Free Vibration Analysis of Rotating Pretwisted Functionally Graded Sandwich Blades

L T Liu,Y X Hao,J Chen,W Zhang

doi:10.1155/2018/2727452

Abstract

A new structural dynamic model for the free vibration characteristic analysis of rotating pretwisted functionally graded (FG) sandwich blades is developed. The sandwich blade is made up of two functionally graded skins and a homogeneous material core. The thick shell theory is applied to derive the basic equations of motion of the rotating FG sandwich blade by considering the effects of centrifugal and Coriolis forces. The mode shapes are expanded in terms of two-dimensional algebraic polynomials in the Rayleigh–Ritz method, and the static and dynamic natural frequencies of the blade are obtained. The convergence analysis is studied, and the accuracy of the proposed model is verified by comparing with the literature results and ANSYS data. The effects of frequency parameters such as the twist angle, the thickness ratio, the aspect ratio, the layer thickness ratio, the scalar parameter of volume fraction, the stagger angle, and the rotation velocity on the vibration characteristics for pretwist FG sandwich blade are investigated in detail. In addition, the phenomena of frequency locus veering and mode shape exchanging occur in the static and dynamic states. Frequency locus veering is essentially caused by the coupling between different modes.

Highlights

The aero gas turbine engine is the key technology of the aircraft; blade is one of the most important parts of the system
Hu et al [8] proposed a numerical procedure for the free vibration analysis of pretwisted thin plates based on the thin shell theory and studied the vibration characteristics considering different twist rates and aspect ratios
The nondimensional frequency parameters ω for the first six modes of the functionally graded (FG) sandwich blade with varying aspect ratios (l from 1 to 5) are given in Table 8 to study the effect of the aspect ratio on the vibration characteristics for the pretwist FG sandwich blade

Summary

Introduction

The aero gas turbine engine is the key technology of the aircraft; blade is one of the most important parts of the system. Hu et al [8] proposed a numerical procedure for the free vibration analysis of pretwisted thin plates based on the thin shell theory and studied the vibration characteristics considering different twist rates and aspect ratios. Sinha and Turner [10] derived the governing partial differential equation of motion for the rotating pretwisted plate by using the thin shell theory and studied the free vibration of a turbomachinery cantilevered airfoil blade with the Rayleigh–Ritz technique by considering the centrifugal force filed as a quasi-static load. Li and Zhang [24] developed a dynamic model for FG plates undergoing large overall motions, studied the free vibration of rotating cantilever FGM rectangular plates, and found frequency locus veering and associated mode shift phenomena. Frequency locus veering and mode shape exchanging phenomena are found both in both static and dynamic states

Theoretical Analysis

Frequency Solving

Numerical Results and Analyses

Conclusion