A boundary element solution for free vibration of FGM beams

Resumo

The main purpose in this article is to derive a new solution based on Boundary Element Method (BEM) for dynamic analysis of Euler-Bernoulli beams made of composites such as Functionally Graded Materials (FGM) that have properties that vary continuously through the thickness direction according to the volume fraction of constituents. In contrast, laminated composite materials are oriented plies bonded together, where each ply may be made of a different material. A boundary element solution for any problem is obtained using integral equations and fundamental solutions defined on continuum, and algebraic equations for the discretized problem. In this paper, original discussions on deriving both integral equations and fundamental solutions for dynamic composite beam problems are properly made. Algebraic representation is also obtained, incorporating rigid and elastic end supports into the BEM solution. Numerical results of different cases of mechanical properties and boundary conditions are considered and compared to other published works.