Size-dependent vibration analysis of a rotating MR sandwich beam with varying cross section in supersonic airflow

Abstract

This article presents a size-dependent vibration analysis of a rotating doubly-tapered sandwich beam in supersonic airflow. The face layers of sandwich beam are made of functionally graded material (FGM) and the core is a magnetorheological (MR) material. The displacement field of face layers is written based on the Euler–Bernoulli beam theory, and aerodynamic pressure duo to supersonic flow is considered in accordance with linear piston theory. To obtain the governing equations, the Hamilton's principal in conjunction with modified first strain gradient theory (MFSGT) is applied. The size-dependent differential equations of motion are solved based on the Galerkin method. To evaluate the accuracy of this research, the first five natural frequencies and corresponding loss factors are compared with those reported in the literature. A parametric study is performed in order to understand the effect of various parameters including small scale parameter, intensity of magnetic field, aerodynamic pressure, rotational speed, hub radius, setting angle, power-law index and taper ratio parameters on the natural frequency and corresponding loss factor. The novelty of this research is size-dependent analysis of rotating MR sandwich structures under aerodynamic pressure. The presented results can be useful in the aviation, aerospace, turbomachinery, and instrument industry.