Influence of temperature and porosities on free vibration of a three-phase bidirectional functionally graded sandwich beam

Abstract

Understanding the influence of practical factors on natural frequencies of beams play an important role in design of this structure. This article explores the influence of temperature and porosities on vibration characteristics of a sandwich beam made from a three-phase bidirectional functionally graded material (BFGSW beam) for the first time. The sandwich beam composed from a homogeneous core and two face layers made of a three-phase composite material. The material properties are graded in both the beam axis and thickness by power-law functions, and they are evaluated by using the Voigt model. Heat loading with uniform temperature rise and even distribution of porosities are also considered. The expressions of the elastic strain energy and the kinetic energy for the beam as well as the strain energy due to temperature are obtained in the framework of the hyperbolic shear deformation theory. A two-node beam element with eight degrees of freedom has been proposed and used to establish the discretized equation of motion for the beam. The proposed method is validated by comparing the fundamental frequency parameters with two previous works. The beam with simply supported ends are used in numerical studies. The convergence of the derived beam element is represented by evaluating the fundamental frequency parameters. The effects of the temperature rise, the porosity volume fraction, the material indexes, the length to height ratio as well as the beam layer thickness ratio on the vibration characteristics are investigated and discussed in detail. It is concluded that the BFGSW beam parameters, the temperature rise and porous parameter play an important role in the natural frequency, which is helpful for the design of beam – like structures with the desired natural frequency.