Exact solution of the bending vibration problem of fgm multilayered sandwich beam with variation of material properties

Abstract eng:
In the theoretical part of this contribution we deal with deriving a fourth-order differential equation of the functionally graded material (FGM) beam deflection with variation of material properties. The variation of effective elasticity modulus and mass density can be caused by variation of both the volume fraction and material properties of the FGM constituents in the sandwich layers. Homogenization of the varying material properties of the multilayered sandwich beam is done by extended mixture rules and laminate theory. The linear beam theory has been used for establishing the equilibrium- and kinematics equations of the FGM beam. The shear forces deformation effect and the effect of consistent mass distribution and mass inertia moment have been taken into account too. Numerical experiments will be done concerning the calculation of the eigenfrequencies and corresponded eigenmodes of chosen multilayered FGM sandwich beams. The solution results will be discussed and compared with the ones obtained by using very fine mesh of the 2D solid elements of a FEM commercial program.

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