Dynamic behavior of nonuniform functionally graded Euler-Bernoulli beams under multiple moving forces

Abstract

The dynamic behavior of nominiíonii Euler-BemouUi beams made of trans- versely íunctìonally graded matenal under multìple moving íorces is studied by the finite element method. The beam cross-section is assumed lo vaiy in the wídth dứection by two diííerenl types. A simple hnile element íormidation, accounting for variation of the mate- rial properties through the beaưi thickness and the shiít in the physically neutral surtace, is derived and employed in the study. The exact varíabon of the cross-sectional protile is employed ưi evaluation of the element stiỉhìess and mass matrices. The dynanuc response of the beam is computeđ with the aid of the impUcit Newmaxk melhod. The ruinerical results show that the derived finite elemenl íonnulation is capable to assess accurately the dynamỉc characteristics of the beam by using just several elcments The effect of the moving spccd, matcrial inhomogencity and scction proẼle on the dynamic bchavior of ổte beams is investigated. The inũuence of the distance between the íorces as well as the number of ÍOKes on the dynamic response is also examined and highlightcd.