Generalized stiffness of laterally functionally graded materials and implementation to dynamic beam element

This study investigates the generalized stiffness of laterally functionally graded materials (LFGMs) and applies these findings to dynamic beam elements. The generalized stiffnesses of LFGM, coupled with material and cross-sectional properties such as flexural and axial rigidity, mass per unit length, and mass-moment of inertia, are explicitly formulated. In the context of LFGM, material properties depend on an asymmetrical power law function with respect to cross-sectional depth. An example of the generalized numerical stiffness of a circular cross-section is provided for various material properties. To illustrate the application of generalized stiffness to dynamic beam elements, free vibration of LFGM beams with rotary inertia is considered. The dimensionless differential equation governing the free vibration of such beams is derived and numerically solved to obtain natural frequencies and corresponding mode shapes. Numerical results demonstrate a good consistency with the finite element method.