Linear Vibration of Functionally Graded Beams in Contact With an Inviscid Incompressible Fluid

Abstract

Abstract In this paper, a finite element formulation to analyze the free vibration response of functionally graded beams interacting with a finite fluid domain is presented. The finite element model of the beam is based on the Third-order Shear Deformation Theory, while the equations of motion are obtained by means of Hamilton’s principle. Additionally, the Functionally Graded Material (FGM) is considered to vary by means of the power-law distribution and that the volume variation of the constituents is only along its thickness coordinate. The constituents are considered in the elastic regime and the beam is subjected to small deformations. The fluid domain is assumed as an inviscid incompressible fluid. The contact between the beam and the fluid generates a coupling between their corresponding finite element models, and this interaction is considered by means of an added mass approach. Numerical comparison with results available in the literature is made, to validate the presented formulation. Additionally, to illustrate the behavior of the functionally graded beams interacting with an inviscid fluid, natural frequencies and vibration modes, for different ratios of fluid density to solid density and length to height, are presented.