Computation of damped nonlinear normal modes for large scale nonlinear systems in a self-adaptive modal subspace

Yuan, Jie; Sun, Yekai; Schwingshackl, Christoph W.; Salles, Loïc

doi:10.1016/j.ymssp.2021.108082

Cited by 19 publications

(4 citation statements)

References 42 publications

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“…Since they are not linear functions of states or explicit functions of time, it is not possible to transform directly to the frequency domain [64]. The nonlinear force response is converted to the frequency domain through the Alternating-time-frequency procedure, which is able to calculate different types of nonlinear functions even with nonsmooth nonlinearties [65]. For each iteration, the predicted values of 𝑋 0 , 𝑋 𝑘,𝑠 , 𝑋 𝑘,𝑐 and 𝜔 are used in Equations 5 to obtain the time domain response over a period.…”

Section: Hbm Based Numerical Continuationmentioning

confidence: 99%

Data-Driven Bayesian Inference for Stochastic Model Identification of Nonlinear Aeroelastic Systems

McGurk,

Lye,

Renson

et al. 2024

AIAA Journal

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The objective of this work is to propose a data-driven Bayesian inference framework to efficiently identify parameters and select models of nonlinear aeroelastic systems. The framework consists of the use of Bayesian theory together with advanced kriging surrogate models to effectively represent the limit cycle oscillation response of nonlinear aeroelastic systems. Three types of sampling methods, namely, Markov chain Monte Carlo, transitional Markov chain Monte Carlo, and the sequential Monte Carlo sampler, are implemented into Bayesian model updating. The framework has been demonstrated using a nonlinear wing flutter test rig. It is modeled by a two-degree-of-freedom aeroelastic system and solved by the harmonic balance methods. The experimental data of the flutter wing is obtained using control-based continuation techniques. The proposed methodology provided up to a 20% improvement in accuracy compared to conventional deterministic methods and significantly increased computational efficiency in the updating and uncertainty quantification processes. Transitional Markov chain Monte Carlo was identified as the optimal choice of sampling method for stochastic model identification. In selecting alternative nonlinear models, multimodal solutions were identified that provided a closer representation of the physical behavior of the complex aeroelastic system than a single solution.

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Section: Hbm Based Numerical Continuationmentioning

confidence: 99%

Data-Driven Bayesian Inference for Stochastic Model Identification of Nonlinear Aeroelastic Systems

McGurk,

Lye,

Renson

et al. 2024

AIAA Journal

Self Cite

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show abstract

“…As they are not linear functions of states or explicit functions of time, it is not possible to transform directly to the frequency domain [58]. The nonlinear force response is converted to the frequency domain through the Alternating-time-frequency procedure [59].…”

Section: Hbm Based Numerical Continuationmentioning

confidence: 99%

Data-driven Bayesian inference for stochastic model identification of nonlinear aeroelastic systems

McGurk,

Lye,

Renson

et al. 2023

Preprint

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The objective of this work is to propose a data-driven Bayesian inference framework to efficiently identify parameters and select models of nonlinear aeroelastic systems. The framework consists of the use of Bayesian theory together with advanced Kriging surrogate models to effectively represent the limit cycle oscillation response of nonlinear aeroelastic systems. Three types of sampling methods, namely Markov Chain Monte-Carlo, Transitional Markov Chain Monte-Carlo, and the Sequential Monte-Carlo sampler, are implemented into Bayesian model updating. The framework has been demonstrated using a nonlinear wing flutter test rig. It is modelled by a two-degree-of-freedom aeroelastic system and solved by the harmonic balance methods. The experimental data of the flutter wing is obtained using control-based continuation techniques. The proposed methodology provided up to 20 % improvement in accuracy compared to conventional deterministic methods. Transitional Markov Chain Monte-Carlo was identified as the optimal choice of the sampling method for stochastic model identification. In selecting alternative nonlinear models, multi-modal solutions were identified that provided a closer representation of physical behaviour suggesting the mathematical model requires further modification.

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“…This method can avoid the time-consuming Monte Carlo simulation. Yuan et al [39] contributed to efficiency improvements by proposing a self-adaptive modal reduce method. Their method only reserves the sliding nodes of the system, resulting in a speedup of up to 120 times compared with the traditional Craig-Bampton (CB) method [40,41].…”

Section: Introductionmentioning

confidence: 99%

Numerical and Experimental Investigation of Friction Damping in Shrouded Blades

Du,

Wang

2024

Preprint

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The blade is a critical turbine engine component that faces a high risk of high-cycle fatigue (HCF). To reduce its vibration, shrouded blades are often employed. However, the dynamic behavior of the shrouded blade is complex, making it challenging to accurately predict its damping ratio and resonance frequency. In this study, an economical experimental setup was designed, which requires only two blades to investigate the dynamic characteristics of shrouded blades. A novel method was adapted to measure the contact force and friction coefficient of the shrouds. Sinusoidal excitations were executed, and frequency response functions (FRFs) were recorded. Subsequently, study established a relationship between resonance frequency to vibrational stress using these FRFs. Additionally, the experiment was simulated by the harmonic balance method (HBM). A hysteresis spring contact model was adapted to simulate the contact of the shrouds. Vibrational stress, resonance frequency and damping ratio were computed base on the displacement outcomes from the HBM simulation. The consistency between the obtained simulation outcomes and experimental results was found to be satisfactory, indicating that the proposed approach effectively captured the complex behavior of the shrouded blades.

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Computation of damped nonlinear normal modes for large scale nonlinear systems in a self-adaptive modal subspace

Cited by 19 publications

References 42 publications

Data-Driven Bayesian Inference for Stochastic Model Identification of Nonlinear Aeroelastic Systems

Data-Driven Bayesian Inference for Stochastic Model Identification of Nonlinear Aeroelastic Systems

Data-driven Bayesian inference for stochastic model identification of nonlinear aeroelastic systems

Numerical and Experimental Investigation of Friction Damping in Shrouded Blades

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