Influence of Winkler and viscoelastic foundation on free vibration of functionally graded beam integrated with Terfenol-D layer

Abstract

Free vibration of functionally graded beam integrated with Terfenol-D layer on Winkler-two parameter and viscoelastic foundation are studied by means of differential quadrature method within the framework of classical beam theory. The material properties of functionally graded beam integrated Terfenol-D layer are estimated by using the rule of mixture. The applied kinematic boundary conditions are implemented using δ-point and modified weighting coefficient approach. The solution of simply supported functionally graded material beam with Terfenol-D layer (FGMT) resting on the Winkler elastic foundation is obtained by using the technique of Navier. The numerical results obtained using differential quadrature method (DQM) and modified differential quadrature method (MDQM) are compared with exact results obtained from analytical formulation where excellent agreement is observed. The parametric study is carried out to encapsulate the influence of Winkler-two parameter and the viscoelastic foundation on the vibration characteristics of functionally graded beams integrated with Terfenol-D layer. © 2020, The Brazilian Society of Mechanical Sciences and Engineering.