Modeling and design of tuned mass dampers using sliding variable friction pendulum bearings

AbstractAn effective vibration control device, the pendulum tuned mass damper (P-TMD), can be easily realized as a mass supported on rolling or sliding pendulum bearings. While the bearings' concavity provides the desired gravitational restoring force, the necessary dissipative force can be obtained either from additional dampers installed in parallel with the bearings or from the same friction resistance developing within each bearing between the roller/slider and the rolling/sliding surface. The latter solution may prove cheaper and more compact but implies that the P-TMD effectiveness will be amplitude dependent if the friction coefficient is kept uniform along the rolling/sliding surface, as in conventional friction bearings. In this case, the friction P-TMD will be as efficient as a viscous P-TMD only at a given vibration level, with large performance reductions at other levels. To avoid this inconvenience, this paper proposes a new type of sliding variable friction pendulum (VFP) TMD, called the VFP-TMD, in which the sliding surface is divided into two concentric regions: a circular inner region, having the lowest possible friction coefficient and the same dimensions of the slider, and an annular outer region, having a friction coefficient set to an optimal value. A similar arrangement has been recently proposed to realize adaptive seismic isolation devices, but no specific application to TMDs is reported. To assess the VFP-TMD performance, first its analytical model is derived, rigorously accounting for geometric nonlinearities as well as for the variable (in time and space) pressure distribution along the contact area, and then, an optimal design methodology is presented. Finally, numerical simulations show the influence of the main design parameters on the device behavior and demonstrate that the VFP-TMD can achieve nearly the same effectiveness of viscous P-TMDs, while considerably outperforming conventional uniform-friction P-TMDs. The proposed analytical model can be used to enhance or validate existing models of VFP isolators that assume a constant and uniform contact pressure distribution

New few parameters differential evolution algorithm with application to structural identification

Differential evolution algorithm (DEA) is a stochastic, population-based global optimization method. In this paper, we propose new schemes for both mutation and crossover operators in order to enhance the performances of the standard DEA. The advantage of these proposed operators is that they are "parameters-less", without a tuning phase of algorithm parameters that is often a disadvantage of DEA. Once the modified differential evolutions are presented, a large comparative analysis is performed with the aim to assess both correctness and efficiency of the proposed operators. Advantages of proposed DEA are used in an important task of modern structural engineering that is mechanical identification under external dynamic loads. This is because of the importance of using a "parameters-less" algorithm in identification problems whose characteristics typically vary strongly case by case, needing of a continuous set up of the algorithm proposed. This important advantage of proposed optimizers, in front of other identification algorithms, is used to develop a computer code suitable for the automatic identification of a simple supported beam subject to an impact load, that has been tested both using numerical simulations and real standard tests dynamic. The results point out that this algorithm is an interesting candidate for standard applications in structural identification problems. Keywords: Differential evolution, Parametric identification, Structural identification, Optimizatio

Shape-Sensing of Beam Elements Undergoing Material Nonlinearities

The use of in situ strain measurements to reconstruct the deformed shape of structures is a key technology for real-time monitoring. A particularly promising, versatile and computationally efficient method is the inverse finite element method (iFEM), which can be used to reconstruct the displacement field of beam elements, plate and shell structures from some discrete strain measurements. The iFEM does not require the knowledge of the material properties. Nevertheless, it has always been applied to structures with linear material constitutive behavior. In the present work, advances are proposed to use the method also for concrete structures in civil engineering field such as bridges normally characterized by material nonlinearities due to the behavior of both steel and concrete. The effectiveness of iFEM, for simply supported reinforced concrete beam and continuous beams with load conditions that determine the yielding of reinforcing steel, is studied. In order to assess the influence on displacements and strains reconstructions, different measurement stations and mesh configurations are considered. Hybrid procedures employing iFEM analysis supported by bending moment-curvature relationship are proposed in case of lack of input data in plastic zones. The reliability of the results obtained is tested and commented on to highlight the effectiveness of the approach

Nonstationary First Threshold Crossing Reliability for Linear System Excited by Modulated Gaussian Process

A widely used approach for the first crossing reliability evaluation of structures subject to nonstationary Gaussian random input is represented by the direct extension to the nonstationary case of the solution based on the qualified envelope, originally proposed for stationary cases. The most convenient way to approach this evaluation relies on working in the time domain, where a common assumption used is to adopt the modulation of stationary envelope process instead of the envelope of modulated stationary one, by utilizing the so-called "preenvelope" process. The described assumption is demonstrated in this work, also showing that such assumption can induce some errors in the envelope mean crossing rate

Seismic behavior of a low-rise horizontal cylindrical tank

Abstract Cylindrical storage tanks are widely used for various types of liquids, including hazardous contents, thus requiring suitable and careful design for seismic actions. The study herein presented deals with the dynamic analysis of a ground-based horizontal cylindrical tank containing butane and with its safety verification. The analyses are based on a detailed finite element (FE) model; a simplified one-degree-of-freedom idealization is also set up and used for verification of the FE results. Particular attention is paid to sloshing and asynchronous seismic input effects. Sloshing effects are investigated according to the current literature state of the art. An efficient methodology based on an "impulsive-convective" decomposition of the container-fluid motion is adopted for the calculation of the seismic force. The effects of asynchronous ground motion are studied by suitable pseudo-static analyses. Comparison between seismic action effects, obtained with and without consideration of sloshing and asynchronous seismic input, shows a rather important influence of these conditions on the final results

Stochastic Multi-objective Optimisation of Exoskeleton Structures

In this study, a structural optimisation problem, addressed through a stochastic multi-objective approach, is formulated and solved. The problem deals with the optimal design of exoskeleton structures, conceived as vibration control systems under seismic loading. The exoskeleton structure is assumed to be coupled to an existing primary inner structure for seismic retrofit: the aim is to limit the dynamic response of the primary structure to prevent structural damage. A non-stationary filtered Gaussian white noise stochastic process is taken as the seismic input. Design variables pertain to the mechanical properties (stiffness, damping) of the exoskeleton structure. Two concurrent and competing objective functions are introduced, in order to take into account not only safety performance but also economic cost considerations. The resulting trade-off is solved searching the Pareto front by way of a controlled elitist genetic algorithm, derived from the Non-dominated Sorting Genetic Algorithm-II. Sensitivities of Pareto fronts and Pareto optimal sets to different system parameters are finally investigated by way of a numerical application

Volume/thrust optimal shape criteria for arches under static vertical loads

Arches are widely used when large spans are necessary, e.g. to overpass large rivers, and further possess unquestioned aesthetics advantages. Their structural efficiency depends primarily on optimal material exploitation, i.e. minimization of internal stress eccentricity, and on minimization of structural material volume. An efficient structure, under these terms, further requires simpler and lighter scaffolding, contributing in minimizing construction costs.Although arches have millenary use and many researches dealing with this typology are available in literature, there is still scope for design optimization. The proposed study is framed within this context. Investigation is limited to statically determinate plane arches under vertical load. The problem of finding the profile of an equal strength catenary subjected to its self-weight is spread out to the case of an inverted catenary of equal strength under its self-weight and an external constant load. In the first optimization step, constant normal stress is imposed at all sections, to maximize material exploitation, and the resulting arch centerline shape is computed in closed form. In the second step, the ensemble of foundations and arch is considered and optimized, taking the linear combination of arch weight and thrust as objective function. The linear combination is dependent on a single variable, and minima of the objective function (i.e. optimal geometric shape parameters) are computed and charted to be simply used in the design process. Keywords: Plane arch, Vertical loads, Optimal shape, Volume/thrust objective functions, Analytical solutio

To compute or not to compute?

In a previous paper "to retrofit or not to retrofit?" (Nuti and Vanzi, 2003) a straightforward procedure able to forecast the economic return of seismic structural upgrading was presented. More recently, the authors realized that the final mathematical results can be much simplified so as to allow back-of-an-envelope computation. The title of this paper tries to highlight precisely this aspect, namely that for many a regular seismic structural upgrading cases, nearly no computation is needed (apart from one subtraction and one multiplication) to assess their economic convenience. These findings are presented and discussed in this paper, together with a state of the art on the cost-studies available in literature and technical codes. The mathematical formulation leading to the proposed approximation is suitably explained, underlining its applicability field and comparing it with the rigorous solution. Also a table and a formula are furnished that alternatively allows to calculate the maximum estimation errors, in order to obtain an upper and lower bound for the maximum amount of money which should be allocated for seismic structural upgrading.Finally an application example is described, dealing with retrofitting of reinforced concrete viaducts, a widespread bridge typology in Italy. The adopted upgrading solution consists of a concrete jacket at the base of some piers, particularly suitable in order to increase their ductility. Keywords: Seismic retrofitting, Structural reliability, Safety, Optimization, Cost minimizatio

Optimal Design of Elastic Circular Plane Arches

Arches represent a structural system adopted in construction practice for thousand years, and they are still widely adopted if large spans have to be covered. The structural efficiency of arches principally depends on the minimization of the eccentricity of the pressure curve, which allow us to reduce their structural weight. Despite the millenarian use and a very abundant literature, there is still scope for design optimization of arches. This study is framed within this context and is focused on plane circular arches under uniformly distributed vertical load and self-weight. The arches are elastically clamped at both end sections. A semianalytical approach is developed to minimize the volume, with the aim of determining the fundamental mechanical parameters governing the optimal design. Finally, the results are charted to allow their use in a design process

Seismic performance of spherical liquid storage tanks: a case study

Abstract Spherical storage tanks are widely used for various types of liquids, including hazardous contents, thus requiring suitable and careful design for seismic actions. On this topic, a significant case study is described in this paper, dealing with the dynamic analysis of a spherical storage tank containing butane. The analyses are based on a detailed finite element (FE) model; moreover, a simplified single-degree-of-freedom idealization is also set up and used for verification of the FE results. Particular attention is paid to the influence of sloshing effects and of the soil–structure interaction for which no special provisions are contained in technical codes for this reference case. Sloshing effects are investigated according to the current literature state of the art. An efficient methodology based on an "impulsive–convective" decomposition of the container-fluid motion is adopted for the calculation of the seismic force. With regard to the second point, considering that the tank is founded on piles, soil–structure interaction is taken into account by computing the dynamic impedances. Comparison between seismic action effects, obtained with and without consideration of sloshing and soil–structure interaction, shows a rather important influence of these parameters on the final results. Sloshing effects and soil–structure interaction can produce, for the case at hand, beneficial effects. For soil–structure interaction, this depends on the increase of the fundamental period and of the effective damping of the overall system, which leads to reduced design spectral values