جستجوی مقالات مرتبط با کلیدواژه « surface elasticity theory » در نشریات گروه « مکانیک »

In this paper, buckling analysis of functionally graded rectangular Nano-plates considering the surface effect is investigated. Also, to define the material properties the Mori-Tanaka scheme is used which according to this scheme the material properties change continuously along the thickness direction. Displacement field is obtained using modified shear deformation theories. In these theories, against classical plate theory, the effects of rotary inertia and transverse shear deformations are considered and various functions such as exponential, trigonometric, hyperbolic and parabolic functions are used to considering these effects along the thickness direction. To considering nonlocal and surface effects the nonlocal elasticity theory and surface elasticity theory are employed respectively. The governing equations of motion are obtained by Hamilton’s principle and the Galerkin method is used to solve these equations. To show the accuracy of the present formulations, the presented results in this thesis are compared with those reported in the literature. Finally, the effects of various parameters which is related to the surface parameters such as residual surface stress, surface elasticity constant and also other parameters such as thickness ratio, aspect ratio, material index and nonlocal parameter of functionally graded nano-plate are investigated.

In the present paper, free axial vibration behavior of functionally graded nanorods is studied using the surface elasticity theory. For modelling of free axial vibration of nanorods, the Simple theory of rods is implemented. Besides using the Simple theory of rods, the surface elasticity theory is used for considering the surface energy parameters in the governing equations and boundary conditions. The surface energy parameters are the surface elasticity, the surface density, and the surface residual stress. The surface and bulk material properties of nanorod are considered to vary in the length direction according to the power law distribution. Then, the governing equation of motion and boundary conditions of nanorod are derived using the Hamilton’s principle. Due to considering the surface energy parameters, the obtained governing equation of motion becomes non-homogeneous. But in none of the previous researches, for example investigation of free transverse vibration of nanobeams and free torsional vibration of nanorods in presence of the surface energy, the surface energy parameters do not cause the non-homogeneity of the governing equation or the boundary conditions. To extract the natural frequencies of the nanorod, firstly the non-homogeneous governing equation is converted to a homogeneous one using an appropriate change of variable, and then for clamped-clamped and clamped-free boundary conditions the governing equation is solved using Galerkin method. In order to have a comprehensive research, effects of various parameters like the length and radius of nanorod on axial frequencies of functionally graded nanorod is investigated.