Semi-analytical method for the dynamic analysis

Aurel M. Alecu; Mihail I. Boiangiu; Viorel I. Anghel

Aurel M. Alecu University "Politehnica" of Bucharest
Mihail I. Boiangiu University "Politehnica" of Bucharest
Viorel I. Anghel University "Politehnica" of Bucharest

Abstract

The paper presents a semi-analytical method for the study of a linear differential system with variable coefficients. The solution is given in terms of real positive integer powers; it is obtained in terms of independent functions which are computed numerically. The paper extended the semi-analytical method from [5] (for one differential equation only), to the study of a linear differential system. The differential system became a system with recurrent expressions between the coefficients of the power series in a matrix form. The strength of this method is shown by application to the dynamic analysis of typical rotor blades. The frequencies and mode shapes are calculated. The results are compared with theoretical results for the degenerate cases and with results obtained through other methods.

Keywords

References

[1] A. Alecu, M. Boiangiu. Dynamic analysis of helicopter blades. Sixth International Congress on Sound and Vibration, Lyngby, Denmark, pp. 1901- 1908, July 5- 8, 1999.
[2] A. Alecu, M. Boiangiu, V.S. Buracu. Coupled bending vibrations of helicopter blades. Scientific Bulletin University "Politehnica" of Bucharest, Series D, Mechanical Engineering, 61(3- 4): 375-385, 1999.
[3] A. Alecu, M. Boiangiu, C. Untăroiu. Coupled bending flap-torsion vibrations of helicopter blades. 5th International Symposium TI-ansport Noise and Vibrations, St.-Petersburg, Russia, June 6-9, 2000.
[4] D.H. Hodges. Nonlinear Equations for the Dynamics of Pretwisted Beams Undergoing Small Strains and Large Rotations. NASA TP 2470, 1985.
[5] V. Giurgiuţiu, R.O. Stafford. Semi-analytic methods for frequencies and mode shape of rotor blades. Vertica, 1(4): 291-306, 1977.