The analysis of thin walled composite laminated helicopter rotor with hierarchical warping functions and finite element method

Abstract

In the present paper, a series of hierarchical warping functions is developed to analyze the static and dynamic problems of thin walled composite laminated helicopter rotors composed of several layers with single closed cell. This method is the development and extension of the traditional constrained warping theory of thin walled metallic beams, which had been proved very successful since 1940s. The warping distribution along the perimeter of each layer is expanded into a series of successively corrective warping functions with the traditional warping function caused by free torsion or free bending as the first term, and is assumed to be piecewise linear along the thickness direction of layers. The governing equations are derived based upon the variational principle of minimum potential energy for static analysis and Rayleigh Quotient for free vibration analysis. Then the hierarchical finite element method is introduced to form a numerical algorithm. Both static and natural vibration problems of sample box beams are analyzed with the present method to show the main mechanical behavior of the thin walled composite laminated helicopter rotor.

Coupled Static and Dynamic Analyses of Shear Deformable Composite Beams with Channel-Sections#

“…They showed that the fiber volume fraction was of significant importance for the vibration behavior, particularly for the flexural-torsional vibration mode. Dechao et al (2001) presented the necessity of the successive correction for the free vibration analysis of both thin-walled metallic and composite beams. Vo and Lee (2009b) and Vo et al (2009) developed the general analytical model for free vibration of the composite I-and box beams, respectively.…”