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

TL;DR

This paper investigates the vibrational behavior of low-dimensional structures like beams and plates using polynomial and NURBS functions within nonlocal elasticity theory, highlighting effects of cracks, geometry, and boundary conditions.

Contribution

It introduces a numerical approach employing polynomial and NURBS functions to analyze nonlocal responses of cracked beams and nanostructures, extending existing models.

Findings

Nonlocal parameter significantly affects natural frequencies.

Cracks alter vibrational characteristics notably.

Method shows good agreement with existing literature.

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.