Size-dependent vibration analysis of an axially moving sandwich beam with MR core and axially FGM faces layers in yawed supersonic airflow

Abstract

The aim of this article is to study the influences of aerodynamic pressure and axially moving behavior on the size-dependent vibration of a sandwich structure. Here, the core of sandwich structure is a magnetorheological (MR) fluid and face layers are made of functionally graded material (FGM). In order to obtain the aerodynamic pressure due to supersonic flow over upper face of structure, the linear piston theory is considered. The displacement field of sandwich structure is written according to layerwise theory and the size-dependent strain energy is obtained based on modified first strain gradient theory (MFSGT). The Hamilton's principle is applied to derive the governing equations of motion. In order to solve the partial differential equations, the Galerkin method is applied. To validate the presented formulation and solution method, the obtained results are compared with the available results in the literature, which shows a good agreement. The first set of results investigate the first five natural frequencies of MR sandwich beam based on the different MR materials. The variations of frequency and corresponding loss factor are plotted against aerodynamic pressure, length scale parameters, axially speed, intensity of external magnetic field, yaw angle, and power-law index, and the resulting trends in the plots are discussed in detail. Also, the parameters of critical aerodynamic pressure and critical axially speed in different conditions are tabulated.