Comparison of different methodologies for the computation of damped nonlinear normal modes and resonance prediction of systems with non-conservative nonlinearities

Sun, Yekai; Yuan, Jie; Vizzaccaro, Alessandra; Salles, Loïc

doi:10.1007/s11071-021-06567-0

Cited by 15 publications

(3 citation statements)

References 41 publications

(61 reference statements)

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“…For the non-conservative nonlinear system, various types of damped nonlinear normal mode (dNNM) base on HBM can be adapted. Extended periodic motion concept (EPMC) [30] and complex nonlinear mode (CNM) [31,32] are two kinds of dNNMs, Sun et al [33] conducted a comprehensive comparison between these two approaches. Base on EPMC, Sun et al [34] introduced extended energy balance method (E-EBM) to predict the resonance response of the non-conservative nonlinear system under specific exciting forces.…”

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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Section: Introductionmentioning

confidence: 99%

Numerical and Experimental Investigation of Friction Damping in Shrouded Blades

Du,

Wang

2024

Preprint

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“…Then a linear modal analysis can be carried out, which is a standard task in every finite element tool. Relatively wellestablished computational methods are available for nonlinear modal analysis as well [9,10,11,12,13,14].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear damping quantification from phase-resonant tests under base excitation

Müller,

Woiwode,

Gross

et al. 2022

Preprint

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The present work addresses the experimental identification of amplitude-dependent modal parameters (modal frequency, damping ratio, Fourier coefficients of periodic modal oscillation). Phase-resonant testing has emerged as an important method for this task, as it substantially reduces the amount of data required for the identification compared to conventional frequency-response testing at different excitation/response levels. In the case of shaker-stinger excitation, the applied excitation force is commonly measured in order to quantify the amplitude-dependent modal damping ratio from the phase-resonant test data. In the case of base excitation, however, the applied excitation force is challenging or impossible to measure. In this work we develop an original method for damping quantification from phase-resonant tests. It relies solely on response measurement; it avoids the need to resort to force measurement. The key idea is to estimate the power provided by the distributed inertia force imposed by the base motion. We develop both a model-free and a model-based variant of the method. We validate the developed method first in virtual experiments of a friction-damped and a geometrically nonlinear system, and then in a physical experiment involving a thin beam clamped at both ends via bolted joints. We conclude that the method is highly robust and provides high accuracy already for a reasonable number of sensors.

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“…This energy balancing method was origi-nally derived based on systems with conservative nonlinearity and, recently, it has been extended to account for non-conservative nonlinearity with applications in full-scale structures [37] using the concept of damped NNMs [20]. This extended energy balancing method has been compared with nonlinear modal synthesis in predicting resonances [38].…”

Section: Introductionmentioning

confidence: 99%

Efficient energy balancing across multiple harmonics of nonlinear normal modes

2022

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Predicting the forced responses of nonlinear systems is a topic that attracts extensive studies. The energy balancing method considers the net energy transfer in and out of the system over one period and establishes connections between forced responses and nonlinear normal modes (NNMs). In this paper, we consider the energy balancing across multiple harmonics of NNMs for predicting forced resonances. This technique is constructed by combining the energy balancing mechanism with restrictions (established via excitation scenarios) on external forcing and harmonic phase-shifts; a semi-analytical framework is derived to achieve both accurate/robust results and efficient computations. With known inputs from NNM solutions, the required forcing amplitudes to reach NNMs at resonances, along with their discrepancy, i.e. the harmonic phase-shifts, are computed via a one-step scheme. Several examples are presented for different excitation scenarios to demonstrate the applicability of this method and to show its capability in accurately predicting the existence of an isola where multiple harmonics play a significant part in the response.

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Comparison of different methodologies for the computation of damped nonlinear normal modes and resonance prediction of systems with non-conservative nonlinearities

Cited by 15 publications

References 41 publications

Numerical and Experimental Investigation of Friction Damping in Shrouded Blades

Numerical and Experimental Investigation of Friction Damping in Shrouded Blades

Nonlinear damping quantification from phase-resonant tests under base excitation

Efficient energy balancing across multiple harmonics of nonlinear normal modes

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