04.2 - Aerostructures Design, Structural Dynamics, Aeroelasticity
STRUCTURAL ANALYSIS OF TWISTED/CURVED BEAMS USING A HYBRID METHOD
A. Siami¹, F. Nitzsche¹; ¹Carleton University, Canada
This paper presents a numerical approach for the structural dynamic analysis of initially twisted and curved beams. The variational asymptotical beam sectional theory due to Hodges is used to extract the set of nonlinear equations associated to the 2D beam cross-sectional analysis. The conventional perturbation solution is used as an analytical solution for the set of nonlinear equations obtained from the cross-sectional analysis. To compensate for the effect of neglecting the higher order terms, which have been eliminated in the perturbation solution of the equations, the Firefly algorithm (FA) as an iterative solution is introduced for the first time to the problem. To eliminate the sensitivity of the method to the initial values, the perturbation solution is chosen as an initial guess for the FA. The stiffness matrix obtained from the Firefly algorithm for twisted/curved beam is then used in the geometrically exact, fully intrinsic equations to analyze the dynamic behavior of the beam. The effect of flexible joints is introduced to the one-dimensional beam equations to consider more realistic boundary conditions. The accuracy of the calculated stiffness matrix of the proposed algorithm is evaluated by comparing the eigenfrequencies of an initially twisted blade with the results of a modal analysis done in ANSYS. The Campbell diagram of an initially twisted/curved rotating blade is extracted from the developed one-dimensional equations to demonstrate that the numerical solution provides a sufficiently accurate and fast solution of the problem.