New Conversion Method from Response Spectrum to PSD Functions

A new approach to directly convert a target response spectrum to an equivalent power spectral density (PSD) function is presented that requires no numerical iterations. Following the same approximation scheme used in Monte Carlo simulations, the unknown PSD function is discretized and expressed as the sum of Dirac delta functions. The discretized power components can be obtained by solving a standard least-squares problem. The method was applied to response spectra with steep slopes and sharp turning points. The Monte Carlo simulation results slightly overestimated the zero-period acceleration values. Otherwise, a close match between the target and simulated response spectra was observed. The proposed conversion algorithm is so simple that the method can easily be implemented in existing structural analysis programs as a small subprogram.