José A. Inaudi

Modulated homogeneous friction : A semi-active damping strategy

A control strategy for semi-active friction devices leading to efficient hysteretic dissipaters is proposed. The control algorithm makes the contact force between the sliding surfaces of the damper proportional to the absolute value of the prior local peak of the damper deformation. This control logic leads to a non-linear force–deformation relation that satisfies homogeneity of degree one; this means that, like in a linear viscoelastic damping model, when the deformation is scaled by a constant, the force results are scaled by the same constant. The closed-loop system shows rectangular hysteresis loops which enclose an area proportional to the square of the deformation of the damper. Some characteristics of the dynamic response of structures incorporating this type of semi-active damper are investigated. It is demonstrated that in the case of single-degree-of-freedom models, the period of vibration and decay ratio are independent of the amplitude of vibration. In the case of multi-degree-of-freedom models with this type of nonlinearity, the free-vibration response can exhibit natural modes of vibration. A linearization method is proposed and modelling tools for the delay associated with actuator dynamics and for the flexibility of the brace connecting the damper to the structure are presented.

Modelling aspects of structures isolated with the frictional pendulum system

Different modelling aspects of structures isolated using the frictional pendulum system and subjected to earthquake ground motions are studied herein. Although the vertical dynamics of these structures is given special emphasis, other effects such as large isolator deformations and bidirectional input motion are also considered. Different structural models of the FPS are developed and tested for single-storey structures and a real four-storey building frame; among them, an ‘exact’ formulation of the FPS force–deformation constitutive relationship is presented. Results show that global building responses can be computed within 20 per cent error in the mean using a simplified model that ignores the vertical motion of the building; however, structural member deformations and forces need to be computed using a model that considers such motion. This is of particular importance when there exist correlation between the horizontal and vertical components of ground motion. Further, a physical model of the FPS is introduced and used to determine the response of a real four-storey frame, including uplift and downward impact. Results from this analysis show that local column responses may vary substantially depending on the stiffness of the isolation storey and the presence of a mass at the isolation level. Such mass is capable of filtering the large increase in column shear that results from the impact of the structure after uplift. Uplift occurs at several instants of the response of the structure considered, leading to an increase in column base shear as large as 3 times the shear obtained by ignoring the vertical dynamics of the building.

TIME‐DOMAIN ANALYSIS OF LINEAR HYSTERETIC DAMPING

Two linear-hysteretic-damping models that provide energy dissipation independent of the deformation frequency, are studied in this paper: a hysteretic Kelvin element and a hysteretic Maxwell element. Both models use the Hilbert transform and yield integro-differential equations for the equations of motion of structures when real-valued signals are utilized in the formulation. It is shown that the use of analytic (complex-valued) signals allows the transformation of these integro-differential equations into differential equations with analytic input signals and complex-valued coefficients. These differential equations show both stable and unstable poles. A technique for the solution of these differential equations is presented; it consists of a conventional modal decomposition of the state-space equations and the integration of the differential equations forward in time for the modal co-ordinates associated with stable poles, and backwards in time for the modal co-ordinates associated with unstable poles. Some numerical examples are presented to illustrate the characteristics of the models and the proposed analysis technique.

Response of Reinforced Concrete Buildings in Concepción during the Maule Earthquake

Detailed observations are reported for eight shear wall buildings from the Concepción region that experienced severe damage during the 27 February 2010 Chile earthquake. The repetitive nature of some of the damage suggests that these field observations may be applicable to similar buildings elsewhere, whereas other damage may be unique. Several shear walls experienced failures that apparently started at the boundaries due to the high compression in these unconfined edges, and propagated into the wall web. Other walls, including horizontal and vertical wall segments in perforated walls, experienced shear failure. Damage also was observed in columns, beams, and coupling slabs. In most cases, the percentage of damaged elements was less than 10% of the lateral force-resisting elements of the building, suggesting that these structures were not capable of distributing damage. Several building indices are calculated, including vibration periods and regularity indices, for comparison with observed behavior.

Accuracy of the modal strain energy method

The modal strain energy (MSE) method is an approximate technique for the approximate analysis of structures with frequency-dependent stiffness and damping matrices. In this paper, the accuracy of this method is investigated by computing the exact and approximate mean square responses of structures containing viscoelastic dampers to random excitation. Closed- form expressions of the mean square error are obtained for single-degree-of-freedom (SDOF) systems under linear hysteretic damping and Maxwell-type damping. The accuracy of the MSE method applied to multi-degree-of-freedom (MDOF) structures with non-classical viscous damping, hysteretic damping and Maxwell-type damping is investigated.

Linear-friction dissipators for truss structures

This paper is concerned with the dynamic response of truss structures containing linear- friction dampers. This type of passive energy dissipator shows different stiffness in loading and unloading, leading to triangular hysteresis loops under cyclic loading. The free and forced vibration responses of simple truss structures incorporating linear-friction dampers are analyzed. The harmonic linearization technique is used in combination with the modal strain energy method to estimate the response of truss structures with linear-friction dampers. The accuracy of this linearization technique is assessed in the context of truss structures in this paper. It is demonstrated that excellent accuracy is achieved using this linearization method.