Free Vibration of Composite Thin-Walled Beams with Chordwise Asymmetric Closed Cross-Sections

Keun-Taek Kim

doi:10.1155/2019/7503097

Abstract

In this paper, some analytical results via extended Galerkin method on free vibration characteristics of an anisotropic composite beam, which is modeled as a nonuniform thin-walled structure with a chordwise asymmetric closed cross-section and corrected the warping functions, are newly presented. For this study, nonclassical parameters such as warping restraint, transverse shear flexibility, and structural couplings induced by two special configurations, such as circumferentially uniform stiffness (CUS) and circumferentially asymmetric stiffness (CAS), are incorporated. And also, design parameters of the beam associated with preset angles, pretwist angles, taper ratios, and section ratios are additionally investigated. The results of this study could play an important role in more efficient designs of composite thin-walled beams.

Highlights

In the theoretical explicit analyses of thin-walled beams, the closed cross-sections of most aircraft wings and rotor blades have been using almost symmetrical contours in the related literatures based on the author’s knowledge [1,2,3,4,5,6,7,8,9]
In general, aircraft wings have an asymmetrical cross-section in the chordwise direction
In order to compensate the warping function of the asymmetric cross-section in the chordwise direction, the shape function of the crosssection contour is derived on the basis of an arbitrary pole of the cross-section and the shape function based on the pole is determined so as to satisfy the equilibrium conditions of the warping constraint

Summary

Introduction

In the theoretical explicit analyses of thin-walled beams, the closed cross-sections of most aircraft wings and rotor blades have been using almost symmetrical contours in the related literatures based on the author’s knowledge [1,2,3,4,5,6,7,8,9]. In this study, we investigated cross-sectional characteristics through the mathematical modeling of asymmetric cross-section and the correction of the warping function. The beam modeled as a chordwise asymmetric cross-section is analyzed for free vibration characteristics numerically, and in order to investigate the effect of the asymmetry of the cross-section, a comparative study was conducted on a symmetrical cross-section model with the same chordwise length and cross-section thickness as a special case of the considered model. In this study, numerical examples were carefully analyzed and compared to investigate the effect of various design parameters on the natural frequencies that provide the basis for dynamic characteristics of beams. The results presented as families of curves or tables, which may be used for the direct estimation of the eigenfrequencies for any given beam

Mathematical Modeling

Numerical Analysis and Discussion

Eigenfrequency of the Model

Conclusion