Time-duration extended Hilbert transform superposition for the reliable time domain analysis of five-layered damped sandwich beams

The direct time domain analysis of five-layered damped sandwich beams subject to impulse load using the discrete Hilbert transform may lead to the unstable growth in damped time responses owing to the incorrectness of Hilbert-transformed imaginary impulse force and the insufficient time duration of applied impulse force. To resolve this problem, a time domain analysis method making use of the Hilbert transform superposition and the time duration extension is introduced in this paper. The incorrect imaginary impulse force near the end of time period, which is caused by the fact that the discrete Hilbert transform using Fourier transform considers the impulse force as a periodic function, is resolved by dividing the external impulse force into a finite number of rectangular impulses. And, the sufficient time duration of applied impulse force is estimated by a Newton-Raphson-based iterative residual method. The validity of the present method is justified from the numerical experiment for analyzing the time response of five-layered damped sandwich beam.