- International Journal of Engineering and Applied Sciences
- Vol: 9 Issue: 4
- Novel Weak Form Quadrature Element Method for Free Vibration Analysis of Hybrid Nonlocal Euler-Berno...
Novel Weak Form Quadrature Element Method for Free Vibration Analysis of Hybrid Nonlocal Euler-Bernoulli Beams with General Boundary Conditions
Authors : Wang Xinwei
Pages : 65-75
Doi:10.24107/ijeas.356197
View : 9 | Download : 3
Publication Date : 2017-12-27
Article Type : Research
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. C ase 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