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arXiv · 1203.3872

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

S. Natarajan·T. Rabczuk·S. Bordas·D. Roy Mahapatra
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Abstract

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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S. Natarajan, T. Rabczuk, S. Bordas, D. Roy Mahapatra. 2012-03-17. On the application of polynomial and NURBS functions for nonlocal response of low dimensional structures. https://arxiv.org/abs/1203.3872

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