On the application of polynomial and NURBS functions for nonlocal response of low dimensional structures

Details On the application of polynomial and NURBS functions for nonlocal response of low dimensional structures On the application of polynomial and NURBS functions for nonlocal response of low dimensional structures

2012-03-17

arxiv.org/abs/1203.3872v1

Mathematics

Numerical Analysis

29 pages, 6 tables, 10 figures

Scientific paper

In this paper, the axial vibration of cracked beams, the free flexural vibrations of nanobeams and plates based on Timoshenko beam theory and first-order shear deformable plate theory, respectively, using Eringen's nonlocal elasticity theory is numerically studied. The field variable is approximated by Lagrange polynomials and non-uniform rational B-splines. The influence of the nonlocal parameter, the beam and the plate aspect ratio and the boundary conditions on the natural frequency is numerically studied. The influence of a crack on axial vibration is also studied. The results obtained from this study are found to be in good agreement with those reported in the literature.

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