Free Vibration Analysis of A Pretwisted Functionally Graded Material Cantilever Timoshenko Beam

Abstract

In the present work the free vibration of a 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. The material properties along the thickness of the beam are assumed to vary according to the power law. Increase in the value of power law index decreases the first two mode frequencies of the beam. Increase in pretwist angle increases first mode frequency and decreases the second mode frequency. The effect of pretwist angle and power law index on the first mode frequency is marginal.