LAUSR

Three-phase bidirectional functionally graded sandwich (BFGSW) beams are particular type of composite beams whose properties are tailored to vary continuously in both the longitudinal and transverse directions, depending on the constituent composition distribution. These beams are known to provide superior mechanical performance and to overcome the drawbacks of the traditional sandwich beams. In this paper, a beam element is formulated for modelling free and forced vibration of a three-phase BFGSW beam carrying a moving mass. The core of the sandwich beam is homogeneous, while the two face sheets are made from power-law bidirectional functionally graded material. In addition to the Voigt micromechanical model, the Maxwell formula is used for the first time to evaluate the effective elastic moduli of the three-phase functionally graded material. The beam element based on the sinusoidal shear deformation theory is derived using hierarchical functions to enrich the conventional Lagrange and Hermite shape functions. Using the derived element, differential equations of motion for the beams are solved to obtain natural frequencies and dynamic response of the beam. The numerical result shows that the derived element is efficient, and it can yield accurate vibration characteristics with small number of elements. An extensive parametric study is carried out to highlight the effects of the material gradation, the beam geometry and velocity of the moving mass on the vibration behaviour of the beam. The influence of the micromechanical model on the vibration of the beam is also examined and discussed.