Theoretical And Experimental Studies Of Elastic Size Effects Of Micro-scale Beams And Plates

With the development of the material science,micromachining technology and microelectronic technology,micro electro mechanical system(MEMS)appeared and has been applied in many fields.The basic components of the MEMS are micro-beams,micro-plates,micro-shells,micro-films and so on,whose geometric feature size is in the scale of micron/sub-micron.While the geometric feature size of the micro-structures is at the scale of micron/sub-micron,the physical and mechanical properties of the micro-structures are very different from the macrostructures,which vary with the decrease of the geometric size,called the size effect.Recent years,the size effect of the micro-structures in the elastic range has been observed in the static experiments about the polymer and silicon microbeams.As the classical continuous mechanical theory cannot predict the micro-scale effect of the micro-structures,the non-classical continuous theories have been developed which contain additional material length scale parameters,including the modified couple stress theory(MCST)and the strain gradient elasticity theory(SGT).Now,the theoretical and experimental studies on the elastic size effect of the micro-structures have been a hot research topic in the field of micro/nano mechanics.With the background of the elastic size effects of micro-structures,based on the modified couple stress theory and the corresponding beam/plate' deformation theory,this paper investigates the steady wave propagation,thermal buckling and vibration of functionally graded(FG)microbeams and the static bending and free vibration of FG microplates.In the other hand,we study the size effects on dynamic behavior of metal microbeam experimentally for the first time based on the laser Doppler vibrometer.The main research works of this dissertation are as folllows:1.We develop a micro-scale FG beam model for steady wave propagation accounting for the higher-order inertia and elastic foundation based on the MCST and the Bernoulli-Euler beam theory.A discrete relationship between the phase velocity and the wave number of FG microbeams and the numerical results are obtained.It reveals that the functionally graded index and the material length scale parameter have important influences on the steady wave propagation of FG microbeams.2.Thermal buckling and vibration of FG microbeams in high temperature environment are investigated.The equations of motion and the corresponding boundary conditions of FG microbeam for thermal behaviors are derived based on the MCST and the sinusoidal shear deformation theory by the Hamilton's principle.Three kinds of temperature distributions and temperature-dependent properties are taken into consideration in this model.The governing equations are solved analytically and numerically by using the Navier procedure and differential quadrature method(DQM)respectively.Numerical examples are performed for demonstrating the influences of temperature distribution,beam thickness,material length scale,slenderness ratio,shear deformation,functionally graded index,boundary conditions and temperature dependent/independent properties on thermal buckling and free vibration behaviors of FG microbeams.3.We presents a size-dependent FG micro-plate model based on the MCST.The model proposed accounts for both shear and normal deformation effects by a parabolic variation of all displacements across the thickness,and satisfies the zero traction boundary conditions on the top and bottom surfaces of the micro-plate.The equations of motion and related boundary conditions are derived from Hamilton's principle.Closed-form solutions for static bending and free vibration analysis are obtained for a simply supported rectangular micro-plate.Numerical examples are presented to investigate the influences of the functionally graded index,material length scale parameter,plate's thickness,shear and normal deformation effects on the mechanical characteristics of the FG micro-plate.The results demonstrate that the inclusion of the size effects results in an increase in the micro-plate's stiffness,and consequently,leads to a reduction of deflections and an increase in natural frequencies,while the shear and normal deformation effects are just the opposite.4.The size-dependent elasticity of a series of nickel cantilever microbeams is investigated experimentally for the first time.The experimental results reveals that the dimensionless natural frequencies of the cantilever microbeams increase to about 2.1 times with the beam thickness decreasing from 15 to 2.1 ?m.Furthermore,based on the SGT and MCST and by using the DQM and the least square method(LSM),the experimental results are interpreted and the material length scale parameters in the scale of micron in elastic range are obtained.Compared to the value of the material length scale of epoxy microbeams,the value of the material length scale of nickel microbeam is smaller than one-tenth of that of epoxy microbeam,it reveals that the material length scale parameters have important relationship with the material's micro-structure.In conclusion,this dissertation investigates the elastic size effects of micro-structures theoretically and experimentally,and it will be useful and helpful for the theoretical and numerical simulation of micro-structures and important for the design of the MEMS.