Construction of a Dynamic Finite Element Model for Vibration Analysis of Reticulate Systems

Abstract

In the present work a model of dynamic finite element for vibration analysis of reticulate systems is proposed. It is proposed a method of construction of dynamic stiffness matrices and inertia matrices for the cases of bending, traction and torsion in free and forced vibrations. From exact analytical solutions of vibration equations it is established the dynamic shape functions allowing obtaining the coefficients of dynamic stiffness matrices and inertia matrices. These coefficients depend on frequency of free vibrations of the system. This dynamic finite element model allows obtaining an exact solution for reticulate systems in classical approach of the dynamic analysis of structures.