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 : 13 | Download : 5

Publication Date : 2017-12-27

Article Type : Research Paper

Abstract :A novel weak form quadrature element method insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(GLL); nodes are explicitly given by using the nodal quadrature method together with the differential quadrature insert ignore into journalissuearticles values(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