Session: 07-12-01: Optimization, Uncertainty and Probability

Paper Number: 119756

119756 - Reliability Analysis of Structures Controlled by Fractional Viscoelastic Dampers With Uncertain Parameters Modeled as Interval Variables 

The present study addresses seismic safety assessment of structures connected to a much more rigid wall (the exoskeleton) by means of a set of viscoelastic dampers.

Experimental tests in capturing the viscoelastic behavior of the material have shown that a power law function must be adopted to fit the theoretical model to the experimental data [1]. It follows that the constitutive law of the viscoelastic material involves a fractional differential equation depending on only two parameters: the fractional derivative order and the anomalous damping coefficient [2]. In this study, both these parameters are assumed uncertain. Under the realistic assumption that only fragmentary or incomplete experimental data are available, the interval model [3] of uncertainty is adopted. The interval model, which is based on the set theory, represents the uncertain parameters as interval variables with assigned lower bound (LB) and upper bound (UB) without requiring complete information on the probabilistic distribution of uncertainties between such bounds.

External excitation is modelled as a zero-mean stationary Gaussian random process fully characterized in the frequency domain by its power spectral density function. Under these assumptions, the motion of the controlled structure is governed by a set of interval fractional differential equations. Reliability analysis is carried out by interval extension of the classical first-passage problem [4]. To this aim, the interval spectral moments of the response process must be evaluated. In this study, these quantities are computed by relying on the Fourier Transform of the fractional differential equations of motion, where the fractional term is defined using the Caputo operator with unbounded lower bound [1]. Then, the bounds of the interval-valued reliability function are computed by an efficient approximate procedure.

A frame structure controlled by external fractional viscoelastic devices with interval properties defined based on experimental results available in the literature [5] is selected as case-study. The performance of the external control system as well as the influence of uncertainty on the seismic behaviour of the controlled structure are investigated.

 

References

[1]   Di Paola, M., Pirrotta, A., and Valenza, A. Visco-elastic behavior through fractional calculus: an easier method for best fitting experimental results. Mechanics of Materials, 43, 799-806 (2011).

[2]  Podlubny I., Fractional Differential Equations, 198, Mathematics in Science and Engineering. Academic Press, San Diego (1999).

[3] Moore, R.E., Kearfott, R.B., and Cloud, M.J. Introduction to Interval Analysis. SIAM, Philadelphia PA (2009).

[4] Sofi A., Giunta F., Muscolino G., Reliability Analysis of Randomly Excited FE Modelled Structures with Interval Mass and Stiffness via Sensitivity Analysis, Mechanical Systems and Signal Processing, 163, 107990 (2022).

[5]  Christopoulos, C. and Montgomery, M. Viscoelastic coupling dampers (VCDs) for enhanced wind and seismic performance of high‐rise buildings. Earthq. Eng. Struct. Dyn. 42, 2217-2233 (2013)

Presenting Author: Giuseppe Muscolino University of Messina

Presenting Author Biography: Since 1992 Giuseppe Muscolino is Professor of Mechanics of Solids and Structures at the Department of Engineering, University of Messina, Italy. Prior to that he was Assistant Professor (1983-1988), Associate Professor (1988-1990), and Full Professor (1990-1992) at the University of Palermo, Italy., He currently is the principal instructor of several bachelor, and master’s thesis at the Department of Engineering of the University of Messina where he teaches Structural Dynamics and Seismic Analysis of Structures. He was the Head of the Interuniversity Centre of Experimental and Theoretical Dynamics (C.I.Di.S.), and the Manager of the Lab of Experimental tests on Materials and Structures. He supervised about 16 Ph.D. students, 10 post-doc students and about 12 projects mainly focused on the modelling and propagation of stochastic and epistemic uncertainties. He (co-)authored over 100 journal papers in peer-reviewed international journals, over 150 scientific papers in international conferences and 3 books (in Italian). He was (co-)chair of about 10 international conferences on uncertainties in Structural Dynamics. He delivered about 12 lectures in international conferences. He is member of the Editorial Board of Computers & Structures and Probabilistic Engineering Mechanics. His primary research interests focus on: Probabilistic, non-Probabilistic and Hybrid Methods for Uncertainty Propagation; Stochastic Dynamics; Structural Reliability, Imprecise Probability; Dynamics of Damaged and Undamaged Beams Under Moving Loads.

Authors:

Alba Sofi University "Mediterranea" of Reggio Calabria
Giuseppe Muscolino University of Messina
Mario Di Paola University of Palermo