Size-dependent transient response of sandwich microbeam with three-phase bidirectional FGM face layers under a moving mass

Abstract

Multi-phase functionally graded materials (FGMs) have more design variables than their two-phase counterparts and thus provide larger space for tailoring effective properties to meet multifunctional requirements. Predicting response of structures to dynamic loading is essential for structural design. In this work, the size-dependent transient response of a sandwich microbeam under a moving mass is studied. The core of the microbeam is homogeneous, while the two face layers are made from a three-phase bidirectional FGM. Based on the quasi-3D theory and modified couple stress theory, differential equations of motion are derived and transferred to a discretized form using a finite element formulation. Dynamic response is evaluated for microbeam with different material distributions and sandwich configurations. Numerical result reveals that the influence of material distribution on the transient response is governed by the microstructural scale parameter, and this influence is less significant for the microbeam associated with a higher scale parameter. The effects of the material gradation, the scale parameter and the mass velocity on the transient behaviour are studied in detail. The effect of micromechanical models, namely the rule of mixture and the extended Mori–Tanaka scheme, used in estimating the effective moduli of the three-phase FGM is also examined and discussed.