Complex Fractional-Spectral Method for Space Curved Struts: Theory and Application

Abstract

Based on the theory of fractional calculus and the complex spectral theory of vibration, a new spectrally-formulated finite-element method of analysis is developed which is capable of making accurate predictions of the dynamic response of damped structures with curved struts. The frequency-dependent and temperature-dependent damping characteristics of structural materials can be modelled accurately using the fractional derivative model. The main features of the complex-spectral element method of analysis are presented in this paper. Although most structural systems can be analysed and designed by using the conventional finite element method, in order to guarantee stability and accuracy of the solution the number of elements used to model the structure may be very large. Hence, it appears that, for large structures, it may be more effective to use the spectral approach presented in this paper.

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References

Horr

A.M.

, (1995), Energy Absorption in Structural Frames, Ph.D. Dissertation, University of Wollongong, Australia.

Horr

A.M.

and Schmidt

L.C.

(1995), Dynamic Response of a Damped Large Space Structure: A New Fractional-Spectral Approach, Int. J. of Space Struct., Vol. 2, No. 10, pp. 113-120.

Horr

A.M.

and Schmidt

L.C.

, (1995), Modelling of Non-Linear Damping Characteristic of a Viscoelastic Structural Damper, Int. J. Engrg. Struct., Vol. 18, No. 2, pp. 154-161.

Doyle

J.F.

, (1989), Wave Propagation in Structures, Berlin:Springer-Verlag.

Britton

W.G.B.

and Langley

G.O.

, (1968), Stress Pulse Dispersion in Curved Mechanical Waveguides, J. of Sound and Vibration, Vol. 7, No. 3, pp. 417-430.

Bagley

R.L.

(1979), Application of Generalised Derivatives to Viscoelasticity, Ph.D. dissertation, Air Force Institute of Technology, Ohio, USA.

Bathe

K.J.

, (1982), Finite Element Procedure in Engineering Analysis, Englewood Cliffs, NJ: Prentice-Hall.

Clough

R.W.

and Penzien

, (1975), Dynamics of Structures, McGraw-Hill, New York.

Timoshenko

S.P.

, (1921), On the Correction for Shear of the Differential Equation for Transverse Vibrations of Prismatic Bars, Phil. Mag., Vol. 41, pp. 744-746.

10.

Horr

A.M.

and Schmidt

L.C.

, (1995), Closed Form Solution for the Timoshenko Theory Using A Computer Based Mathematical Package, Int. J. Computers Struct., Vol. 55, pp. 405-412.