The logarithmic decrement (log-dec) is one of the most popular methods for viscous damping estimation in linear, single degree of freedom systems. It estimates the damping ratio by examining the decay in the amplitude between two peaks some number of cycles apart. The accuracy in the estimation is sensitive to the chosen number of cycles, where the latter can be optimized such that the uncertainty in the estimation is minimized. However, the log-dec method is not suitable for systems with high damping ratios (approximately > 0.3). Another recent approach for damping estimation is based on considering a ratio of the amplitudes of the positive and negative areas in the free response of the oscillator. Although prior works on the areas method only tested lightly damped systems, we show here that — in contrast to log-dec — this approach can estimate the damping ratio over the whole range of underdamped linear oscillators. However, in contrast to log-dec, there are no available guidelines on how many areas to include in the damping estimation. In this work, we derive uncertainty analysis expressions for the areas method and we utilize them to obtain the optimal number of areas to use. Our results show that for a very low damping ratio (< 0.01), choosing more than two areas in the estimation increases the uncertainty. In contrast, for moderate to high damping (between 0.05 and 1), we need to consider all the available areas in the estimation. One caveat in the range of high damping (between 0.3 and 1) is that while it is desirable to include all the available areas, uncertainty increases when considering up to 3 areas. Therefore, if only 4 areas are available in this range, then to reduce the uncertainty in the estimate only the first two areas must be considered. The results are verified using a large number of numerical simulations including different levels of noise.
{"title":"Guidelines for Optimizing the Error in Area Ratio Damping Estimation Method","authors":"Balija Santoshkumar, Firas A. Khasawneh","doi":"10.1115/detc2021-70590","DOIUrl":"https://doi.org/10.1115/detc2021-70590","url":null,"abstract":"\u0000 The logarithmic decrement (log-dec) is one of the most popular methods for viscous damping estimation in linear, single degree of freedom systems. It estimates the damping ratio by examining the decay in the amplitude between two peaks some number of cycles apart. The accuracy in the estimation is sensitive to the chosen number of cycles, where the latter can be optimized such that the uncertainty in the estimation is minimized. However, the log-dec method is not suitable for systems with high damping ratios (approximately > 0.3). Another recent approach for damping estimation is based on considering a ratio of the amplitudes of the positive and negative areas in the free response of the oscillator. Although prior works on the areas method only tested lightly damped systems, we show here that — in contrast to log-dec — this approach can estimate the damping ratio over the whole range of underdamped linear oscillators. However, in contrast to log-dec, there are no available guidelines on how many areas to include in the damping estimation. In this work, we derive uncertainty analysis expressions for the areas method and we utilize them to obtain the optimal number of areas to use. Our results show that for a very low damping ratio (< 0.01), choosing more than two areas in the estimation increases the uncertainty. In contrast, for moderate to high damping (between 0.05 and 1), we need to consider all the available areas in the estimation. One caveat in the range of high damping (between 0.3 and 1) is that while it is desirable to include all the available areas, uncertainty increases when considering up to 3 areas. Therefore, if only 4 areas are available in this range, then to reduce the uncertainty in the estimate only the first two areas must be considered. The results are verified using a large number of numerical simulations including different levels of noise.","PeriodicalId":425665,"journal":{"name":"Volume 10: 33rd Conference on Mechanical Vibration and Sound (VIB)","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124209980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work deals with the amplitude-frequency response subharmonic resonance of 1/4 order of electrostatically actuated circular plates. The method of multiple scales is used to model the hard excitations and to predict the response. This work predicts that the steady state solutions are zero amplitude solutions, and non-zero amplitude solutions which consist of stable and unstable branches. The effects of parameters such as voltage and damping on the response are predicted. As the voltage increases, the non-zero amplitude solutions are shifted to lower frequencies. As the damping increases, the non-zero steady-state amplitudes are shifted to higher amplitudes, so larger initial amplitudes for the MEMS plate to reach non-zero steady-state amplitudes.
{"title":"Subharmonic Resonance of One Fourth Order of Electrostatically Actuated MEMS Circular Plates: Amplitude-Frequency Response","authors":"D. Caruntu, Julio Beatriz, Miguel Martinez","doi":"10.1115/detc2021-70415","DOIUrl":"https://doi.org/10.1115/detc2021-70415","url":null,"abstract":"\u0000 This work deals with the amplitude-frequency response subharmonic resonance of 1/4 order of electrostatically actuated circular plates. The method of multiple scales is used to model the hard excitations and to predict the response. This work predicts that the steady state solutions are zero amplitude solutions, and non-zero amplitude solutions which consist of stable and unstable branches. The effects of parameters such as voltage and damping on the response are predicted. As the voltage increases, the non-zero amplitude solutions are shifted to lower frequencies. As the damping increases, the non-zero steady-state amplitudes are shifted to higher amplitudes, so larger initial amplitudes for the MEMS plate to reach non-zero steady-state amplitudes.","PeriodicalId":425665,"journal":{"name":"Volume 10: 33rd Conference on Mechanical Vibration and Sound (VIB)","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133800625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Dielectric elastomers (DEs) are widely used in soft transducers with mechanical or electrical loads. DE devices are mainly used for applications under dynamic loads, such as, ocean wave generators, loudspeakers, oscillators, and artificial muscles. It is still a challenge to analytically solve the vibration equation of a DE transducer. For example, for a DE membrane undergoing stretching deformation that is studied in this paper, its vibration equation is highly nonlinear with high-order and fractional-order polynomials. Numerical integration (NI) methods or traditional harmonic balance (HB) methods were used in previous works, but the two methods have low efficiency for strong and complex nonlinearities, and it is difficult to improve the accuracy of the solution. In this work, a free-energy model is used to study the dynamic characteristics of a DE membrane undergoing in-plane deformation, which undergoes a combined load excited by mechanical compression and electric fields. To improve the calculation efficiency and accuracy, we employ a modified incremental harmonic balance (IHB) method based on the fast Fourier transform to solve the periodically-excited nonlinear dynamic equation of the DE membrane. Finally, results of the example verify that the modified IHB method is fast and accurate, and has a very good performance in solving a problem with high nonlinearities.
{"title":"A Modified Incremental Harmonic Balance Method for Periodic Forced Oscillations of a Dielectric Elastomer Membrane Undergoing In-Plane Deformation","authors":"Jian Zhang, Jian Zhao, Xuefeng Wang, Hongyu Wang","doi":"10.1115/detc2021-70823","DOIUrl":"https://doi.org/10.1115/detc2021-70823","url":null,"abstract":"\u0000 Dielectric elastomers (DEs) are widely used in soft transducers with mechanical or electrical loads. DE devices are mainly used for applications under dynamic loads, such as, ocean wave generators, loudspeakers, oscillators, and artificial muscles. It is still a challenge to analytically solve the vibration equation of a DE transducer. For example, for a DE membrane undergoing stretching deformation that is studied in this paper, its vibration equation is highly nonlinear with high-order and fractional-order polynomials. Numerical integration (NI) methods or traditional harmonic balance (HB) methods were used in previous works, but the two methods have low efficiency for strong and complex nonlinearities, and it is difficult to improve the accuracy of the solution. In this work, a free-energy model is used to study the dynamic characteristics of a DE membrane undergoing in-plane deformation, which undergoes a combined load excited by mechanical compression and electric fields. To improve the calculation efficiency and accuracy, we employ a modified incremental harmonic balance (IHB) method based on the fast Fourier transform to solve the periodically-excited nonlinear dynamic equation of the DE membrane. Finally, results of the example verify that the modified IHB method is fast and accurate, and has a very good performance in solving a problem with high nonlinearities.","PeriodicalId":425665,"journal":{"name":"Volume 10: 33rd Conference on Mechanical Vibration and Sound (VIB)","volume":"268 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121220962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
To obtain detail in elastic, frictional contact problems involving contact many — at least tens, and more suitably hundreds [1] — of nodes are necessary over the contact patch. Generally, this fine discretization results in intractable numbers of system equations that must be solved, but this problem is greatly mitigated when the elasticity of the contacting bodies is represented by elastic compliance matrices rather than stiffness matrices. An examination of the classical analytic expressions for the contact of disks — an example of smooth contact — shows that for most standard engineering metals, such as brass, steel, or titanium, the pressures that would cause more than one degree of arc of contact would push the materials past the elastic limit. The discretization necessary to capture the interface tractions would be on the order of at least tens of nodes. With the resulting boundary integral formulation would involve several hundreds of nodes over the disk, and the corresponding finite element mesh would have tens of thousands. The resulting linear system of equations must be solved at each load step and the numerical problem becomes extremely difficult or intractable. A compliance method of facilitating extremely fine contact patch resolution can be achieved by exploiting Fourier analysis and the Michell solution. The advantages of this compliance method are that only degrees of freedom on the surface are introduced and those not in the region of contact are eliminated from the system of equations to be solved.
{"title":"A Strategy for Fine Mesh Resolution in Contact Mechanics","authors":"Gaurav Chauda, D. Segalman","doi":"10.1115/detc2021-71360","DOIUrl":"https://doi.org/10.1115/detc2021-71360","url":null,"abstract":"\u0000 To obtain detail in elastic, frictional contact problems involving contact many — at least tens, and more suitably hundreds [1] — of nodes are necessary over the contact patch. Generally, this fine discretization results in intractable numbers of system equations that must be solved, but this problem is greatly mitigated when the elasticity of the contacting bodies is represented by elastic compliance matrices rather than stiffness matrices.\u0000 An examination of the classical analytic expressions for the contact of disks — an example of smooth contact — shows that for most standard engineering metals, such as brass, steel, or titanium, the pressures that would cause more than one degree of arc of contact would push the materials past the elastic limit.\u0000 The discretization necessary to capture the interface tractions would be on the order of at least tens of nodes. With the resulting boundary integral formulation would involve several hundreds of nodes over the disk, and the corresponding finite element mesh would have tens of thousands. The resulting linear system of equations must be solved at each load step and the numerical problem becomes extremely difficult or intractable.\u0000 A compliance method of facilitating extremely fine contact patch resolution can be achieved by exploiting Fourier analysis and the Michell solution. The advantages of this compliance method are that only degrees of freedom on the surface are introduced and those not in the region of contact are eliminated from the system of equations to be solved.","PeriodicalId":425665,"journal":{"name":"Volume 10: 33rd Conference on Mechanical Vibration and Sound (VIB)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122949784","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper demonstrates various data augmentation techniques that can be used when working with limited run-to-failure data to estimate health indicators related to the remaining useful life of roller bearings. The PRONOSTIA bearing prognosis dataset is used for benchmarking data augmentation techniques. The input to the networks are multi-dimensional frequency representations obtained by combining the spectra taken from two accelerometers. Data augmentation techniques are adapted from other machine learning fields and include adding Gaussian noise, region masking, masking noise, and pitch shifting. Augmented datasets are used in training a conventional CNN architecture comprising two convolutional and pooling layer sequences with batch normalization. Results from individually separating each bearing’s data for the purpose of validation shows that all methods, except pitch shifting, give improved validation accuracy on average. Masking noise and region masking both show the added benefit of dataset regularization by giving results that are more consistent after repeatedly training each configuration with new randomly generated augmented datasets. It is shown that gradually deteriorating bearings and bearings with abrupt failure are not treated significantly differently by the augmentation techniques.
{"title":"Data Augmentation for Roller Bearing Health Indicator Estimation Using Multi-Channel Frequency Data Representations","authors":"Jacob Hendriks, P. Dumond","doi":"10.1115/detc2021-66701","DOIUrl":"https://doi.org/10.1115/detc2021-66701","url":null,"abstract":"\u0000 This paper demonstrates various data augmentation techniques that can be used when working with limited run-to-failure data to estimate health indicators related to the remaining useful life of roller bearings. The PRONOSTIA bearing prognosis dataset is used for benchmarking data augmentation techniques. The input to the networks are multi-dimensional frequency representations obtained by combining the spectra taken from two accelerometers. Data augmentation techniques are adapted from other machine learning fields and include adding Gaussian noise, region masking, masking noise, and pitch shifting. Augmented datasets are used in training a conventional CNN architecture comprising two convolutional and pooling layer sequences with batch normalization. Results from individually separating each bearing’s data for the purpose of validation shows that all methods, except pitch shifting, give improved validation accuracy on average. Masking noise and region masking both show the added benefit of dataset regularization by giving results that are more consistent after repeatedly training each configuration with new randomly generated augmented datasets. It is shown that gradually deteriorating bearings and bearings with abrupt failure are not treated significantly differently by the augmentation techniques.","PeriodicalId":425665,"journal":{"name":"Volume 10: 33rd Conference on Mechanical Vibration and Sound (VIB)","volume":"115 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127319590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：