Random vibration of nonlinear structures with stiffness and strength deterioration by modified tail equivalent linearization method

Abstract

In this research the tail equivalent linearization method (TELM) has been extended to study structures with degrading materials. The responses of such structures to excitations are non-stationary, even if the excitations are stationary. Non-stationary behavior of the system cannot be considered by conventional TELM. Applying the conventional TELM, the only distinction in the design point excitation for two stationary excitations with different durations is in the addition of a zero value part at the beginning of the design point of the longer excitation. This means that the failure probability is the same for the non-stationary systems under excitations with different durations. Therefore, this solution cannot be correct. In this study, in using TELM for systems with degrading materials, hysteretic energy is replaced by average hysteretic energy, calculated by averaging the obtained hysteretic energy of the structure subjected to a few random sample load realization. In this way, the degradation parameters under design point coincide with those under sample load realizations. Since the average of the hysteretic energy is converges very fast, the modified TELM only requires about tens to hundreds solutions of the response in addition to the ordinary calculations of conventional TELM.