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The design of footbridges has begun to receive more attention in recent years due to cases in which undesirable vibrations occurred. The utilization of passive energy dissipation systems to control bridge responses has become popular as a remedy for this matter. This paper proposes the use of inerters to mitigate pedestrian bridge vibrations, and explores their potential. This is done by presenting a topology and sizing optimization methodology for pedestrian bridges equipped with fluid viscous dampers and inerters. Planar truss-like bridges are examined, loaded under dynamic and static loads. All constructive elements' sizes (including dampers) serve as continuous design variables. The objective is to minimize a cost function of the bridge. The optimization process is constrained by demanding responses of interest not to exceed allowable values, along with global and local buckling. A first-order gradient-based optimization algorithm is adopted to lessen the computational effort. Lastly, a discretization postprocess is offered to lead to discrete designs of relevant design variables, such as steel cross sections. The results shed light on the advantages of combining inerters in pedestrian bridges. [ABSTRACT FROM AUTHOR]

This paper presents a formal optimization methodology for the design of seismic retrofitting of three-dimensional irregular buildings. The damping coefficients of viscous dampers potentially allocated in given feasible locations as well as the stiffness of their supporting braces are adopted as design variables. The objective function minimizes a cost function of the dampers while constraints are added to limit various responses of interest to allowable values under a filtered white noise excitation (e.g., interstory drift at each location separately, total acceleration at each location separately, force of each damper, stress in each supporting brace, force/forces of each structural member, base shear, overturning moment at the base, side constraints on dampers' forces and braces' cross sections, etc.). A first-order optimization method is adopted for that purpose. The constraints on various normalized responses are condensed to a single constraint on their maximum value and the gradient required is efficiently derived analytically using the adjoint analytical method. Thus, a computational effort at the order of a single additional analysis is required for the evaluation of the gradient of the constraint regardless of the number of design variables considered or responses to be constrained. This efficient scheme enables a study on the effect of limiting the brace size with and without a limit on its stresses. [ABSTRACT FROM AUTHOR]

Highlights: [•] Multi-modal optimal seismic design methodology using MTMDs in 3D irregular buildings is presented. [•] The methodology enables achieving a performance-based-design. [•] The gradients required are efficiently derived analytically using the adjoint analytical method. [•] MTMDs overcome some of the limitations of single TMDs in seismic control. [•] MTMDs can mitigate both structural and nonstructural earthquake damage. [ABSTRACT FROM AUTHOR]

This paper examines the sensitivity of the response of optimally damped frames to uncertainty in structural and damping properties. Viscous dampers are first optimally designed for given nominal properties of the retrofitted structures and a given ensemble of records for each structure. The behavior of the retrofitted structures (in terms of the maximum envelope peak inter-story drift) considering uncertainty in their properties as well as in the dampers’ properties is then tested using Monte Carlo simulation. It is shown that the uncertainties lead to larger mean drifts than expected, and that some designs are more sensitive than others. The physical reasons for this behavior are discussed and some rules as to what designs are expected to be more sensitive are given. [ABSTRACT FROM AUTHOR]

This paper presents a methodology for the design of peripheral multiple tuned mass dampers (MTMD) in 3D irregular buildings. A Performance-Based Design (PBD) control strategy is proposed to reduce structural response to a desired acceptable level. Therefore, a limit is assigned to the accelerations experienced at the floors' edges for a specific seismic hazard. In parallel, an attempt is made to keep the total mass of the added TMDs to its lowest possible level. The formulation of the design methodology relies on full utilization of control resources as presented herein; hence, a two stage iterative analysis/redesign procedure that is based on analysis tools is developed. The solution is compared to a formal gradient-based optimization solution, showing that the solution obtained by the analysis/redesign process is close to optimal, while it is much more computationally efficient than formal optimization and requires no gradient computation. The methodology applies to all types of structural irregularities, which allows its application in a practical design process of any structure. [ABSTRACT FROM AUTHOR]

This paper deals with the allocation and sizing of multiple-tuned mass dampers (MTMDs) in an attempt to retrofit footbridges with multiple critical modes resulting from the excitation of pedestrian traffic. The simple and practical methodology proposed herein includes the use of an iterative analysis/redesign type procedure that converges to a given allowable level of accelerations. An example that uses this methodology to retrofit an existing footbridge is presented. [ABSTRACT FROM AUTHOR]

One of the founders of structural control theory and its application in civil engineering, Professor Emeritus Tsu T. Soong, envisioned the development of the integral design of structures protected by active control devices. Most of his disciples and colleagues continuously attempted to develop procedures to achieve such integral control. In his recent papers published jointly with some of the authors of this paper, Professor Soong developed design procedures for the entire structure using a design - redesign procedure applied to elastic systems. Such a procedure was developed as an extension of other work by his disciples. This paper summarizes some recent techniques that use traditional active control algorithms to derive the most suitable (optimal, stable) control force, which could then be implemented with a combination of active, passive and semi-active devices through a simple match or more sophisticated optimal procedures. Alternative design can address the behavior of structures using Liapunov stability criteria. This paper shows a unified procedure which can be applied to both elastic and inelastic structures. Although the implementation does not always preserve the optimal criteria, it is shown that the solutions are effective and practical for design of supplemental damping, stiffness enhancement or softening, and strengthening or weakening. [ABSTRACT FROM AUTHOR]

Previous research has shown that weakening of inelastic structures can limit the maximum response accelerations they experience during ground motions, but may lead to an increase in the displacements (or interstory drifts). Added damping by using fluid viscous devices, on the other hand, reduces the interstory drifts and has no significant effect on total accelerations, when structures behave inelastically. The weakening and damping technique, thus, limits the total acceleration due to the weakening, and reduces the interstory drifts by adding damping, and hence addresses the two main causes for both structural and nonstructural damage in buildings. Optimal weakening and damping, which is the subject of this paper, involves the determination of the optimal locations and amount of weakening of the structural components as well as the optimal locations and magnitudes of added dampers. Weakening of the structure might create stability issues in the building that can be automatically considered, if active control theory is used for design. Based on a nonlinear active control procedure, control forces are calculated and implemented using equivalent passive dampers and weakening elements in order to achieve the closest effects. The methodology is applied to a case study of an eight-story nonlinear building tested using a set of ground motions corresponding to different hazard levels. Results show that the optimal design leads to a reduction of both peak interstory drifts and peak total accelerations. [ABSTRACT FROM AUTHOR]

Abstract: The free vibrational response of homogeneous or symmetrically laminated polar orthotropic annular plates subjected to non-uniform boundary conditions on the inner and outer rims is scrutinized in detail, using a finite-difference method. Although the same sets of boundary conditions are considered, the angular location at which the altered boundary conditions are applied and the segments that they cover are allowed to be different on the inner and outer circumferences. The sensitivity of vibrational frequencies to the extent and relative location of the non-uniformities is investigated and shown to be strongly influenced by the material properties with the orthotropy ratio for the plate (defined here by ) being the predominant parameter for indicating the sensitivity to non-uniformity. The behavior of higher modes of vibration is also discussed and the phenomenon of crossover, whereby two modes having the same frequency exist, is found to occur. Unlike the crossover previously reported in the literature, for which only higher modes of frequency were involved, in the current context, it was discovered that the phenomenon may also be associated with the lowest mode of vibration. The circumstances under which crossover transpires are dependent on the relative location of the boundary non-uniformities, the relative length over which the non-uniformities are applied and the orthotropy ratio. [Copyright &y& Elsevier]

Abstract: The free vibrational response of clamped homogeneous or symmetrically laminated orthotropic annular plates with edge damage on the outer circumference has been studied for the first time, using the finite difference method. The edge damage is modeled via the application of a non-uniform boundary condition. The sensitivity of vibrational frequencies to the extent of the edge damage is investigated and shown to be strongly influenced by the material properties and the relative thicknesses of the materials comprising the laminated plates. It is shown that the orthotropy ratio for the plate (defined here by ) is a convenient compact parameter for indicating the sensitivity to edge damage. Mode shapes are also computed and found to be profoundly affected by the orthotropy ratio. The behavior of higher modes of vibration is also discussed and the phenomenon of cross over, whereby two modes exist having the same frequency, is observed. [Copyright &y& Elsevier]

• An efficient methodology for the seismic optimization of steel MRFs is presented. • Non-linear time history analysis is utilized to evaluate structural responses. • This is done, for the first time, using an efficient gradient-based approach. • The adjoint method is employed to derive the sensitivities in an efficient manner. • The examples reveal the efficiency of the proposed approach. In this paper an efficient optimized seismic design of steel moment resisting frames is presented. Non-linear time history analysis is utilized to evaluate structural responses under seismic excitations. The goal is to optimize the cross-section properties of all elements comprising the frame, in order to achieve the minimal structural steel volume as a representation of the cost. Performance based design constraints are formulated to limit the inter-story drifts for desired levels. As efficiency is of concern, a gradient based optimization is adopted. The design variables are formulated as continuous and along with the discrete material optimization (DMO) function, standard steel table sections can be attained. The adjoint analytical method is employed to derive the sensitivities in an efficient manner. Numerical examples demonstrate the effectiveness of the methodology. Even in cases of irregular, real-scale, moment resisting frames – optimized desired discrete designs have been achieved in a reasonable computational effort. [ABSTRACT FROM AUTHOR]