Past, present and future of nonlinear system identification in structural dynamics

Reliable collapse assessment of structural systems under earthquake loading requires analytical models that are able to capture component deterioration in strength and stiffness. For calibration and validation of these models, a large set of experimental data is needed. This paper discusses the development of a database of experimental data of steel components and the use of this database for quantification of important parameters that affect the cyclic moment-rotation relationship at plastic hinge regions in beams. On the basis of information deduced from the steel component database, empirical relationships for modeling of precapping plastic rotation, postcapping rotation, and cyclic deterioration for beams with reduced beam section (RBS) and other-than-RBS beams are proposed. Quantitative information is also provided for modeling of the effective yield strength, postyield strength ratio, residual strength, and ductile tearing of steel components subjected to cyclic loading.

https://ascelibrary.org/doi/pdf/10.1061/%28ASCE%29ST.1943-541X.0000376

Deterioration Modeling of Steel Components in Support of Collapse Prediction of Steel Moment Frames under Earthquake Loading

Structural systems often show nonlinear behavior under severe excitations generated by natural hazards. In that condition, the restoring force becomes highly nonlinear showing significant hysteresis. The hereditary nature of this nonlinear restoring force indicates that the force cannot be described as a function of the instantaneous displacement and velocity. Accordingly, many hysteretic restoring force models were developed to include the time dependent nature using a set of differential equations. This survey contains a review of the past, recent developments and implementations of the Bouc-Wen model which is used extensively in modeling the hysteresis phenomenon in the dynamically excited nonlinear structures.

The Hysteresis Bouc-Wen Model, a Survey

Aseismic base isolation: review and bibliography

Experiences from past strong earthquakes, such as the 1968 Miyakiken-Oki earthquake in Japan and the 1971 San Fernando earthquake in California, have shown the vulnerability of reinforced concrete buildings to strong ground shakings. For economic reasons, however, some level of damage should be expected and permitted in the aseismic design of structures, particularly of low-rise buildings. In spite of this recognition, the potential seismic damage of structures and the associated aseismic provisions are based largely on qualitative engineering judgment. In order to assess the seismic safety of reinforced concrete buildings, the quantitative analysis of structural damage under random earthquake excitations needs to be improved.

Seismic Damage Analysis of Reinforced Concrete Buildings

A differential equation model for hysteretic systems is analyzed under nonzero mean random excitation. Under certain conditions, a closed form linearization of the equations of motion is possible. Resulting mean and zero time lag covariance responses agree well with Monte Carlo response simulations. Generalization to degrading systems is straightforward. Skewness coefficients computed from simulation results indicate significantly asymmetric response. Stationary response statistics are found to relate closely to the zero mean case.

Nonzero Mean Random Vibration of Hysteretic Systems

A model for the random vibration of hysteretic and degrading plane frames to Gaussian shot noise or filtered shot noise is presented. The model, which combines the discrete hinge concept previously used in deterministic frame analysis with Bouc's smooth system hysteresis, results in a non-linear set of differential equations which can be linearized in closed form without recourse to the Krylov-Bogoliubov assumptions. Solution is iterative in the stationary case and by numerical integration with stepwise updates in the non-stationary case. Numerical studies are presented of strong girder and strong column two storey, one bay frames. These studies indicate that the model can locate the sites of yielding and provide reasonable values of structural response as compared with simulation data. Moreover, the model can provide a joint by joint breakdown of the structure energy dissipation rate.

Stochastic response of multistorey yielding frames

Nonzero mean random vibration of hysteretic frames

An algorithm is presented for the direct stiffness formulation of hysteretic frames which is suitable for random vibration analysis under zero mean or non-zero mean random excitation. A modal transformation is used to reduce the number of active degrees of freedom. First and second order response statistics are presented for two example frames using stochastic equivalent linearization and Monte Carlo simulation. The modal transformation stabilizes the stationary response calculation algorithm by eliminating superfluous higher modes. The iterations for transient response calculations under non-zero mean excitations are destabilized by elimination of too many modes. The modal transformation allows reasonable response estimates to be obtained with significant reductions in computing time. The expected lower modes dominate the response, but inclusion of several higher modes is necessary to provide reasonable response estimates.

Modal analysis for random vibration of hysteretic frames

A new general hysteresis model which is developed based on the mathematical modelling technique of Baber-Noori[3] is presented. The capabilities of the model in generating numerous hysteretic models such as Wen-Baber, Pinching hysteresis and bilinear are discussed. In addition, the ability of the model in simulating unloading stiffness degradation, which no other available model can predict, is shown. The method of Equivalent Linearization is used to predict the first and second order statistics for a SDOF system having this hysteretic restoring force and under different levels of input excitation. It is shown that the linearized response statistics are in good agreement with Monte Carlo simulation results.

Thomas T. Baber

Papers

Nonzero Mean Random Vibration of Hysteretic Systems

Stochastic response of multistorey yielding frames

Nonzero mean random vibration of hysteretic frames

Modal analysis for random vibration of hysteretic frames

Equivalent Linearization of a Newly Introduced General Hysteretic Model