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Exact modal analysis of an idealised whole aircraft using symbolic computation

Published online by Cambridge University Press:  04 July 2016

J. R. Banerjee
J. R. Banerjee*
Affiliation:
Department of Mechanical Engineering and Aeronautics, City University, London, UK
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Abstract

Exact expressions for the frequency equations and mode shapes of an idealised whole aircraft are derived using the symbolic computation package REDUCE. The aircraft is idealised as a bending-torsion coupled beam for the wing with the associated mass and inertia of the fuselage, tail-plane, fin and rudder assembly being concentrated at the root. The governing differential equation of motion of the aircraft is then solved in its most general form. The analysis is split into symmetric and anti-symmetric cases to formulate the equations from which the natural frequencies and the corresponding mode shapes of the unrestrained aircraft are derived. The analytical approach used here is of great significance, particularly from an aeroelastic optimization point of view, for which repetitive calculations of natural frequencies and mode shapes are often required. The application of the theory is demonstrated by numerical results. These results have been compared with those obtained from the dynamic stiffness and finite element methods.

Type
Research Article
Information
The Aeronautical Journal , Volume 104 , Issue 1035 , May 2000 , pp. 247 - 255
Copyright
Copyright © Royal Aeronautical Society 2000 

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References

1. Tse, F. S., Morse, I. E. and Hinkle, R. T. Mechanical Vibrations: Theory and Applications, London: Allyn and Bacon, Inc; second edition,1978.Google Scholar
2. Horr, A. M. and Schmidt, L. C. Closed-form solution for the Timoshenko beam theory using a computer-based mathematical package, Comput Struct,\995,55, pp 405–412.Google Scholar
3. White, M. W. D. and Heppler, G. R. Vibration modes and frequencies of Timoshenko beams with attached rigid bodies, J Appl Mech, 1995, 62, pp 193–199.Google Scholar
4. Farohaly, S. H. and Shebl, M. G. Exact frequency and mode shape formulae for studying vibration and stability of Timoshenko beam system, J Sound Vibr, 1995, 180, pp 205–227.Google Scholar
5. Banerjee, J. R. Explicit frequency equation and mode shapes of a cantilever beam coupled in bending and torsion, J Sound Vibr, 1999, 224, pp 267–281.Google Scholar
6. Banerjee, J. R. An exact analytical method of flutter analysis using symbolic computation, 40th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and Materials Conference, St Louis, Missouri, 1999, AIAA Paper 99-1354, ppl332–1341.Google Scholar
7. Fitch, J. Solving algebraic problems using REDUCE, J Symb Comptng 1985, l,pp 211–227.Google Scholar
8. Rayna, G. Reduce Software for Algebraic Computation, Springer, New York, 1986.Google Scholar
9. Banerjee, J. R. Coupled bending-torsional dynamic stiffness matrix for beam elements, Int J Numer MethEng, 1989, 28, pp 1283–1298.Google Scholar
10. Documaci, E. An exact solution for coupled bending and torsion vibrations of uniform beams having single cross-sectional symmetry, J Sound Vibr, 1987, 119, pp 443–449.Google Scholar
11. Hallauer, W. L. and Liu, R. Y. L. Beam bending-torsion dynamic stiffness method for calculation of exact vibration modes, J Sound Vibr, 1982, 85, pp 105–113.Google Scholar
12. Banerjee, J. R. Use and capability of CALFUN: A program for Calculation of Flutter Speed using Normal Modes, Proceedings of the International AMSE Conference on Modelling and Simulation, Athens, Greece, June 1984, pp 121–131.Google Scholar