A reduced modal subspace approach for damped stochastic dynamic systems

Kasinos, Stavros; Palmeri, Alessandro; Lombardo, Mariateresa; Adhikari, Sondipon

doi:10.1016/j.compstruc.2021.106651

Cited by 15 publications

(4 citation statements)

References 53 publications

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“…The methods that combine PC‐based stochastic finite element analyses with deterministic and stochastic reduced‐order methods are developed in Reference 39, where deterministic/stochastic reduced bases are obtained by using deterministic/stochastic Krylov subspace techniques. In Reference 40, a high‐order perturbation technique coupled with reduced modal subspaces is developed to solve stochastic dynamic systems, which exhibits better performance than the classical perturbation methods. The spline chaos expansion (SCE) and the spline dimensional decomposition (SDD) methods are proposed in Reference 41 for stochastic modal analyses.…”

Section: Introductionmentioning

confidence: 99%

Efficient stochastic modal decomposition methods for structural stochastic static and dynamic analyses

Zheng,

Beer,

Nackenhorst

2024

Numerical Meth Engineering

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This article presents unified and efficient stochastic modal decomposition methods to solve stochastic structural static and dynamic problems. We extend the idea of deterministic modal decomposition method for structural dynamic analysis to stochastic cases. Standard/generalized stochastic eigenvalue equations are adopted to calculate the stochastic subspaces for stochastic static/dynamic problems and they are solved by an efficient reduced‐order method. The stochastic solutions of both static and dynamic equations are approximated by stochastic bases of the stochastic subspaces. Original stochastic static/dynamic equations are then transformed into a set of single‐degree‐of‐freedom (SDoF) stochastic static/dynamic equations, which are efficiently solved by the proposed non‐intrusive methods. Specifically, a non‐intrusive stochastic Newmark method is developed for the solution of SDoF stochastic dynamic equations, and the element‐wise division of sample vectors is used to solve the SDoF stochastic static equations. All of these methods have low computational effort and are weakly sensitive to the stochastic dimension, thus the proposed methods avoid the curse of dimensionality successfully. Two numerical examples, including two‐ and three‐dimensional spatial problems with low and high stochastic dimensions, are given to show the efficiency and accuracy of the proposed methods.

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Section: Introductionmentioning

confidence: 99%

Efficient stochastic modal decomposition methods for structural stochastic static and dynamic analyses

Zheng,

Beer,

Nackenhorst

2024

Numerical Meth Engineering

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“…Along with H ∞ optimization mechanism, another optimization method is concerned with deriving mathematical closed-form expressions for the damper’s optimal design parameters, called H 2 optimization, applicable for randomly excited dynamic systems (Adhikari et al, 2016; Chowdhury et al, 2022b; Khodaparast et al, 2008; Palmeri and Lombardo, 2011). An immense study was conducted on the TMD to mitigate the dynamic responses of automotive suspension systems, offshore platforms, buildings, and bridges with different solution procedures, analytical and numerical (Adhikari and Bhattacharya, 2012; Batou and Adhikari, 2019; Kasinos et al, 2021). The vibration reduction performance of TMD was amplified through a conventional approach, increasing the static mass of the damper, causing increasing the dead load, and affecting collapse during any seismic events with the presence of the damper.…”

Section: Introductionmentioning

confidence: 99%

The optimum enhanced viscoelastic tuned mass dampers: Exact closed-form expressions

Chowdhury

Banerjee

Adhikari

2023

Journal of Vibration and Control

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This paper introduces the inertial amplifier viscoelastic tuned mass dampers (IAVTMD). The viscoelastic materials are implanted inside the core material of the inertial amplifier tuned mass dampers. The standard linear solid models are applied mathematically to formulate the viscoelastic material. H2 and H ∞ optimization mechanisms apply to derive the exact mathematical closed-form formulations for optimal design parameters for novel inertial amplifier viscoelastic tuned mass dampers. The optimum IAVTMD installs at the top of the structures to mitigate the dynamic responses, determining the dynamic responses analytically through transfer function formation. At first, IAVTMD’s dynamic response reduction capacity compares with the conventional tuned mass damper’s (CTMD) dynamic response reduction capacity. As a result, H2 optimized IAVTMD’s dynamic response reduction capacity is significantly 20.87% and 26.47% superior to two well-established H2 optimized conventional tuned mass damper’s dynamic response reduction capacity. In addition, H ∞ optimized IAVTMD has 15.48% more dynamic response reduction capacity than H ∞ conventional tuned mass damper. H2 and H ∞ optimized tuned mass damper inerters with optimal closed-form solutions are introduced in this paper. A higher damper mass ratio and a lower inerter mass ratio are recommended to produce H2 and H ∞ optimized tuned mass damper inerter (TMDI) with a lower frequency and damping ratio in an affordable range. Accordingly, H2 and H ∞ optimized IAVTMD’s dynamic response reduction capacities are significantly 6.94% and 23.29% superior to H2 and H ∞ optimized TMDI’s dynamic response reduction capacity. The closed-form expressions for optimal design parameters of inertial amplifier viscoelastic tuned mass dampers and tuned mass damper inerters are mathematically correct and effective for practical applications.

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“…11 Successively, this improved perturbation method has been used in various contexts, for example, in the stochastic dynamic analysis of uncertain systems 12 or in the definition of new mode subspace definition. 13 All the above perturbation approaches are characterized by an accuracy that is strictly related to the level of uncertainties of the input RV, moreover, the computation effort of these approaches increases with higher orders of perturbation. In order to overcome the drawbacks related to the use of the above-mentioned approaches, in the last years, an approach working directly on the input-output PDFs, in the context of the probabilistic transformation method (PTM), has been proposed.…”

Section: Introductionmentioning

confidence: 99%

“…Some years ago, it was proposed the so‐called “improved” perturbation approach which considers mean and correlation information on uncertain parameters in computing the mathematical expectation of the response 11 . Successively, this improved perturbation method has been used in various contexts, for example, in the stochastic dynamic analysis of uncertain systems 12 or in the definition of new mode subspace definition 13 . All the above perturbation approaches are characterized by an accuracy that is strictly related to the level of uncertainties of the input RV, moreover, the computation effort of these approaches increases with higher orders of perturbation.…”

Section: Introductionmentioning

confidence: 99%

A new stochastic method based on the Taylor expansion to compute response probability densities of uncertain systems

Navarro‐Quiles

Laudani

Falsone

2022

Numerical Meth Engineering

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In this article, a new stochastic approach is proposed for the analysis of structural systems with uncertainties. This novel strategy method combines the probability transformation method, expressed in terms of characteristic function with a probabilistic version of the Taylor expansion. Some notes about the convergence and the accuracy of the proposed method are reported. The results of these notes and several examples here reported evidence an optimum level of accuracy, coupled with great simplicity of application of this approach, even for relatively high levels of uncertainties. Hence, this method can be considered a valuable tool for the solution of stochastic analyses of engineering systems. Several examples are performed to show the capability of the results established. These applications show how the method is a useful technique for engineering analysis.

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A reduced modal subspace approach for damped stochastic dynamic systems

Cited by 15 publications

References 53 publications

Efficient stochastic modal decomposition methods for structural stochastic static and dynamic analyses

Efficient stochastic modal decomposition methods for structural stochastic static and dynamic analyses

The optimum enhanced viscoelastic tuned mass dampers: Exact closed-form expressions

A new stochastic method based on the Taylor expansion to compute response probability densities of uncertain systems

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