Reliability-based optimal design of nonlinear viscous dampers for the seismic protection of structural systems

Abstract

Viscous dampers are widely employed for enhancing the seismic performance of structural systems, and their design is often carried out using simplified approaches to account for the uncertainty in the seismic input. This paper introduces a novel and rigorous approach that allows to explicitly consider the variability of the intensity and characteristics of the seismic input in designing the optimal viscous constant and velocity exponent of the dampers based on performance-based criteria. The optimal solution permits controlling the probability of structural failure, while minimizing the damper cost, related to the sum of the damper forces. The solution to the optimization problem is efficiently sought via the constrained optimization by linear approximation (COBYLA) method, while Subset simulation together with auxiliary response method are employed for the performance assessment at each iteration of the optimization process. A 3-storey steel moment-resisting building frame is considered to illustrate the application of the proposed design methodology and to evaluate and compare the performances that can be achieved with different damper nonlinearity levels. Comparisons are also made with the results obtained by applying simplifying approaches, often employed in design practice, as those

Towards realistic minimum-cost optimization of viscous fluid dampers for seismic retrofitting

“…Essentially, the adjoint sensitivity analysis consists in solving for each time-step i → i − 1 the linear system of equations Eq. (23). It results in a linear time-history analysis solved backwards in time, and with known final conditions:…”

“…The dimensions of the system of equations for the evaluation of the structural response (9) are [N dof × N dof ], once the Newmark's method is implemented. However, also the dimensions of the system of equations (23) can be reduced to [N dof ×N dof ] if, for example, λ v,i and λ a,i are expressed in terms of λ u,i . Once the adjoint variables ξ i are known in each time-step i, the constraint gradient is calculated as follows:…”

“…A first group consists of those approaches that rely on continuous design variables (i.e. damping coefficients) [8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23] In practice, the damping coefficients of the dampers are a continuous design variable that can be adapted to the needs of each specific project. This leads to an optimization problem computationally efficient and applicable also to large scale problems.…”

Stochastic Seismic Analysis and Comparison of Alternative External Dissipative Systems

“…Moreover, as in the case of the FRF, the peaks are located approximately in correspondence of the same frequencies in the case of the NR and FB configurations, while in the RB case only the first peak is close to the first peak of the other systems, as a result of the changes that the RB system induces through the added stiffness on the dynamic behaviour of the existing frame. The peak force that a damper has to withstand is an important response parameter, influencing the damper cost together with the damper stroke [37]. Figure 7(f) shows that the PSD of the sum of the damper forces is largely higher for the RB case than for the FB case.…”

Optimization‐based minimum‐cost seismic retrofitting of hysteretic frames with nonlinear fluid viscous dampers

“…Recently, it was also observed that considering a more realistic finite stiffness of the brace would significantly affect the damper-brace mechanical behavior. 26 Moreover, nowadays viscous dampers with a nonlinear force-velocity behavior are considered by researchers, [27][28][29][30][31] engineers, 32 and producers. 33 Nonlinear dampers also proved to be able to achieve the same level of response reduction of a structure retrofitted with linear viscous dampers, but with smaller forces in the nonlinear dampers case.…”