Waves dispersion in an imperfect functionally graded beam resting on visco Pasternak foundation

What is it about?

This article investigates the effect of viscoelastic foundations on the waves' dispersion in a beam made of ceramic metal functionally graded material (FGM) with microstructural defects. The beam is considered to be shear deformable, and a simple three unknown sinusoidal integral higher order shear deformation beam theory is applied to represent the beam’s displacement field. Novel to this study is the investigation of the impact of viscosity damping on imperfect FG beams, utilizing a few unknowns theory. The stresses and strains are obtained using the two dimensional elasticity relations of FGM, neglecting the normal strain in the beam’s depth direction. The variational operation is employed to define the dispersion relations of the FGM beam. The influences of the material gradation exponent, the beam’s thickness, the porosity, and visco Pasternak foundation parameters are represented. Results showed that phase velocity was inversely proportional to the damping and porosity of the beams. Additionally, the foundation viscous damping had a stronger influence on wave velocity when porosity volume fractions were low.

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Photo by Joris Berthelot on Unsplash

Photo by Joris Berthelot on Unsplash

Why is it important?

the present study investigates the influences of the material gradation exponent, the beam’s thickness, the porosity, and visco-Pasternak foundation parameters on the wave propagation in FGM porous beams. A simple threeunknown integral higher-order shear deformation beam theory is presented in the study. Unlike the previous works in this area, the present model requires less computational cost due to the use of fewer variables. New literatureenriching results were obtained, illustrated, and discussed in this article.

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