Wavelet based response spectrum compatible synthesis of accelerograms and statistical linearization based analysis of the peak response of inelastic systems
Doctor of Philosophy thesis
A novel method for producing seismic accelerograms whose response spectra comply with the pertinent seismic code criteria has been proposed. It encompasses a stochastic dynamics formulation for defining an evolutionary power spectrum that is related to a given design (target) spectrum in a statistical sense, and a deterministic harmonic wavelet-based procedure to iteratively modify seismic accelerograms on an individual basis. The incorporation of the stochastic dynamics formulation allows for generating ensembles of artificial design spectrum compatible accelerograms, without the need to consider any recorded strong ground motion. Several such ensembles pertaining to the design spectrum prescribed by the European aseismic code provisions (EC8) are provided. Moreover, in the developed wavelet-based procedure the unique attributes of harmonic wavelets are exploited to "surgically" modify the frequency content of seismic accelerograms to meet the commonly prescribed compatibility criteria. An example involving the modification of a suite of real recorded accelerograms to be used for the design of base-isolated buildings according to the EC8 code provisions is included. Appropriate wavelet-based joint time-frequency analysis of the original and of the modified signals have been provided suggesting that the modified signals maintain the main patterns of the evolutionary frequency content of the original accelerograms. Appended to the above a computationally efficient methodology is suggested for estimating the maximum seismic response of nonlinear systems exposed to excitations specified by a given design spectrum. Specifically, stationary design spectrum compatible power spectra are considered in conjunction with the method of statistical linearization to derive effective linear stiffness and damping properties associated with certain nonlinear oscillators. The cases of Duffing bilinear hysteretic, and smooth hysteretic systems described by the Bouc-Wen differential model are considered. It is found via pertinent Monte Carlo analyses that the peak response of the nonlinear and of the derived equivalent linear systems compare reasonably well. Furthermore, it is shown through appropriate numerical examples that the latter methodology is capable of deriving inelastic response spectra from elastic design spectra without the need to integrate numerically the underlying nonlinear equations of motion.
Engineering, Civil; Engineering, Mechanical