Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

A wavelet-based spectral finite element for analysis of coupled wave propagation in composite beam

Mira Mitra*, S. Gopalakrishnan
Department of Aerospace Engineering, Indian Institute of Science, C.V. Raman Road, Bangalore 560012, India

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In this paper, a spectrally formulated wavelet finite element is developed and is used to study coupled wave propagation in composite beam. The formulation uses Daubechies wavelet approximation in time to reduce the governing PDE to a set of ODEs. Similar to conventional FFT-based Spectral Finite Element (FSFE) formulations, these transformed ODEs are solved using finite element (FE) techniques by deriving exact interpolation functions in the transformed domain to obtain the exact dynamic stiffness matrix. The use of the compactly supported Daubechies wavelet basis circumvents several drawbacks of the FSFE due to the required assumption of periodicity, particularly for time domain analysis. In the Wavelet-based Spectral Finite Element (WSFE) formulation, a constraint on the time sampling rate is placed to avoid spurious dispersion being introduced in the analysis. Numerical examples are presented to study wave propagation with the formulated element and emphasize the advantages of WSFE formulation over FSFE for wave propagation analysis of finite length structure. Numerical experiments are also performed to study the dispersion of waves and show the presence of spurious dispersions. Simultaneous existence of various propagating modes are graphically captured using modulated sinusoidal pulse excitation.

Keywords:  Wavelet; Wave propagation; Composite beam; Finite element; Spectral finite element

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