The numerical solution of equation of motion using B-spline wavelet

The numerical solution of equation of motion using B-spline wavelet

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Part of #The numerical solution of equation of motion using B-spline wavelet# :

Publishing year : 2012

Conference : Fourth International Conference on Reinforcement

Number of pages : 10

Abstract: Wavelets are mathematical functions that cut data into different frequency components, and then study each component with a resolution matched to its scale. Wavelets were developed independently in the fields of mathematics, quantum physics, electrical engineering, and seismic geology. Interchanges between these fields over the last ten years have led to many new wavelet applications such as image compression, turbulence, human vision, radar and earthquake prediction. In this paper, we introduce a procedure using B-spline wavelet basis functions to solve the dynamic equation of motion. In the proposed approach, a straightforward formulation was derived from the approximation of the displacement function of the system with the B-spline wavelet basis. In this way, the B-spline wavelet matrix is derived and applied in dynamic analysis. The validity and effectiveness of the proposed method is verified with several examples. The results were compared with some of the numerical methods such as Haar wavelet, Duhamel integration and Newark (linear acceleration).