Sharif Digital Repository

The goal of this thesis is to survey natural frequencis of nanostructures such as nanobeams and nanoplates using nonlocal theory of elasticity by finite element method. In nonlocal theory of elasticity,the constitutive relation appears as an integral form so that the stress of a point is a function of the strain of all points in the field such that by getting away from the assumed point, the effect of strains on the stress of that point decreases. In fact, the stress on a point is an average of stress in the field and the effect of stress of other points in determined by a function called the kernel function. In order to achieve natural frequencies and shape modes of a structure, we need to...