Novel Weak Form Quadrature Element Method for Free Vibration Analysis of Hybrid Nonlocal Euler-Bernoulli Beams with General Boundary Conditions

Year 2017, Volume: 9 Issue: 4, 65 - 75, 27.12.2017

Wang Xinwei

https://doi.org/10.24107/ijeas.356197

Cited By: 1

Abstract

A
novel weak form quadrature element method (QEM) is presented
for free vibration analysis
of hybrid nonlocal Euler-Bernoulli beams with general boundary conditions.
For demonstrations, the stiffness and mass matrices of a beam
element with Gauss-Lobatto-Legendre (GLL) nodes are explicitly given by using
the nodal quadrature method together with the differential quadrature (DQ) law.
Convergence studies are performed and comparisons are made with exact solutions
to show the excellent behavior of the proposed beam element. Case studies on hybrid nonlocal
Euler-Bernoulli beams
with different length scale parameters have been conducted.
Accurate
frequencies of the
beams with different combinations of boundary conditions are obtained and
presented.

Keywords

Weak form quadrature element method, hybrid nonlocal Euler-Bernoulli beam, multiple boundary conditions, free vibration

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