On the convergence and causality of a frequency domain method for dynamic structural analysis

Venanico-Filho et al. developed an elegant matrix formulation for dynamic analysis by frequency domain (FD), but the convergence, causality and extended period need further refining. In the present paper, it was argued that: (1) under reasonable assumptions (approximating the frequency response function by the discrete Fourier transform of the discretized unitary impulse response function), the matrix formulation by FD is equivalent to a circular convolution; (2) to avoid the wraparound interference, the excitation vector and impulse response must be padded with enough zeros; (3) provided that the zero padding requirement satisfied, the convergence and accuracy of direct time domain analysis, which is equivalent to that by FD, are guaranteed by the numerical integration scheme; (4) the imaginary part of the computational response approaching zero is due to the continuity of the impulse response functions.