Free Vibration Analysis of Uniform and Asymmetric Composite Pretwisted Rotating Thin Walled Beam

Abstract

Composite pretwisted rotating thin walled beams (TWB) can be used as the structural model for composite helicopter and wind turbine blades for the study of aeroelastic response of the blades. In the present study, semi-analytical solution is performed for the free vibration analysis of uniform and asymmetric composite pretwisted rotating TWB. The approximation of the Green-Lagrange strain tensor is adopted to derive the strain field of the system. The Euler–Lagrange governing equations of the dynamic system and the related boundary conditions are derived via Hamilton’s principle. In order to solve the governing set of equations, the Extended Galerkin’s Method (EGM) is employed. For this purpose, the structural variables are separated in space and time and the assumed mode shapes are defined to satisfy the essential boundary conditions. For the purpose of validating the TWB model developed, the commercial finite element analysis tool, MSC Nastran is used to compare the results of modal analysis obtained by the present structural model with the finite element solution. With the results obtained in this paper, it is aimed to ascertain the effect of various coupling in circumferentially asymmetric stiffness (CAS) and circumferentially uniform stiffness CUS configurations, pretwist, angular velocity and fibre orientation, on the natural frequencies and the mode shapes of the rotating thin-walled composite beams. The results are expected to propose better predictions of the vibrational behavior of thin walled structures in general, and in the design of rotor blades of turbomachinery, rotorcraft and wind turbine systems, in particular.

Eğrisel Fiber Yollu İkili Motorlu-Kanat Sisteminin Aeroelastik Enerji Optimizasyonu

“…The structural model considered is similar to the model developed in Refs. [10,13,28] in linear form. For a detailed description of the original structural model, the reader is referred to the aforementioned references.…”

“…The ij Q components are used to transform the stiffness coefficients from the principle axes to the material axes. All the above components are defined explicitly in Ref [13]. The 2D first order force and moment resultants of the cross-section of the TWB are defined in terms of the 3D stresses.…”

“…(15). Details of force and moment resultants are explicitly defined in our previous study [10,13].…”

“…where F, A, D are the one dimensional beam forces and moment resultants, the resulting stiffness matrix, and generalized strain, respectively. For a single cell thin walled beam, stiffness coefficients ij a are given by the contour integral of the stiffness coefficients as shown in [13]. Potential energy due to engine thrust is given as,…”

“…In order to have slender and lighter wing structure, advanced composite materials with thin walled beams (TWBs) structure has been developed. Application of TWBs in aircraft wings as a load carrying part of the wing and studying their dynamic behavior has been the topic of many researches [8][9][10][11][12][13]. Librescu [9] thoroughly investigated the theoretical foundations of composite TWBs and derived the necessary relations.…”