Abstract
This study develops a frequency-domain method for modelling general transient linear-elastic dynamic problems using the semi-analytical scaled boundary finite element method (SBFEM). This approach first uses the newly-developed analytical Frobenius solution to the governing equilibrium equation system in the frequency domain to calculate complex frequency-response functions (CFRFs). This is followed by a fast Fourier transform (FFT) of the transient load and a subsequent inverse FFT of the CFRFs to obtain time histories of structural responses. A set of wave propagation and structural dynamics problems, subjected to various load forms such as Heaviside step load, triangular blast load and ramped wind load, are modelled using the new approach. Due to the semi-analytical nature of the SBFEM, each problem is successfully modelled using a very small number of degrees of freedom. The numerical results agree very well with the analytical solutions and the results from detailed finite element analyses.