Investigations On Size-dependent Mechanical Behaviors Of PZT/PLZT Micro-Beams

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.