Dynamic Analysis of Shaft with Variable Mechanical Property under Dynamic Load by FEM Method

Abstract

The paper introduces the dynamic responses of a circular shaft with variable mechanical properties under dynamic loads. The direct construction of finite element formulation for dynamic problems, which include stiffness matrix, and mass matrix for circular axis. The Functionally Graded Material (FGM) shaft with material properties is assumed to vary continuously in the longitudinal direction investigated. Building a numerical program for the problem based on Bernoulli beam theory, and Newmark numerical algorithm. The obtained numerical results have found the kinematic response of the shaft with the longitudinal variation of mechanical properties under the action of dynamic loads. The results were also compared with the analytical results in some special cases to clarify the reliability of the calculation method.