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

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.