Equivalent linear systems of nonlinear systems

Friis, Tobias; Tarpø, Marius; Katsanos, Evangelos; Brincker, Rune

doi:10.1016/j.jsv.2019.115126

Cited by 11 publications

(4 citation statements)

References 37 publications

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Section: Introductionmentioning

confidence: 99%

“…The other is to linearize the SIBs equivalently and calculate equivalent linearization (EL) parameters, that is, the equivalent damping coefficient (EDC) and equivalent additional stiffness (EAS), thereby obtaining the seismic response by mode analysis method or time history analysis method. [23][24][25] This approach has significant meaning for practical applications owing to its low computational cost and high efficiency. The equations of the equivalent damping ratio proposed by Diotallevi et al and Landi et al are derived based on Single-Degree-of-Freedom (SDoF) systems under the assumption that the external action is sinusoidal excitation.…”

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confidence: 99%

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The inter‐history iteration method for seismic response analysis of seismically isolated structures and its secondary development based on ABAQUS

Jia,

Li,

et al. 2023

Structural Design Tall Build

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SummaryIn seismic response analysis of seismically isolated structures (SISs), the nonlinearity is concentrated in the isolation layer while the upper structure behaves linearly, making SISs locally nonlinear systems. This paper proposed a novel seismic analysis method based on equivalent linearization (EL) and iterative solution for SISs. In this method, the equilibrium equations of an SIS are expressed by the second‐order ordinary differential equations of the structural system as well as the hysteretic force of seismic isolation bearings (SIBs). Based on EL theory, the linearized equilibrium equations of the overall system were reconstructed in which the EL parameters are derived theoretically. The inter‐history iteration (IHI) method was proposed to solve the linearized equation system and calculate the EL parameters in sequence iteratively for seismic response analysis of SISs, thus reducing computational cost without excessive loss of accuracy. In addition, the secondary development of the proposed method was programmed in ABAQUS for ease of engineering applications. Finally, the convergence and accuracy of the method were investigated through numerical simulation of an SIS case study. As the numerical investigation indicates, the proposed method considers the coupling between structural response and the EL parameters, achieving a high convergence rate and satisfactory solution accuracy. The ABAQUS secondary development program utilizes the powerful pre‐processor, post‐processor, and solvers of ABAQUS, making the IHI method more appropriate for engineering applications.

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Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

The inter‐history iteration method for seismic response analysis of seismically isolated structures and its secondary development based on ABAQUS

Jia,

Li,

et al. 2023

Structural Design Tall Build

View full text Add to dashboard Cite

show abstract

“…ough calculation of the direct nonlinear responses has been studied for many years, it is still in difficulty for dealing with engineering structures with a huge number of degrees of freedom (DOFs), especially under random excitations. e equivalent linearization to deal with nonlinearity is currently adopted because of the maturity and convenience to calculate the random vibration response [4,5]. Friis et al [4] summarized three commonly used equivalent methods with numerical examples, including the energy balance method, the intensity balance method, and the direct linear fit in the least squares sense.…”

Section: Introductionmentioning

confidence: 99%

“…e equivalent linearization to deal with nonlinearity is currently adopted because of the maturity and convenience to calculate the random vibration response [4,5]. Friis et al [4] summarized three commonly used equivalent methods with numerical examples, including the energy balance method, the intensity balance method, and the direct linear fit in the least squares sense. Alibrandi and Mosalam [6] proposed three linear equivalence methods for reliability evaluation of random vibration structures, that is, Gaussian linear equivalent linearization, tail equivalent linearization, and tail probability equivalent linearization.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Uncertainty Identification of Model Parameters for the Jointed Structures with Nonlinearity

Shen

Liu

Zang

et al. 2021

Shock and Vibration

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Jointed structures in engineering naturally perform with some of nonlinearity and uncertainty, which significantly affect the dynamic characteristics of the structural system. In this paper, the method of Bayesian uncertainty identification of model parameters for the jointed structures with local nonlinearity is proposed. Firstly, the nonlinear stiffness and damping of the joints under the random excitation are represented with functions of excitation magnitude in terms of the equivalent linearization. The process of uncertainty identification is separated from the representation of local nonlinearity. In this way, the dynamic behavior of the joints is penetratingly characterized instead of ascribing the nonlinearity to uncertainty. Secondly, a variable-expanded Bayesian (VEB) method is originally proposed to identify the mixed of aleatory and epistemic uncertainties of model parameters. Different from traditional Bayesian identification, the aleatory uncertainties of model parameters are identified as one of the most important parts rather than only measurement noise of output. Notablely, a series of intermediate variables are introduced to expand the parameter with aleatory uncertainty in order to overcome the difficulty of establishing the likelihood function. Moreover, a 3-DOF numerical example is illustrated with case studies to verify the proposed method. The influence of observed sample size and prior distribution selection on the identification results is tested. Furthermore, an engineering example of the jointed structure with rubber isolators is performed to show the practicability of the proposed method. It is indicated that the computational model updated with the accurately identified parameters with both nonlinearity and uncertainty has shown the excellent predictive capability.

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An investigation into model extrapolation and stability in the system identification of a nonlinear structure

et al. 2023

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Estimating a nonlinear model from experimental measurements of a vibrating structure remains a challenge, despite huge progress in recent years. A major issue is that the dynamical behaviour of a nonlinear structure strongly depends on the magnitude of the displacement response. Thus, the validity of an identified model is generally limited to a certain range of motion. Also, outside this range, the stability of the solutions predicted by the model are not guaranteed. This raises the question as to how a nonlinear model derived using data from relatively low amplitude excitation can be used to predict the dynamical behaviour for higher amplitude excitation. This paper focuses on this problem, investigating the extrapolation capabilities of data-driven nonlinear state-space models based on a subspace approach. The experimental vibrating structure consists of a cantilever beam in which magnets are used to generate strong geometric nonlinearity. The beam is driven by an electrodynamic shaker using several levels of broadband random noise. Acceleration data from the beam tip are used to derive nonlinear state-space models for the structure. It is shown that model predictions errors generally tend to increase when extrapolating towards higher excitation levels. Furthermore, the validity of the estimated nonlinear models become poor for very strong nonlinear behaviour. Linearised models are also estimated to have a complete view of the performance of each candidate model for each level of excitation.

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Equivalent linear systems of nonlinear systems

Cited by 11 publications

References 37 publications

The inter‐history iteration method for seismic response analysis of seismically isolated structures and its secondary development based on ABAQUS

The inter‐history iteration method for seismic response analysis of seismically isolated structures and its secondary development based on ABAQUS

Bayesian Uncertainty Identification of Model Parameters for the Jointed Structures with Nonlinearity

An investigation into model extrapolation and stability in the system identification of a nonlinear structure

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