Bilinear Hysteretic Model Research Articles

Identification of dynamic properties of isolated structures

This paper develops an identification scheme to investigate the dynamic behaviour of isolated structures in which laminated rubber bearings are used. A linear model is used for the superstructure while a bilinear hysteretic model is chosen for the isolation system. The modal parameters of the superstructure are estimated on the basis of an iterative identification algorithm and are employed to identify the parameter values of the isolation system. The essence of this study is the application of the Masing criterion by which hysteretic loops of bearings may be characterized through the skeleton curve. The multivalue restoring force is then transformed into a single-value function so that the ordinary identification process can be carried out with only minimal computational effort beyond that required for the identification of a linear system. Numerical examples include the four-storey Foothill Communities Law and Justice Center in California and show the feasibility of the proposed technique for identifying the hysteretic isolation system.

Dynamic Behavior of a Bilinear Hysteretic Elasto-Plastic Oscillator, Part I: Free Oscillations

Free oscillations of an elasto-plastic oscillator with kinematic hardening are analyzed in this paper. A bilinear hysteretic model is used to represent the material non-linearity. The coefficient of kinematic hardening is used as a problem parameter in the equations of motion. By solving the governing equations on each branch of the hysteretic cycle and matching the transition conditions, an iterative map is obtained for the plastic displacements. The map is analyzed and a bifurcation of the system's dynamic behavior due to change in the hardening parameter is discussed. A theorem is presented to identify two distinct subranges of this parameter, and the dynamic behavior of the oscillator is discussed in each subrange.

The stochastic response of strongly yielding systems

The bilinear hysteretic model is used to examine the nature of the stochastic response of strongly yielding (nearly elasto-plastic) systems. Both second-order and third-order equivalent linearization schemes are examined. It is shown that although these approximate techniques generally give acceptable results for second-order response statistics they fail to yield an accurate description of the nature of the response in the frequency domain. The influence of the excitation Power Spectrum on the response is examined. The desirability of decomposing the response into an elastic and inelastic component is demonstrated.

Inelastic Modeling and Seismic Energy Dissipation

The influence of inelastic load-deformation behavior on seismic energy imparted and dissipated is assessed. Stiffness degrading and bilinear hysteretic models are considered. The load-deformation model has a pronounced influence on the energy imparted to the system and on the energy absorbed by inelastic action. The use of the simpler bilinear model in evaluating the seismic energies is restricted to systems within certain ranges of natural frequency and displacement ductility.

Inelastic seismic response of simple eccentric structures

AbstractThe maximum ductility demand and the edge displacement of a simple single mass eccentric model is evaluated when the system is subjected to ground motions represented by the El Centro 1940 and Taft 1952 earthquake records. The resisting elements are taken to be bilinear hysteretic. It is found that the ductility demand depends to a great extent on the energy content of the ground motions, particularly in the period range beyond the elastic period of the system. Unlike elastic response, the coincidence of uncoupled torsional and lateral frequencies does not lead to exceptionally high inelastic response. An increase by a factor of two in ductility demand is not uncommon for a system with large eccentricity as compared to a symmetrical system. Therefore, system eccentricity has a larger effect on ductility demand than earlier studies indicated. Using Clough's model to allow for stiffness degradation effect, results are found to be within 20 per cent of those calculated based on the bilinear hysteretic model.

Hysteretic response of a nine‐storey reinforced concrete building

AbstractThe Millikan Library on the campus of the California Institute of Technology was strongly shaken during the San Fernando earthquake of 9 February 1971. The building was not damaged structurally, but the observed E‐W response of the building showed a fundamental period of about 1.0 sec, significantly longer than the 0.66 sec observed in pre‐earthquake vibration tests. In this study, the response of the fundamental mode was treated as that of a single‐degree‐of‐freedom hysteretic structure, and four simple models, two stationary and two with changing properties, were examined to see if they could describe the observed response. It was found that an equivalent linear model and a bilinear hysteretic model both could match the response, provided their properties were changed during the earthquake. (Four changes were used.) A linear model with constant properties and a stationary, bilinear hysteretic model did not give nearly as good agreement as the non‐stationary models. The results indicated, in general, a degrading of the stiffness and energy dissipation capacity of the building, with the suggestion that the changes were sudden rather than gradual.

Stochastic Seismic Response of Structures

Records of strong-motion earthquakes are simulated using a filtered shot noise. Twenty sample records are then used to simulate the response of a structure subjected to earthquake excitation. The stochastic model used to generate the artificial ground acceleration records is designed to produce sample records similar to those of real strong-motion earthquakes of magnitude 8.3 recorded on firm soil at about 45 miles from the epicenter. It is concluded that a filtered shot noise is very suitable for this simulation. An 8-story shear type building with inelastic force-deflection characteristics represented by a bilinear hysteretic model and having various values of stiffness and viscous damping is subjected to twenty samples of the artificial ground acceleration records. Major response parameters are evaluated and Monte-Carlo estimates of the statistics of these parameters are obtained to allow predictions of their values during future earthquakes.

The Steady-State Response of the Double Bilinear Hysteretic Model

The steady-state response of a one-degree-of-freedom double bilinear hysteretic model is investigated and it is shown that this model gives rise to the jump phenomenon which is associated with certain nonlinear systems. The stability of the steady-state solution is discussed and it is shown that the model predicts an unbounded resonance for finite excitation.