Examination of How Size-Effect Modifies the Stiffness and Mass Matrices of Nanotrusses/Nanoframes

Abstract

The effect of the nonlocal parameter on the free vibration analysis of nano scaled trusses and frames is examined. Accordingly, firstly, the axial and bending vibrations of the nano scaled longitudinal element are formulated. Simple rod and Euler-Bernoulli assumptions are considered for axial and bending vibrations, respectively. Finite element matrices are obtained by applying the average weighted residue to the nonlocal equation of motion for free vibration. These matrices are combined according to the freedoms of longitudinal element and the matrix displacement method is explained for structures consisting of discrete longitudinal elements. It is discussed how the classical stiffness and mass matrices are modified by the atomic parameter.

Keywords

• Free vibration
• mass matrix
• matrix displacement method
• nanoframe
• nanotruss
• nonlocal parameter
• stiffness matrix.

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