的力学行为;推导了绑定0-1极化PLZT驱动器的欧拉-伯努利梁的控制方程;分析了上述这些微米级梁结构的尺寸效应。论文的主要工作和成果如下:(1)结合修正偶应力理论和经典的欧拉-伯努利梁理论,推导了微米级欧拉-伯努利梁的本构方程;结合修正偶应力理论和经典的层合梁理论,利用哈密顿变分原理,推导了微米级层合梁的运动控制方程。(2)均质、非均质PZT双晶片是两种经典类型的驱动器。当这两种驱动器的特征尺寸达到微米量级,在外部载荷、电场作用下产生的力学行为,将明显具有尺寸效应。考虑力-电耦合效应,根据修正偶应力理论,建立了微米悬臂结构的均质、非均质PZT双晶片的力学模型,推导了两种结构在外载荷和电场作用下的本构方程;根据本构方程,给出了归一化端挠度、归一化滞阻力和归一化等效弯矩具体表达式,分析了这三个物理量随尺寸参数变化和不同基体弹性层材料变化的规律;同时,分析了弹性基体层厚度对均质、非均质PZT双晶片驱动器力学行为尺寸效应的影响。进一步,推导了微米级悬臂结构的均质、非均质PZT双晶片自由振动微分方程,给出固有频率表达式;对微米级均质、非均质PZT双晶片驱动器归一化固有频率在不同弹性基体层材料、尺寸参数的变化规律进行了分析。(3)0-1极化PLZT陶瓷在光照作用下,内部产生力-热-光-电多场耦合现象,本文分析了不同光强照射下,0-1极化PLZT光致电场、温度场的变化规律。基于修正偶应力理论,建立0-1极化PLZT均质、非均质双晶片力学模型;考虑力-热-光-电多场耦合效应,推导了在外载荷和光照共同作用下,输入物理量与输出物理量对应的本构方程。对比分析两种结构在不同基体层厚度时,归一化端挠度和归一化固有频率随尺寸参数的变化规律;对比分析两种结构,在同一尺寸参数下,归一化端挠度、归一化滞阻力和归一化固有频率随基体层厚度增加的变化规律。(4)不同于0-1极化PLZT情况,0-3极化PLZT的极化方向与光照方向相同,垂直于光照方向的光致变形量随照射深度增加而减小。因此,0-3极化的PLZT陶瓷在光照后能够自行弯曲,0-3极化PLZT陶瓷可制作成单晶片和非均质双晶片,单晶片仅包含一个0-3极化PLZT层;非均质双晶片结构由一个0-3极化的PLZT层加一个基体弹性层组成。本文分析了0-3极化PLZT陶瓷中,光致电场强度和光致电压随PLZT层厚度的变化情况;推导了考虑力-热-光-电多场耦合作用下,0-3极化PLZT单晶片和非均质双晶片的本构方程;对比分析了在不同基体材料、不同基体弹性层厚度下,两种结构的归一化端挠度、归一化固有频率随尺寸参数的变化情况。根据2、3、4中推导结果,由PZT、0-1/0-3极化PLZT组装的智能驱动器的本构方程就像个黑匣子,能够避免中间复杂的能量耦合和计算过程,直接给出外加载荷或电场、光照下,对应的输出物理量。(5)结合修正偶应力理论和经典的欧拉-伯努利梁理论,推导了绑定0-1极化PLZT光致驱动器的微米级欧拉-伯努利梁的控制方程;给出悬臂结构、简支结构、一端固支一端铰支结构和两端固支结构,四种边界条件下梁挠曲线方程的解析解;对比分析了考虑驱动器刚度和不考虑驱动器刚度下,梁最大挠度的变化情况。结果显示,忽略驱动器刚度会影响计算结果的准确性。更多还原

【Abstract】 In Micro Electro Mechanical systems(MEMS),the size effect would occur if the size of the components reaches to micron or sub micron.The mechanical properties of these components can not be explained by the macroscopic continuum Mechanics.Based on the modified couple stress theory,the classical Euler-Bernoulli beam theory and the classical laminated beam theory,the mechanical behaviors of heterogeneous and symmetrical PZT/0-1 polarized PLZT bimorphs,0-3 polarized unimorph and 0-3 polarized heterogeneous bimorph are analyzed.The control equations of the Euler-Bernoulli beam bound a 0-1 polarized PLZT actuator are derived.The size effect of these micro structures is analyzed.The main work and research achievements performed in this dissertation include:(1)Based on the modified couple stress theory and the classical Euler-Bernoulli beam theory,the constitutive equations of the micron Euler-Bernoulli beam are derived.Based on the modified couple stress theory and the classical laminated beam theory,the control equations of a micron laminated beam are derived by Hamilton variational principle.(2)Heterogeneous or symmetrical PZT bimorphs are two typical mode actuators.When the characteristic demension of the two typical structures reaches to the magnitude of micron order,the size effect of the mechanical behaviors under external loads or electric field will become obviously.Based on the modified couple stress theory and the Euler-Bernoulli beam theory,the mechanical models of heterogeneous and symmetrical PZT bimorphs are established,which considered the couple effect of the mechanical and electrical fields.These two type actuators usually are cantilever structure.The expressions of the normalized tip deflection,normalized blocking force and normalized equivalent moment are given.The change regulations of these three important physical quantities are analyzed with the different thicknesses of the elastic layers and the material length scale parameters.Further,the free vibration equations of the micro heterogeneous and symmetrical PZT bimorphs are derived.The natural frequency of the two type bimorphs with cantilever structures are supplied.The normalized natural frequency of heterogeneous and symmetrical PZT bimorphs are discussed by different materials of the elastic layers and the material length scale parameters.(3)The phenomenon of the couple of photo-induced electrical,thermal and mechanical fields can be generated in 0-1 polarized PLZT ceramics subjected to light illumination.The change regulations of the photo-induced electrical and thermal fields are analyzed under the different light strengths.Based on the modified couple stress theory and the Euler-Bernoulli beam theory,the mechanical models of heterogeneous and symmetrical 0-1 polarized PLZT bimorphs are established.The relation ships of external loads and light with output physical quantities are derived.By contrast,the change regulations of the normalized tip deflections and natural frequencies are discussed with the different material length scale parameters.Meanwhile,the change regulations of the normalized tip deflections,blocking forces and natural frequencies also are discussed with different thicknesses of the elastic layers.(4)Different from the situation of the 0-1 polarization,the polarization direction of the 0-3 polarized PLZT is the same as the direction of illumination,and the amount of elongation decreased with the depth of illumination.Therefore,the 0-3 polarized PLZT can bent by itself under a UV irradiation,can be assembled by itself and would not need a elastic layer.The 0-3 polarized PLZT heterogeneous bimorph is assembled by a elastic layer and a 0-3 polarized PLZT layer.The change regulations of the photoinduced electric field intensity and photoinduced voltage with the thickness of PLZT layer are discussed.The constitutive equations of unimorph and heterogeneous bimorph are derived by considering the couple effect of photo-induced electrical,thermal and mechanical fields.The normalized deflection and the normalized natural frequency are compared in two structures with different material length scale parameters of material.By utilizing the constituent equations derived,the intelligent structures mentioned above can be used as a black-box without involving details of the complex energy transfer processes and calculation in PZT or PLZT intelligent actuators,directly supply the output physical quantities.(5)Based on the modified couple stress theory and the classical Euler-Bernoulli beam theory,the control equations of micron Euler-Bernoulli beam bound a 0-1 polarized PLZT actuator are derived.The analytic solutions of deflection curves for the four structures including cantilever beam,simple beam,propped cantilever beam and fixed-end beam are derived.The relations between the stiffness of PLZT actuator and the maximum deflection of the beams are discussed with different ratios of the host beam and the actuator.The results show that the stiffness of the actuator will affect the accuracy of the calculation results.更多还原