This paper presents a statistically refined Bouc-Wen model of tri-axial interactions for the identification of structural systems under tri-directional seismic excitations. Through limited vibration measurements in th...This paper presents a statistically refined Bouc-Wen model of tri-axial interactions for the identification of structural systems under tri-directional seismic excitations. Through limited vibration measurements in the National Center for Research on Earthquake Engineering in Taiwan conducting model-based experiments, the 3-D Bouc-Wen model has been statistically and repetitively refined using the 95% confidence interval of the estimated structural parameters to determine their statistical significance in a multiple regression setting. When the parameters＇ confidence interval covers the ＂null＂ value, it is statistically sustainable to truncate such parameters. The remaining parameters will repetitively undergo such parameter sifting process for model refinement until all the parameters＇ statistical significance cannot be further improved. The effectiveness of the refined model has been shown considering the effects of sampling errors, of coupled restoring forces in tri-directions, and of the under-over-parameterization of structural systems. Sifted and estimated parameters such as the stiffness, and its corresponding natural frequency, resulting from the identification methodology developed in this study are carefully observed for system vibration control.展开更多
When an elastic string with fixed ends is subjected to transverse vibrations, its length varies with the time: this introduces changes of the tension in the string. This induced Kirchhoff to propose a nonlinear correc...When an elastic string with fixed ends is subjected to transverse vibrations, its length varies with the time: this introduces changes of the tension in the string. This induced Kirchhoff to propose a nonlinear correction of the classical D’Alembert equation. Later on, WoinowskyKrieger (Nash & Modeer) incorporated this correction in the classical Euler-Bernoulli equation for the beam (plate) with hinged ends.Here a new equation for the small transverse vibrations of a simply supported beam is proposed. Such equation takes into account Kirchhoff’s correction, as well as the correction for rotary inertia of the cross section Of the beam and the influence of shearing strains, already present in the Timoshenko beam equation (of the Mindlin-Timoshenko equation for the plate).The model is inspired by a remark of Rayleigh, and by a joint paper with Panizzi & Paoli. It looks more complicated than the one proposed by Sapir & Reiss, but as a matter of fact it is easier to study if a suitable change of variables is performed.The author proves the local well-posedness of the initial-boundary value problem in Sobolev spaces of order ≥2.5. The technique is abstract, i.e. the equation is rewritten as a fourth order evolution equation in Hilbert space (thus the results could be applied also to the formally analogous equation for the plate).展开更多
文摘This paper presents a statistically refined Bouc-Wen model of tri-axial interactions for the identification of structural systems under tri-directional seismic excitations. Through limited vibration measurements in the National Center for Research on Earthquake Engineering in Taiwan conducting model-based experiments, the 3-D Bouc-Wen model has been statistically and repetitively refined using the 95% confidence interval of the estimated structural parameters to determine their statistical significance in a multiple regression setting. When the parameters＇ confidence interval covers the ＂null＂ value, it is statistically sustainable to truncate such parameters. The remaining parameters will repetitively undergo such parameter sifting process for model refinement until all the parameters＇ statistical significance cannot be further improved. The effectiveness of the refined model has been shown considering the effects of sampling errors, of coupled restoring forces in tri-directions, and of the under-over-parameterization of structural systems. Sifted and estimated parameters such as the stiffness, and its corresponding natural frequency, resulting from the identification methodology developed in this study are carefully observed for system vibration control.
文摘When an elastic string with fixed ends is subjected to transverse vibrations, its length varies with the time: this introduces changes of the tension in the string. This induced Kirchhoff to propose a nonlinear correction of the classical D’Alembert equation. Later on, WoinowskyKrieger (Nash & Modeer) incorporated this correction in the classical Euler-Bernoulli equation for the beam (plate) with hinged ends.Here a new equation for the small transverse vibrations of a simply supported beam is proposed. Such equation takes into account Kirchhoff’s correction, as well as the correction for rotary inertia of the cross section Of the beam and the influence of shearing strains, already present in the Timoshenko beam equation (of the Mindlin-Timoshenko equation for the plate).The model is inspired by a remark of Rayleigh, and by a joint paper with Panizzi & Paoli. It looks more complicated than the one proposed by Sapir & Reiss, but as a matter of fact it is easier to study if a suitable change of variables is performed.The author proves the local well-posedness of the initial-boundary value problem in Sobolev spaces of order ≥2.5. The technique is abstract, i.e. the equation is rewritten as a fourth order evolution equation in Hilbert space (thus the results could be applied also to the formally analogous equation for the plate).
