Vol. 3, No. 4, 2008

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ISSN: 1559-3959
Perturbation technique for wave propagation analysis in a notched beam using wavelet spectral element modeling

Mira Mitra, S. Gopalakrishnan, Massimo Ruzzene, Nicole Apetre and S. Hanagud

Vol. 3 (2008), No. 4, 659–673
Abstract

In this paper, spectral finite element is formulated for an Euler–Bernoulli beam with through-width notch type defect. In spectral finite element modeling, exact shape functions are derived and finite element procedure is followed in the transformed frequency domain. Here spectral finite element formulation is done using Daubechies scaling function bases for temporal approximation. In comparison to the conventional Fourier transform based spectral finite element method, the use of localized bases functions in the Daubechies scaling function based spectral finite element method allows accurate wave propagation analysis of finite length structures. The wave propagation response of the damaged beam is considered as a perturbation of the undamaged beam response within the restriction of small damage. First, numerical experiments are performed with narrow banded modulated pulse loading to obtain the location of damage from wave arrival time. Next, a broad banded impulse load is considered and effects of parameters like damage width, depth, and location on the responses are studied in time and frequency domains.

Keywords
wave propagation, Euler–Bernoulli beam, spectral element, Daubechies scaling functions, perturbation technique
Milestones
Received: 2 May 2007
Revised: 18 August 2007
Accepted: 14 December 2007
Published: 1 June 2008
Authors
Mira Mitra
Department of Aerospace Engineering
Indian Institute of Technology
Bombay 400 076
India
http://www.aero.iitb.ac.in/~mira
S. Gopalakrishnan
Department of Aerospace Engineering
Indian Institute of Science
Bangalore 560 012
India
http://www.aero.iisc.ernet.in/~krishnan
Massimo Ruzzene
School of Aerospace Engineering
Georgia Institute of Technology
270 Ferst Drive
Atlanta, GA
United States
Nicole Apetre
School of Aerospace Engineering
Georgia Institute of Technology
270 Ferst Drive
Atlanta, GA
United States
S. Hanagud
School of Aerospace Engineering
Georgia Institute of Technology
270 Ferst Drive
Atlanta, GA
United States