Wavelet based spectral finite element for analysis of coupled wave propagation in higher order composite beams

In this paper, a spectrally formulated wavelet finite element is developed and is used to study coupled wave propagation in higher order composite beams. The beam element has four degrees of freedom at each node, namely axial and transverse displacements, shear and contraction. The formulation is used to perform both frequency and time domain analysis. The formulation is similar to conventional FFT based Spectral Finite Element (FSFE) except that, here Daubechies wavelet basis is used for approximation in time to reduce the governing PDE to a set of ODEs. The localized nature of the compactly supported Daubechies wavelet basis helps to circumvent several problems associated with FSFE due to the required assumption of periodicity, particularly for time domain analysis. However, in Wavelet based Spectral Finite Element (WSFE), a constraint on the time sampling rate has to be placed to avoid the introduction of spurious dispersion in the analysis. Numerical experiments are performed to study spectrum and dispersion relation. In addition, the wave propagation in finite length structures due to broad band impulse loading is studied to bring out the higher order effects. Simultaneous existence of various propagating modes are graphically captured using modulated sinusoidal pulse excitation. In all the cases comparison are provided with FSFE.