Modal analysis of the FGM-beams with continuous transversal symmetric and longitudinal variation of material properties with effect of large axial force

In this contribution we deal with modelling and simulation of a free vibration of the 2D functionally graded material (FGM) beams with continuous spatial variation of material properties. The fourth-order differential equation of the second order beam theory has been presented which was used in modal analysis with effect of large axial force. The continuous variation of the effective elasticity modulus and mass density can be caused by continuous variation of both the volume fraction and material properties of the FGM constituents in the transversal and longitudinal direction. The polynomial variation of these parameters has been considered. Homogenization of the varying material properties and the calculation of other parameters have been done by two methods. In the first one, the extended mixture rules and laminate theory have been used, where the real composite beam has been transformed to the multilayer beam. In the second one, the direct integration method has been used. Not only the shear force deformation effect and the effect of consistent mass distribution and mass moment of inertia but also the effect of large axial force has been taken into account. Numerical experiments have been done concerning the calculation of the eigenfrequencies and eigenmodes of chosen FGM beams. Effect of division fineness of the beam to the layers in transversal direction on the solution results has been evaluated. The solution results obtained by the both methods have been discussed and compared with the ones obtained using very fine meshes of 2D solid elements of a FEM commercial program.