Lateral vibration attenuation of a beam with circular cross-section by a support with integrated piezoelectric transducers shunted to negative capacitances

Götz, Benedict; Schaeffner, M; Platz, Roland; Melz, Tobias

doi:10.1088/0964-1726/25/9/095045

Cited by 13 publications

(16 citation statements)

References 18 publications

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“…With the estimated distribution of X we generate a samples of size L n and N 2,n . We use the first sample to generate the data set (3). The second one is necessary in the density estimation later on.…”

Section: Definition Of the Estimatementioning

confidence: 99%

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Estimation of Uncertainty in the Lateral Vibration Attenuation of a Beam with Piezo-Elastic Supports by Neural Networks

Götz

Kersting

2018

AMM

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Quantification of uncertainty in technical systems is often based on surrogate models of corresponding simulation models. Usually, the underlying simulation model does not describe the reality perfectly, and consequently the surrogate model will be imperfect.In this article we propose an improved surrogate model of the vibration attenuation of a beam with shunted piezoelectric transducers. Therefore, experimentally observed and simulated variations in the vibration attenuation are combined in the model estimation process, by using multi--layer feedforward neural networks. Based on this improved surrogate model, we construct a density estimate of the maximal amplitude in the vibration attenuation.The density estimate is used to analyze the uncertainty in the vibration attenuation, resulting from manufacturing variations.

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Section: Definition Of the Estimatementioning

confidence: 99%

“…The used values are λ * 1 = 9.11, λ * 2 = 5.68, λ * 3 = 13.97 and λ * 4 = 1.64. We set v m (x) =x 1 + tan(x 2 ) + x 3 3 + log(x 4 + 0.1)…”

Section: Application To Simulated and Real Datamentioning

confidence: 99%

Estimation of Uncertainty in the Lateral Vibration Attenuation of a Beam with Piezo-Elastic Supports by Neural Networks

Götz

Kersting

2018

AMM

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“…The reference structure for the application of the global sensitivity analysis is a beam with piezo-elastic supports that is used for two different applications of passive and active structural control: active buckling control [11] and passive lateral vibration attenuation [12]. Figure 1 shows the beam structure with piezo-elastic supports and the sectional view of the piezoelastic support.…”

Section: Structure Descriptionmentioning

confidence: 99%

“…Figure 2: Simplified model of the beam structure with piezo-elastic supports A and B [12] rotational stiffness k 'y,A = k 'z,A = k r,A and k 'y,B = k 'z,B = k r,B around the y-and z-axes. The spring stiffness values are assumed to be equal in y-and z-direction for this study since both directions are modeled symmetric and independent of each other.…”

Section: Structure Descriptionmentioning

confidence: 99%

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Approach to Prove the Efficiency of the Monte Carlo Method Combined With the Elementary Effect Method to Quantify Uncertainty of a Beam Structure With Piezo-Elastic Supports

Li¹,

Goetz²,

Schaeffner³

et al. 2017

Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Abstract. In this paper, a new approach is presented to prove the efficiency of the direct Monte Carlo method combined with the Elementary Effect method to quantify structural data uncertainty under uncertain input parameters of a beam structure. Normally, the application of the direct Monte Carlo method requires high computational cost when all input parameters are taken into account. It is proposed to use a combination of the direct Monte Carlo method and the Elementary Effect method for the variance-based sensitivity analysis, named the combined Monte Carlo method. By the application of the Elementary Effect method as a screening method, the truely influential input parameters are identified. Then, the parametric uncertainty is analyzed only under these influential input parameters' uncertainty by the use of the Monte Carlo method. Through a combination of these two methods, the number of simulations can be significantly reduced due to the reduction of the number of analyzed input parameters.The novelty of this paper is to investigate the accuracy and the efficiency of this combined approach by the use of a beam structure with piezo-elastic supports for buckling and vibration control as a reference structure. The uncertain structural input parameters are the geometric, material, and stiffness parameters of the piezo-elastic supports. The output variable is the first lateral resonance frequency of the beam structure. Its uncertainty will be analyzed by the application of the combined Monte Carlo method applied for only a few but influential input parameters and will also be analyzed by the application of the direct Monte Carlo method for all input parameters. The results by the two methods will be compared based on the analysis accuracy to estimate the sensitivity of the input parameters on the first lateral resonance frequency and the minimal required number of the simulations.

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Analysis, Quantification and Evaluation of Uncertainty

Schäffner

Abele

Anderl

et al. 2021

Springer Tracts in Mechanical Engineering

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This chapter describes the various approaches to analyse, quantify and evaluate uncertainty along the phases of the product life cycle. It is based on the previous chapters that introduce a consistent classification of uncertainty and a holistic approach to master the uncertainty of technical systems in mechanical engineering. Here, the following topics are presented: the identification of uncertainty by modelling technical processes, the detection and handling of data-induced conflicts, the analysis, quantification and evaluation of model uncertainty as well as the representation and visualisation of uncertainty. The different approaches are discussed and demonstrated on exemplary technical systems.

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Lateral vibration attenuation of a beam with circular cross-section by a support with integrated piezoelectric transducers shunted to negative capacitances

Cited by 13 publications

References 18 publications

Estimation of Uncertainty in the Lateral Vibration Attenuation of a Beam with Piezo-Elastic Supports by Neural Networks

Estimation of Uncertainty in the Lateral Vibration Attenuation of a Beam with Piezo-Elastic Supports by Neural Networks

Approach to Prove the Efficiency of the Monte Carlo Method Combined With the Elementary Effect Method to Quantify Uncertainty of a Beam Structure With Piezo-Elastic Supports

Analysis, Quantification and Evaluation of Uncertainty

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