Vibration and Dynamic Stability of Pre-Twisted Thick Cantilever Beam Made of Functionally Graded Material

Abstract

In the present work, the vibration and dynamic stability of functionally graded ordinary (FGO) pre-twisted cantilever Timoshenko beam has been investigated. Finite element shape functions are established from differential equations of static equilibrium. Expressions for element stiffness and mass matrices are obtained from energy considerations. Floquet's theory is used to establish the stability boundary. The material properties along the thickness of the beam are assumed to vary according to the power law. The effects of power law index and pre-twist angle on the natural frequencies and dynamic stability of the beam have been investigated. Increase in pre-twist angle enhances the stability of the beam for first mode whereas it makes the beam more prone to parametric instability for the second mode. The increase in power law index is found to have a detrimental effect on the stability of the beam. The chance of parametric instability is enhanced with the increase in static load factor.