Calculation of Nonlinear Systems Under Narrow Band Excitation Using Equivalent Linearization and Path Continuation

2021 ◽  
Author(s):  
Alwin Förster ◽  
Lars Panning-von Scheidt
Keyword(s):  
Nonlinear Systems ◽  
Narrow Band ◽  
Gaussian White Noise ◽  
Random Excitation ◽  
Mean Value ◽  
Equivalent Linearization ◽  
Efficient Procedure ◽  
Stochastic Excitations ◽  
Wide Range ◽  
The One

Abstract Turbomachines experience a wide range of different types of excitation during operation. On the structural mechanics side, periodic or even harmonic excitations are usually assumed. For this type of excitation there are a variety of methods, both for linear and nonlinear systems. Stochastic excitation, whether in the form of Gaussian white noise or narrow band excitation, is rarely considered. As in the deterministic case, the calculations of the vibrational behavior due to stochastic excitations are even more complicated by nonlinearities, which can either be unintentionally present in the system or can be used intentionally for vibration mitigation. Regardless the origin of the nonlinearity, there are some methods in the literature, which are suitable for the calculation of the vibration response of nonlinear systems under random excitation. In this paper, the method of equivalent linearization is used to determine a linear equivalent system, whose response can be calculated instead of the one of the nonlinear system. The method is applied to different multi-degree of freedom nonlinear systems that experience narrow band random excitation, including an academic turbine blade model. In order to identify multiple and possibly ambiguous solutions, an efficient procedure is shown to integrate the mentioned method into a path continuation scheme. With this approach, it is possible to track jump phenomena or the influence of parameter variations even in case of narrow band excitation. The results of the performed calculations are the stochastic moments, i.e. mean value and variance.

scholarly journals Linearization of randomly excited nonlinear systems by using local mean square error criterion

2000 ◽  
Vol 22 (2) ◽  
pp. 111-123 ◽  
Author(s):  
Luu Xuan Hung
Keyword(s):  
Nonlinear Systems ◽  
Linear Systems ◽  
Mean Square Error ◽  
Random Excitation ◽  
Equivalent Linearization ◽  
Mean Square ◽  
Error Criterion ◽  
Local Mean ◽  
Non Linear Systems ◽  
Mean Square Error Criterion

The paper presents the analysis of three non-linear systems under random excitation by using Local Mean Square Error Criterion which is an extension of Gaussian Equivalent Linearization proposed by Caughey. The obtained results shows that the new technique allows to get much more accurate solutions than .that using Caughey Criterion. The paper leads out some new conclusions which have not been found yet by the previous researches. The new conclusions more clarify the significance of this technique.

scholarly journals Computation of the Optimal Normal Load of a Friction Damper Under Different Types of Excitation

1999 ◽  
Author(s):  
D. Cha ◽  
A. Sinha
Keyword(s):  
White Noise ◽  
Narrow Band ◽  
Normal Load ◽  
Harmonic Balance Method ◽  
Random Excitation ◽  
Linearization Method ◽  
Equivalent Linearization ◽  
Friction Damper ◽  
Different Types ◽  
Sinusoidal Excitation

In this paper, forced responses of a frictionally damped turbine blade are investigated for three different types of excitation: white noise excitation, narrow band random excitation and deterministic sinusoidal excitation. To determine the steady state nonlinear response, the harmonic balance method is used for sinusoidal excitation, and the equivalent linearization method is used for white noise and narrow band random excitations. Using a new set of nondimensionalized variables, the optimal value of normal load of a friction damper is found to be almost independent of the nature of excitation. The effectiveness of the damper in reducing the vibration level is also examined for the aforementioned three different types of excitation.

scholarly journals Frequency transfer of the ventriloquism aftereffect

2021 ◽  
Author(s):  
Rachel Ege ◽  
A. John van Opstal ◽  
Marc Mathijs van Wanrooij
Keyword(s):  
Visual Stimulus ◽  
Narrow Band ◽  
Gaussian White Noise ◽  
Low Frequency ◽  
Head Movements ◽  
Visual Distracter ◽  
Ventriloquism Aftereffect ◽  
The One ◽  
The Right ◽  
Adaptation Phase

The ventriloquism aftereffect (VAE) describes the persistent shift of perceived sound location after having been adapted to a ventriloquism condition, in which the sound was repeatedly paired with a displaced visual stimulus. In the latter case, participants consistently mislocalize the sound in the direction of the visual stimulus (ventriloquism effect, VE). Previous studies provide conflicting reports regarding the strength of the VAE, ranging from 0 to nearly 100%. Moreover, there is controversy about its generalization to different sounds than the one inducing the VE, ranging from no transfer at all, to full transfer across different sound spectra. Here, we imposed the VE for three different sounds: a low-frequency and a high-frequency narrow-band noise, and a broadband Gaussian white noise (GWN). In the adaptation phase, listeners generated fast goal-directed head movements to localize the sound, presented across a 70 deg range in the horizontal plane, while ignoring a visual distracter that was consistently displaced 10 deg to the right of the sound. In the post-adaptation phase, participants localized narrow-band sounds with center frequencies from 0.5 to 8 kHz, as well as GWN, without the visual distracter. Our results show that the VAE amounted to approximately 40% of the VE and generalized well across the entire frequency domain. We also found that the strength of the VAE correlated with the pre-adaptation sound-localization performance. We compare our results with previous reports and discuss different hypotheses regarding optimal audio-visual cue integration.

scholarly journals Friction Damping of Random Vibration in Gas Turbine Engine Airfoils

1987 ◽  
Author(s):  
Alok Sinha
Keyword(s):  
White Noise ◽  
Numerical Simulations ◽  
Gas Turbine ◽  
Turbine Blade ◽  
Random Vibration ◽  
Gaussian White Noise ◽  
Random Excitation ◽  
Equivalent Linearization ◽  
Turbine Engine ◽  
Optimal Value

The optimal value of slip load is calculated for a frictionally damped turbine blade subjected to random excitation. The nature of excitation is assumed to be Gaussian white noise and the statistics of response are obtained using equivalent linearization approach. The results from this technique are compared with those from numerical simulations.

Statistics of Responses of a Mistuned and Frictionally Damped Bladed Disk Assembly Subjected to White Noise and Narrow Band Excitations

2000 ◽  
Author(s):  
D. Cha ◽  
A. Sinha
Keyword(s):  
White Noise ◽  
Narrow Band ◽  
Random Excitation ◽  
Linearization Method ◽  
Equivalent Linearization ◽  
Friction Dampers ◽  
Analytical Technique ◽  
Bladed Disk ◽  
Bladed Disk Assembly ◽  
Equivalent Linearization Method

In this paper, the effects of friction dampers on the vibration of a mistuned bladed disk assembly are examined for the following types of random excitation: white noise and narrow band. To compute the statistics of nonlinear response, an analytical technique is developed based on the equivalent linearization method. The validity of the analytical technique has been established by comparison with the results from numerical simulations. The relation between the vibration mode of the system and the performance of friction dampers is investigated.

General Trend of Negative Transference Number in Li Salt/Ionic Liquid Mixtures

2019 ◽  
Author(s):  
Nicola Molinari ◽  
Jonathan P. Mailoa ◽  
Boris Kozinsky
Keyword(s):  
Ionic Liquid ◽  
Transference Number ◽  
Liquid Mixtures ◽  
Single Linkage ◽  
Self Diffusion ◽  
Wide Range ◽  
Single Linkage Cluster ◽  
Concentrated Solution ◽  
The One ◽  
Dynamics Simulations

We show that strong cation-anion interactions in a wide range of lithium-salt/ionic liquid mixtures result in a negative lithium transference number, using molecular dynamics simulations and rigorous concentrated solution theory. This behavior fundamentally deviates from the one obtained using self-diffusion coefficient analysis and agrees well with experimental electrophoretic NMR measurements, which accounts for ion correlations. We extend these findings to several ionic liquid compositions. We investigate the degree of spatial ionic coordination employing single-linkage cluster analysis, unveiling asymmetrical anion-cation clusters. Additionally, we formulate a way to compute the effective lithium charge that corresponds to and agrees well with electrophoretic measurements and show that lithium effectively carries a negative charge in a remarkably wide range of chemistries and concentrations. The generality of our observation has significant implications for the energy storage community, emphasizing the need to reconsider the potential of these systems as next generation battery electrolytes.<br>

A Comparison of Physiological Demand between Self-Propelled and Motorized Treadmill Exercise

2018 ◽  
Vol 7 (4) ◽  
pp. 13-21
Author(s):  
Todd Backes ◽  
Charlene Takacs
Keyword(s):  
Respiratory Exchange Ratio ◽  
Treadmill Exercise ◽  
Cardiopulmonary Exercise Testing ◽  
Mean Value ◽  
The Self ◽  
Mixing Chamber ◽  
Wide Range ◽  
The Subject ◽  
The Mean ◽  
Computer Controlled

There are a wide range of options for individuals to choose from in order to engage in aerobic exercise; from outdoor running to computer controlled and self-propelled treadmills. Recently, self-propelled treadmills have increased in popularity and provide an alternative to a motorized treadmill. Twenty subjects (10 men, 10 women) ranging in age from 19-23 with a mean of 20.4 ± 0.8 SD were participants in this study. The subjects visited the laboratory on three occasions. The purpose of the first visit was to familiarize the subject with the self-propelled treadmill (Woodway Curve 3.0). The second visit, subjects were instructed to run on the self-propelled treadmill for 3km at a self-determined pace. Speed data were collected directly from the self-propelled treadmill. The third visit used speed data collected during the self-propelled treadmill run to create an identically paced 3km run for the subjects to perform on a motorized treadmill (COSMED T150). During both the second and third visit, oxygen consumption (VO2) and respiratory exchange ratio (R) data were collected with COSMED’s Quark cardiopulmonary exercise testing (CPET) metabolic mixing chamber system. The VO2 mean value for the self-propelled treadmill (44.90 ± 1.65 SE ml/kg/min) was significantly greater than the motorized treadmill (34.38 ± 1.39 SE ml/kg/min). The mean R value for the self-propelled treadmill (0.91 ± 0.01 SE) was significantly greater than the motorized treadmill (0.86 ± 0.01 SE). Our study demonstrated that a 3km run on a self-propelled treadmill does elicit a greater physiological response than a 3km run at on a standard motorized treadmill. Self-propelled treadmills provide a mode of exercise that offers increased training loads and should be considered as an alternative to motorized treadmills.

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