Modal Analysis of the Fgm Beams with Spatial Variation of Material Properties Under Longitudinal Variable Elastic Winkler Foundation

Abstract eng:
A differential equation of the homogenized functionally graded material (FGM) beam deflection will be presented which will be used for free vibration analysis of the beams with continuous longitudinal and transversal variation of material properties. The FGM beams with continuous spatial variation of material properties of double symmetric crosssection have been transformed into the multilayer FGM beams. Symmetrical layering according the neutral plane in transversal direction is assumed: the corresponding layers have the same height and material properties. The material properties vary continuously in longitudinal direction, but they are constant along the height and width of competent layers. The FGM beams are considered to be resting on longitudinal variable (Winkler) elastic foundation. The first and second order beam theories have been used for establishing the kinematics and kinetic equations. Not only the shear force deformation effect and the effect of consistent mass distribution and mass moment of inertia have been taken into account, but also the effect of large axial forces have been considered. Numerical experiments were performed to calculate the eigenfrequencies and corresponding eigenmodes of chosen FGM beams. The solution results are discussed and compared with those obtained using a very fine mesh of twodimensional solid finite elements. The effects of material properties variation, layering fineness, the shear force correction factor and large axial forces have been evaluated and discussed.

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