<p>Fluid-structure interaction is an important research area in engineering. One of the main reasons is that this phenomenon is presented in both natural and man-made structures. Making some assumptions, the complexity of these structures can be reduced to simpler elements, like beams, plates, or shells. Generally, these structural elements are made of steel; however, due to the demand of greater structural efficiency in many engineering sectors, as in the case of the aerospace or biomedical industries, the use of other materials has been considered. One of these alternatives are the Functionally Graded Materials (FGMs), which are a mixture of two of more materials with a continuous smooth variation of their mechanical properties along one-direction or more. Furthermore, the fluid that interacts with these structural elements can be modeled using different approaches. In cases where the velocity is very small, the fluid can be considered as inviscid. For the reasons aforementioned, 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 (where a shear correction factor is not needed), while the equations of motion are obtained by means of Hamilton’s principle. Unlike the isotropic materials, where the equations of motion are uncoupled of the axial direction, the inhomogeneity of the functionally graded materials causes an axial-bending coupling effect of the equations of motion; a simple way to take this effect into account is to consider the axial displacement. Additionally, the 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, where the fluid effect is taken into account as an additional mass in the mass matrix of the structure’s finite element model. 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.</p>

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

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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