Wave motion analysis and modeling of membrane structures using the wavelet finite element method

In this study, we present an application of the B-spline wavelet on the interval element method to analyze the in-plane elastic wave motion in a two-dimensional membrane structure. In contrast to traditional polynomial interpolation in classical finite element methods, the scaling function at a certain scale is used to form the shape functions and to construct wavelet-based elements. Other numerical wavelet methods add the wavelets directly, whereas the element displacement field represented by the coefficients of wavelets expansions in the proposed method is transformed from wavelet space to physical space via the corresponding transformation matrix. Numerical experiments are presented to demonstrate the effects of in-plane wave propagation in intact/notched membranes, particularly the propagations of the primary wave, secondary wave, and Rayleigh wave. In order to ensure a comprehensive analysis of the problem, the responses of the membrane are simulated under broad-band and narrow-band excitation.