Vibration analysis of sandwich beams with non-uniform cross-section made of FGP core and FGM faces resting on Winkler elastic foundation

Abstract

This research proposes the complementary functions method (CFM) and the Laplace transformation to carry out the free vibration frequencies of sandwich beams resting on the Winkler elastic foundation. The beam is assumed to have a variable width and a constant height. The top and bottom faces are made of functionally graded materials (FGM) while the core has a functionally graded porous material (FGPM). The governing equations are canonical ones based on the first-order shear deformation theory. The Laplace transformation is implemented in this set of equations. The transferred equations are solved numerically by reducing them from two-point boundary value problems to initial value problems via the CFM. The comparison with the available literature shows that the CFM can be used efficiently in the numerical solution of the present class of problems. It is observed that the dependence of the natural frequencies are highly influenced by boundary conditions, spring constants, porosity functions, porosity coefficients, face-core-face layer ratios, length/height ratios, and material gradient index. Notably, as the non-dimensional Winkler spring constants increase, the effect of the material gradient index on the natural frequencies becomes less pronounced.