The fast Fourier transform and its applications
The fast Fourier transform and its applications
Crack tip interpolation, revisited
SIAM Journal on Applied Mathematics
Computation of the second fracture parameter in elastodynamics by the boundary element method
Advances in Engineering Software
Evaluation of singular integrals in the symmetric Galerkin boundary element method
Advances in Engineering Software
Efficiency improvement of the frequency-domain BEM for rapid transient elastodynamic analysis
Computational Mechanics
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Dynamic analysis of a system can be carried out either in the time or frequency domain. Time responses/ histories of this system may be directly obtained using time-domain analysis. In case of frequency domain analysis in the Fourier space, the inverse fast Fourier transform (inverse FFT) would naturally be an appropriate choice for converting frequency solutions to the desired time responses. However, the standard FFT can not be applied to undamped systems as the free-vibration terms of these systems never decay which violates the periodic nature of the standard FFT algorithm. In addition, the FFT may be computationally expensive for lightly damped systems. An alternative to overcome the above limitations is the so-called exponential window method (EWM) commonly used in digital signal processing. This paper presents a combination of the EWM and the symmetric-Galerkin boundary element method for 2-D elastodynamic analysis in the frequency domain of undamped and lightly damped systems. Several numerical examples, including fracture problems, are given to illustrate the efficiency and accuracy of the proposed frequency domain analysis.