Research On The Scale Effect And Linear/Nonlinear Mechanical Properties Of Functionally Graded Nanobeams

With the micromachining technology and micro electro mechanical systems mechanics developing rapidly,MEMS has been widely used in many fields such as manufacture,aerospace,biomedicine and military for its small size,light weight and stable performance,etc.However,the negligible factors in the macrostructure may be significant in the microstructure,which leads to a strong scale effect on its mechanical properties.The classical mechanics theory can not make accurate prediction and interpretation of the scale effect for lacking the parameters describing the internal characteristics of the material.Therefore,it is necessary to develop a theory or modify a model that can describe the size effect of microstructures.In this paper,a size-dependent high-order deformable nanobeams model is proposed within the framework of the nonlocal strain gradient theory.Hamilton's principle is applied to derive the governing equations and boundary conditions.The analytical solutions of deflection,rotation,natural frequencies and the critical buckling load are obtained by using the Separation variable method for bending,vibration and buckling analysis respectively.Based on the nonlocal strain gradient theory and Hamilton principle,the nonlinear analysis model which contains a material intrinsic length and a nonlocal parameter of the functionally graded nanobeams is also derived.The present model contains the nonlocal effects of the strain field and first gradient strain field as well as high-order shear deformation effect,and its boundary conditions consist of traditional boundary conditions and high-order boundary conditions.The asymptotic expressions of load-deflection under nonlinear bending,frequency-amplitude under nonlinear vibration,and the analytic asymptotic solution of the equilibrium path under post buckling are derived from the two-step perturbation method.The results are consistent with the nonlocal continuum theory results as the material characteristic parameter is set to zero and are accord with the strain gradient theory results as the nonlocal parameter is set to zero.Parametric studies are performed to exhibit the static bending,free vibration and buckling behaviors of nanobeams with different groups of geometrical and material parameters.It is found that the nonlocal effect produces a softening effect on the stiffness of the beam while the strain gradient effect produces a hardening effect.The established model can describe the two kinds of scale effects of the micro-nanostructure well.