Multi-objective optimal design of inerter-based vibration absorbers for earthquake protection of multi-storey building structures

In recent years different inerter - based vibration absorbers (IVAs) emerged for the earthquake protection of building structures coupling viscous and tuned - mass dampers with an inerter device . In the three most popular IVAs the inerter is functioning either as a motion amplifier [tuned - viscous - mass - damper (TVMD) configuration], mass amplifier [tuned - mass - damper - inerter (T MDI) configuration], or mass substitute [tuned - inerter - damper (TID) configuration]. Previous work has shown that through proper tuning , IVAs achieve enhanced earthquake - induced vibration suppression and/or weight reduction compared to conventional dampers/absorbers , but at the expense of increased control forces exerted from the IVA to the host building structure . These potentially large forces are typically not accounted for by current IVA tuning approaches. In this regard, a multi-objective IVA design approach is herein developed to identify the compromise between the competing objectives of (i) suppressing earthquake-induced vibrations in buildings, and (ii) avoiding development of excessive IVA (control) forces, while, simultaneously, assessing the appropriateness of different modeling assumptions for practical design of IVAs for earthquake engineering applications . The potential of the approach to pinpoint Pareto optimal IVA designs against the above objectives is illustrated for different IVA placements along the height of a benchmark 9-storey steel frame structure. Objective (i) is quantified according to current performanc e-based seismic design trends using first-passage reliability criteria associated with the probability of exceeding pre-specified thresholds of storey drifts and/or floor accelerations being the engineering demand parameters (EDPs) of interest . A variant, simpler, formulation is also considered using as performance quantification the sum of EDPs variances in accordance to traditional tuning methods for dynamic vibration absorbers. Objective (ii) is quantified through the variance of the IVA force. It is found that reduction of IVA control force of up to 3 times can be achieved with insignificant deterioration of building performance com pared to the extreme Pareto optimal IVA design targeting maximum vibration suppression , while TID and TMDI a chieve practically the same building performance and significantly outperform the TVMD. Moreover, it is shown that the simpler variant formulation may provide significantly suboptimal reliability performance . Lastly, it is verified that the efficacy of optimal IVA designs for stationary conditions is maintained for non-stationary stochastic excitation model capturing typical evolutionary features of earthquake excitations

Comparison of collapse-resistance capacities of RC frames with and without viscous dampers

In modern seismic design, damping devices are often used to dissipate seismic energy and therefore enable a control of the structural response to earthquake ground excitation. As a result, the member section sizes or the amount of reinforcement in a structure with dampers may be reduced from those without dampers. Although both designs may be made as equivalent in terms of their performances under design earthquakes, their capacities in resisting collapse under the worst credible earthquake scenarios could be different, and there is little information from the literature that addresses this concern. In this paper, the collapse-resistance capacities of RC frames designed for different seismic hazard levels with and without dampers are calculated through a collapse fragility analysis using an incremental dynamic analysis approach, and the results are compared. On this basis, a proposal is put forward for the purpose to enhance the collapse-resistance capacities of structures with dampers in high seismic hazard levels. The effectiveness of the proposed enhancement is demonstrated

Using a damper amplification factor to increase energy dissipation in structures

AbstractFluid dampers are an important tool for dissipating unwanted vibrations in a range of engineering structures. This paper examines the effects of amplifying the displacements transferred to a non-linear damper, to increase the effectiveness of the damper in a range of situations commonly encountered in civil engineering structures. These include, (i) the ability to “fine tune” the required damping for a particular size damper, (ii) the ability to have a set of the same size dampers, but with different amplification factors to achieve a specific damping task, and (iii) to increase the sensitivity of the damper to small movements which effectively extends the range over which the damper works. Through numerical simulations and experimental tests conducted on a non-linear damper, we quantify the potential advantages of adding an amplification factor and the range of parameters where the benefit to this device is significant. The example of a two-storey structure is used as a test case and real-time dynamic substructuring tests are used to assess the complete system performance using a range of different amplification factors. The results show that the structural performance is most improved for frequencies close to resonance and that the amplification factor has an effective limit that for the case considered in this study is of approximately 3. The effects of the mechanism compliance are also assessed

Shake table testing of a tuned mass damper inerter (Tmdi)-equipped structure and nonlinear dynamic modeling under harmonic excitations

This paper presents preliminary experimental results from a novel shaking table testing campaign investigating the dynamic response of a two-degree-of-freedom (2DOF) physical specimen with a grounded inerter under harmonic base excitation and contributes a nonlinear dynamic model capturing the behavior of the test specimen. The latter consists of a primary mass connected to the ground through a high damping rubber isolator (HDRI) and a secondary mass connected to the primary mass through a second HDRI. Further, a flywheel-based rack-and-pinion inerter prototype device is used to connect the secondary mass to the ground. The resulting specimen resembles the tuned mass damper inerter (TMDI) configuration with grounded inerter analytically defined and numerically assessed by the authors in a number of previous publications. Physical specimens with three different inerter coefficients are tested on the shake table under sine-sweep excitation with three different amplitudes. Experimental frequency response functions (FRFs) are derived manifesting a softening nonlinear behavior of the specimens and enhanced vibration suppression with increased inerter coefficient. Further, a 2DOF parametric nonlinear model of the specimen is established accounting for non-ideal inerter device behavior and its potential to characterize experimental response time-histories, FRFs, and force-displacement relationships of the HDRIs and of the inerter is verified

Centrifuge modeling of rocking-isolated inelastic RC bridge piers

Experimental proof is provided of an unconventional seismic design concept, which is based on deliberately underdesigning shallow foundations to promote intense rocking oscillations and thereby to dramatically improve the seismic resilience of structures. Termed rocking isolation, this new seismic design philosophy is investigated through a series of dynamic centrifuge experiments on properly scaled models of a modern reinforced concrete (RC) bridge pier. The experimental method reproduces the nonlinear and inelastic response of both the soil-footing interface and the structure. To this end, a novel scale model RC (1:50 scale) that simulates reasonably well the elastic response and the failure of prototype RC elements is utilized, along with realistic representation of the soil behavior in a geotechnical centrifuge. A variety of seismic ground motions are considered as excitations. They result in consistent demonstrably beneficial performance of the rocking-isolated pier in comparison with the one designed conventionally. Seismic demand is reduced in terms of both inertial load and deck drift. Furthermore, foundation uplifting has a self-centering potential, whereas soil yielding is shown to provide a particularly effective energy dissipation mechanism, exhibiting significant resistance to cumulative damage. Thanks to such mechanisms, the rocking pier survived, with no signs of structural distress, a deleterious sequence of seismic motions that caused collapse of the conventionally designed pier. © 2014 The Authors Earthquake Engineering & Structural Dynamics Published by John Wiley & Sons Ltd

Vibration analysis and models of adjacent structures controlled by magnetorheological dampers

This paper deals with the vibration analysis of adjacent structures controlled by a magnetorheological (MR) damper and with the discussion of a numerical procedure for identification and definition of a reliable finite element model. The paper describes an extensive experimental campaign investigating the dynamic response, through shaking table tests, of a tridimensional four-story structure and a two-story structure connected by an MR device. Several base excitations and intensity levels are considered. The structureswere tested in nonconnected and connected configuration, with theMRdamper operating in passive or semiactivemode. Moreover, the paper illustrates a procedure for the structural identification and the definition of a reliable numerical model valid for adjacent structures connected by MR dampers. The procedure is applied in the original nonconnected configuration, which represents a linear system, and then in the connected configuration, which represents a nonlinear system due to theMR damper. In the end, the updated finite element model is reliable and suitable for all the considered configurations and the mass, damping, and stiffness matrices are derived.The experimental and numerical responses are compared and the results confirmthe effectiveness of the identification procedure and the validation of the finite element model

Numerical treatment of seismic accelerograms and of inelastic seismic structural responses using harmonic wavelets

The harmonic wavelet transform is employed to analyze various kinds of nonstationary signals common in aseismic design. The effectiveness of the harmonic wavelets for capturing the temporal evolution of the frequency content of strong ground motions is demonstrated. In this regard, a detailed study of important earthquake accelerograms is undertaken and smooth joint time-frequency spectra are provided for two near-field and two far-field records; inherent in this analysis is the concept of the mean instantaneous frequency. Furthermore, as a paradigm of usefulness for aseismic structural purposes, a similar analysis is conducted for the response of a 20-story steel frame benchmark building considering one of the four accelerograms scaled by appropriate factors as the excitation to simulate undamaged and severely damaged conditions for the structure. The resulting joint time-frequency representation of the response time histories captures the influence of nonlinearity on the variation of the effective natural frequencies of a structural system during the evolution of a seismic event. In this context, the potential of the harmonic wavelet transform as a detection tool for global structural damage is explored in conjunction with the concept of monitoring the mean instantaneous frequency of records of critical structural responses

Effective linear damping and stiffness coefficients of nonlinear systems for design spectrum based analysis

A stochastic approach for obtaining reliable estimates of the peak response of nonlinear systems to excitations specified via a design seismic spectrum is proposed. This is achieved in an efficient manner without resorting to numerical integration of the governing nonlinear equations of motion. First, a numerical scheme is utilized to derive a power spectrum which is compatible in a stochastic sense with a given design spectrum. This power spectrum is then treated as the excitation spectrum to determine effective damping and stiffness coefficients corresponding to an equivalent linear system (ELS) via a statistical linearization scheme. Further, the obtained coefficients are used in conjunction with the (linear) design spectrum to estimate the peak response of the original nonlinear systems. The cases of systems with piecewise linear stiffness nonlinearity, along with bilinear hysteretic systems are considered. The seismic severity is specified by the elastic design spectrum prescribed by the European aseismic code provisions (EC8). Monte Carlo simulations pertaining to an ensemble of nonstationary EC8 design spectrum compatible accelerograms are conducted to confirm that the average peak response of the nonlinear systems compare reasonably well with that of the ELS, within the known level of accuracy furnished by the statistical linearization method. In this manner, the proposed approach yields ELS which can replace the original nonlinear systems in carrying out computationally efficient analyses in the initial stages of the aseismic design of structures under severe seismic excitations specified in terms of a design spectrum

The Commonality of Earthquake and Wind Analysis

Earthquakes and wind loadings constitute dynamic effects that often must be considered in the design of buildings and structures. The primary purpose of this research study was to investigate the common features of general dynamic analysis procedures employed for evaluating the effects of wind and earthquake excitation. Another major goal was to investigate and develop a basis for generating response spectra for wind loading, which in turn would permit the use of modal analysis techniques for wind analysis in a manner similar to that employed for earthquake engineering. In order to generate wind response spectra, the wind loading is divided into two parts, a mean load treated as a static component and a fluctuating load treated as a dynamic component. The spectral representation of the wind loading constitutes a simple procedure for estimating the forces associated with the dynamic component of the gusting wind. Several illustrative examples are presented demonstrating the commonality.National Science Foundation Grants ENV 75-08456 and ENV 77-0719