Bending and free vibrations of beams with symmetrically varying mechanical properties—Shear effect

Abstract

The subject of the paper is a beam with symmetrically varying mechanical properties in the depth direction. The proposed formulation of the functions of the properties makes a certain generalization in the research of functionally graded materials and allows to describe homogeneous, nonlinearly variable and sandwich structures with the use of only one, consistent analytical model. The individual nonlinear hypothesis for planar cross section is assumed. Basing on the Hamilton's principle two differential equations of motion are obtained. The system of equations is analytically solved. The results are compared with numerical solutions obtained with FEM.