On The Size-Dependent Mechanical And Electro-Mechanical Properties Of The Partially Covered Laminated Micro Components

Microbeam/plate are the basic components of the micro electro mechanical system.The performance of theses devices are highly dependent on the mechanical and electro-mechanical responses of the microbeam/plate.Due to have no material length-scale parameters,classical theory fails to explain it.The strain gradient elasticity theory is proposed to describe the size effects.The strain gradient elasticity theory is applied widely to develop the size-dependent monolayer or bilayer beam and plate models.Few models are focused on the mechanical and electro-mechanical responses of the partially covered laminated beam or plate.The simplified strain gradient theory is used to establish the size-dependent partially covered laminated beam or plate models.However,due to contain only part of the strain gradients,the simplified strain gradient theory underestimates the size-dependent mechanical and electro-mechanical responses of the partially covered laminated beam or plate.Therefore,to accurately predict the mechanical and electro-mechanical responses of the partially covered laminated beam or plate,it is urgent to develop the size-dependent partially covered laminated beam or plate models with all the strain gradients.This research focuses on the mechanical and electro-mechanical responses of partially covered laminated beam or plate.Based on the general strain gradient theory with independent material length-scale parameter and the isotropic flexoelectric theory,we establish the size-dependent partially covered laminated beam or plate models.The size-depedent responses of the mechanical and electro-mechanical responses are discussed.The research contents are as follows:The relations and differences between the general strain gradient theory and the simplified theories are discussed.By ignoring some strain gradients,the general strain gradient theory respectively reduces to the classical couple stress theory and the simplified strain gradient theory.The reduction relation between the general strain gradient elasticity theory and the simplified theories is confirmed.Then,these theories are used to establish the size-dependent bending and vibration models of the microbeam?buckling and tensle models of the microbar.The size-dependency of the static deflection,vibration frequency,buckling load and tensile strain is discussed.The differences of the strain gradient elasticity theory and the reduced theories in describing the size effects are revealed.Results show that compared with the the general strain gradient theory,the reduced theories predict larger deflection and tensile strain while smaller frequency and buckling load.The reduced theories underestimate the size effects.Therefore,the general strain gradient theory are more suitable to describe the size effects.Based on the general strain gradient theory,the size-dependent bending model of partially covered laminated microbeam is developed.The size dependency of bending deflection under different load and boundary conditions is discussed.The effects of the material length-scale parameter,the thickness and length of the laminated region on the deflection are analysed.Results reveal that the static bending responses of the beam are size-dependent.The deflection is dependent on the ratio of the material length-scale parameter and the thickness.In addition,the thickness and length of the laminated region is important for the deflection.For a clamped-clamped microbeam under the uniform distributed load,when the thickness of the laminated region is fixed,the increase of the length makes the deflection first increase and then decrease.The deflection achieved the maximum value when the thickness ratio is taken as 1 and length ratio is taken as 0.78.The variation trend of the static deflection with the laminated region offers the theoretical guidance for the structure optimum of the partially covered laminated microbeam.Based on the general strain gradient theory,the size-dependent bending model of the partially covered laminated microplate is developed.The size-dependent bending responses of plate under different boundary conditions are studied.The effects of the material length-scale parameter,the thickness and length of the laminated region on the deflection are analysed.Results show that the variation of bending deflection of the plate is dependent on the ratio of the thickness and the length scale parameter,and shows size dependency obviously.In addition,the thickness and length of the laminated region play an important role on the plate deflection.For a clamped-clamped microbeam under the uniform distributed load,when the thickness of the laminated region is fixed,the increase of the length makes the deflection first increase and then decrease.The deflection achieved the maximum value when the thickness ratio is taken as 1 and length ratio is taken as 0.85.The variation law of the deflection with the length and thickness of laminated region offers the theoretical basis for the structure deign of the partially covered laminated microplate.Based on the general isotropic flexoelectric theory,the flexoelectric response model of the partially covered laminated microbeam is developed.The direct and inverse flexoelectric process of the beam is discussed.Using the Method of Weighted Residuals,the high order partial differential equation is solved.The analytical expressions of the deflection,polarization and electric potential including the flexoelectric effects,the strain gradient effects and the polarization gradient effects are derived.The size-dependent bending response of the beam under different boundary conditions and the voltage is studied.Results show that the charge,the polarization,the electric potential and the deflection induced in the flexoelectric response process show size dependency.In the direct flexoelectric process,the induced charge,the polarization and the electric potential increase with the increase of the ratio of the beam thickness and the material length-scale parameter.In the converse flexoelectric process,the generated deflection is dependent on the ratio of the beam thickness and the material length-scale parameter.Moreover,the direction of the deflection is decided by the positive or negative of the applied voltage.The proposed size-dependent models of the mechanical and electro-mechanical responses of the partially covered laminated microbeam or plate can offer theoretical basis for the experiment study and structural design of the partially covered laminated components.