Wave Propagation Analysis In The Frequency Domain: Initial Conditions Contribution
Free (open access)
W J Mansur, A I Abreu R, J A M Carrer & M A C Ferro
This work describes a new methodology to consider initial conditions contributions in one-dimensional BEM frequency domain analyses of transient problems governed by the scalar wave equation. The superposition principle is valid and the problem is solved in the transformed domain by employing the Fourier transform. Non periodic perturbations are represented by harmonic waves series; each component is analysed separately by the BEM formulation and, finally, the solution is obtained in the time-domain by numerical inversion of the transformed solution spectrum. The proposition of an algorithm for the inclusion of initial conditions (displacements or velocities) in frequency domain analyses of transient problems, by means of the Fast Fourier Transform (FFT), is the main contribution of this work. The numerical implementation of this new algorithm in a BEM formulation is carried out. The examples presented at the end of the article show the accuracy of the proposed formulation and its applicability to such kind of analysis.