Epicyclic gears also commonly referred to as planetary gears, are power transfer components that are commonly used in several industrial applications. The structural compliance of thin-rimmed annular ring gear can significantly influence the performance of an epicyclic gear set. As powertrain components are continually being optimized to their design limits, this influence becomes prominent and can no longer be ignored. Therefore to capture the influence associated with ring gear flexibility, the current study will incorporate a finite element based ring gear formulation into the three-dimensional planetary dynamic load distribution model of Ryali et al. [1]. The proposed contact model employs a modified simplex algorithm to iteratively solve for the elastic gear mesh contacts in conjunction with a numerical integration scheme, which enables it to inherently capture the influence of several component and system level design variations without the need for an empirical mesh stiffness formulation or transmission error excitation of the system. The developed formulation will be used to study the dynamic response of planetary gear sets where the ring gear is a rotating member. The discussed results demonstrate the fidelity of the developed model, thus making it an excellent tool for the design and analysis of planetary gears.
{"title":"A Contact Load Distribution Model to Capture the Influence of Structurally Compliant Rotating Ring Gear on the Dynamic Response of Epicyclic Gear Sets","authors":"L. Ryali, D. Talbot","doi":"10.1115/1.4062116","DOIUrl":"https://doi.org/10.1115/1.4062116","url":null,"abstract":"\u0000 Epicyclic gears also commonly referred to as planetary gears, are power transfer components that are commonly used in several industrial applications. The structural compliance of thin-rimmed annular ring gear can significantly influence the performance of an epicyclic gear set. As powertrain components are continually being optimized to their design limits, this influence becomes prominent and can no longer be ignored. Therefore to capture the influence associated with ring gear flexibility, the current study will incorporate a finite element based ring gear formulation into the three-dimensional planetary dynamic load distribution model of Ryali et al. [1]. The proposed contact model employs a modified simplex algorithm to iteratively solve for the elastic gear mesh contacts in conjunction with a numerical integration scheme, which enables it to inherently capture the influence of several component and system level design variations without the need for an empirical mesh stiffness formulation or transmission error excitation of the system. The developed formulation will be used to study the dynamic response of planetary gear sets where the ring gear is a rotating member. The discussed results demonstrate the fidelity of the developed model, thus making it an excellent tool for the design and analysis of planetary gears.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85175569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Built-up structures exhibit nonlinear dynamic phenomena due to friction at the surfaces that are held together using mechanical fasteners. This nonlinearity is hysteretic, or history dependent. Additionally, interfacial slip results in stiffness and damping variations that are dependent on the vibration amplitude. In the microslip regime, the dissipation varies as a power of the amplitude. The four-parameter Iwan model can capture both the hysteretic and power-law dissipation behavior that is characteristic of many bolted joints. However, simulating the dynamic response of this model is computationally expensive since the states of several slider elements must be tracked implicitly, necessitating the use of fixed-step integration schemes with small time steps. The Bouc-Wen model is an alternative hysteretic model in which the restoring force is given by a first order nonlinear differential equation. Numerical integration of this model is much faster because it consists of just one additional state variable, i.e. the hysteretic variable. Existing literature predominantly focuses on studying the steady-state behavior of this model. This paper tests the effectiveness of the Bouc-Wen model in capturing power-law dissipation by comparing it to four-parameter Iwan models with various parameters. Additionally, the effect of each Bouc-Wen parameter on the overall amplitude-dependent damping is presented. The results show that the Bouc-Wen model cannot capture power-law behavior over the entire microslip regime, but it can be tuned to simulate the response over a smaller amplitude range.
{"title":"A Parametric Study of the Bouc-Wen Model for Bolted Joint Dynamics","authors":"D. Shetty, M. Allen","doi":"10.1115/1.4062103","DOIUrl":"https://doi.org/10.1115/1.4062103","url":null,"abstract":"\u0000 Built-up structures exhibit nonlinear dynamic phenomena due to friction at the surfaces that are held together using mechanical fasteners. This nonlinearity is hysteretic, or history dependent. Additionally, interfacial slip results in stiffness and damping variations that are dependent on the vibration amplitude. In the microslip regime, the dissipation varies as a power of the amplitude. The four-parameter Iwan model can capture both the hysteretic and power-law dissipation behavior that is characteristic of many bolted joints. However, simulating the dynamic response of this model is computationally expensive since the states of several slider elements must be tracked implicitly, necessitating the use of fixed-step integration schemes with small time steps. The Bouc-Wen model is an alternative hysteretic model in which the restoring force is given by a first order nonlinear differential equation. Numerical integration of this model is much faster because it consists of just one additional state variable, i.e. the hysteretic variable. Existing literature predominantly focuses on studying the steady-state behavior of this model. This paper tests the effectiveness of the Bouc-Wen model in capturing power-law dissipation by comparing it to four-parameter Iwan models with various parameters. Additionally, the effect of each Bouc-Wen parameter on the overall amplitude-dependent damping is presented. The results show that the Bouc-Wen model cannot capture power-law behavior over the entire microslip regime, but it can be tuned to simulate the response over a smaller amplitude range.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80439413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Magnetic plucking is an enabling technique to harvest energy from a rotary host as it converts the low-frequency excitation of rotational energy sources to high-frequency excitation that leads to resonance of small-scale piezoelectric energy harvesters. Traditional nonlinear analysis of the plucking phenomenon has relied on numerical integration methods. In this work, a semi-analytical method is developed to investigate the stability and bifurcation behaviors of rotary magnetic plucking, which integrates a second-order perturbation technique and discrete Fourier transform. Analysis through this method unfolds that the oscillatory response of the beam can lose stability through the saddle-node bifurcation and Hopf bifurcation, which eventually causes the beam to collide with the rotary host. Further, the influence of the magnetic gap and rotational speed on the stability is discussed. The study also reveals that the nonlinearity of the magnetic force can amplify the electrical power at primary resonance. As a result, the traditional impedance matching approach that neglects the nonlinearity of the magnetic force fails to predict the optimal electrical resistance. Finally, a finite element analysis shows that the instability is sensitive to damping, and the traditional single mode approximation can lead to considerable error.
{"title":"Instability and parametric amplification of a piezoelectric energy harvester periodically plucked by a rotating magnet","authors":"Wei-Che Tai","doi":"10.1115/1.4057015","DOIUrl":"https://doi.org/10.1115/1.4057015","url":null,"abstract":"\u0000 Magnetic plucking is an enabling technique to harvest energy from a rotary host as it converts the low-frequency excitation of rotational energy sources to high-frequency excitation that leads to resonance of small-scale piezoelectric energy harvesters. Traditional nonlinear analysis of the plucking phenomenon has relied on numerical integration methods. In this work, a semi-analytical method is developed to investigate the stability and bifurcation behaviors of rotary magnetic plucking, which integrates a second-order perturbation technique and discrete Fourier transform. Analysis through this method unfolds that the oscillatory response of the beam can lose stability through the saddle-node bifurcation and Hopf bifurcation, which eventually causes the beam to collide with the rotary host. Further, the influence of the magnetic gap and rotational speed on the stability is discussed. The study also reveals that the nonlinearity of the magnetic force can amplify the electrical power at primary resonance. As a result, the traditional impedance matching approach that neglects the nonlinearity of the magnetic force fails to predict the optimal electrical resistance. Finally, a finite element analysis shows that the instability is sensitive to damping, and the traditional single mode approximation can lead to considerable error.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81697991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A mathematical model is developed based on the thin-walled beams theory for free vibration analysis of nano/micro scale beams having nonlocal property and arbitrary cross-section. Constitutive relations are defined by using two-phase local-nonlocal constitutive formulation. Equations of motion are derived by use of Hamilton's principle. Both the local and nonlocal part of the model is solved by the displacement-based finite element method. Numerical results are obtained and examined for nonlocal box beams and collapsed carbon nanotubes. In general, it is observed that the natural frequency decreases by increasing the nonlocal parameter or the volume fraction of the nonlocal part.
{"title":"Free Vibration Analysis of Thin-Walled Beams Using Two-Phase Local-Nonlocal Constitutive Model","authors":"Muhsin Gökhan Günay","doi":"10.1115/1.4056908","DOIUrl":"https://doi.org/10.1115/1.4056908","url":null,"abstract":"\u0000 A mathematical model is developed based on the thin-walled beams theory for free vibration analysis of nano/micro scale beams having nonlocal property and arbitrary cross-section. Constitutive relations are defined by using two-phase local-nonlocal constitutive formulation. Equations of motion are derived by use of Hamilton's principle. Both the local and nonlocal part of the model is solved by the displacement-based finite element method. Numerical results are obtained and examined for nonlocal box beams and collapsed carbon nanotubes. In general, it is observed that the natural frequency decreases by increasing the nonlocal parameter or the volume fraction of the nonlocal part.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79057806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work concerns the response of a damped Mathieu equation with hard cyclic excitation at the same frequency as the parametric excitation. A second-order perturbation analysis using the method of multiple scales unfolds resonances and stability. Superharmonic and subharmonic resonances are analyzed and the effects of different parameters on the responses are examined. While superharmonic resonances of order two have been captured by a first-order analysis, the second-order analysis improves the prediction of the peak frequency. Superharmonic resonances of order three are captured only by the second-order analysis. The order-two superharmonic resonance amplitude is of order epsilon^0, and the order-three superharmonic is of order epsilon. As the parametric excitation level increases, the superharmonic resonances increase. An n-th order multiple scales analysis will indicate conditions of superharmonic resonances of order n+1. At the subharmonic of order one half, there is no steady-state resonance, but known subharmonic instability is unfolded consistently. Analytical expressions for resonant responses are presented and compared with numerical results for specific system parameters. The behavior of this system could be relevant to applications such as large wind-turbine blades and parametric resonators.
{"title":"Responses of a strongly forced Mathieu equation Part 1: cyclic loading","authors":"V. Ramakrishnan, B. Feeny","doi":"10.1115/1.4056906","DOIUrl":"https://doi.org/10.1115/1.4056906","url":null,"abstract":"\u0000 This work concerns the response of a damped Mathieu equation with hard cyclic excitation at the same frequency as the parametric excitation. A second-order perturbation analysis using the method of multiple scales unfolds resonances and stability. Superharmonic and subharmonic resonances are analyzed and the effects of different parameters on the responses are examined. While superharmonic resonances of order two have been captured by a first-order analysis, the second-order analysis improves the prediction of the peak frequency. Superharmonic resonances of order three are captured only by the second-order analysis. The order-two superharmonic resonance amplitude is of order epsilon^0, and the order-three superharmonic is of order epsilon. As the parametric excitation level increases, the superharmonic resonances increase. An n-th order multiple scales analysis will indicate conditions of superharmonic resonances of order n+1. At the subharmonic of order one half, there is no steady-state resonance, but known subharmonic instability is unfolded consistently. Analytical expressions for resonant responses are presented and compared with numerical results for specific system parameters. The behavior of this system could be relevant to applications such as large wind-turbine blades and parametric resonators.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80799001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The present study deals with the response of a damped Mathieu equation with hard constant external loading. A second-order perturbation analysis using the method of multiple scales (MMS) unfolds resonances and stability. Nonresonant and low-frequency quasi-static responses are examined. Under constant loading, primary resonances are captured with a first-order analysis, but are accurately described with the second-order analysis. The response magnitude is of order ε0, where epsilon is the small bookkeeping parameter, but can become arbitrarily large due to a small denominator as the Mathieu system approaches the primary instability wedge. A superharmonic resonance of order two is unfolded with the second-order MMS. The magnitude of this response is of order epsilon and grows with the strength of parametric excitation squared. An n-th order multiple scales analysis under hard constant loading will indicate conditions of superharmonic resonances at order n. Subharmonic resonances do not produce a nonzero steady-state harmonic, but have the instability property known to the regular Mathieu equation. Analytical expressions for predicting the magnitude of responses are presented and compared with numerical results for a specific set of system parameters. In all cases, the second-order analysis accommodates slow time-scale effects, which enables responses of order epsilon or ε0. The behavior of this system could be relevant to applications such as large wind-turbine blades and parametric amplifiers.
{"title":"Responses of a strongly forced Mathieu equation Part 2: constant loading","authors":"V. Ramakrishnan, B. Feeny","doi":"10.1115/1.4056907","DOIUrl":"https://doi.org/10.1115/1.4056907","url":null,"abstract":"\u0000 The present study deals with the response of a damped Mathieu equation with hard constant external loading. A second-order perturbation analysis using the method of multiple scales (MMS) unfolds resonances and stability. Nonresonant and low-frequency quasi-static responses are examined. Under constant loading, primary resonances are captured with a first-order analysis, but are accurately described with the second-order analysis. The response magnitude is of order ε0, where epsilon is the small bookkeeping parameter, but can become arbitrarily large due to a small denominator as the Mathieu system approaches the primary instability wedge. A superharmonic resonance of order two is unfolded with the second-order MMS. The magnitude of this response is of order epsilon and grows with the strength of parametric excitation squared. An n-th order multiple scales analysis under hard constant loading will indicate conditions of superharmonic resonances at order n. Subharmonic resonances do not produce a nonzero steady-state harmonic, but have the instability property known to the regular Mathieu equation. Analytical expressions for predicting the magnitude of responses are presented and compared with numerical results for a specific set of system parameters. In all cases, the second-order analysis accommodates slow time-scale effects, which enables responses of order epsilon or ε0. The behavior of this system could be relevant to applications such as large wind-turbine blades and parametric amplifiers.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77831643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Editor-in-Chief and Editorial Board of the ASME Journal of Vibration and Acoustics would like to thank all of the reviewers for volunteering their expertise and time reviewing manuscripts in 2022. Serving as reviewers for the journal is a critical service necessary to maintain the quality of our publication and to provide the authors with a valuable peer review of their work. Below is a complete list of reviewers for 2022. We would also like to acknowledge two outstanding Reviewers of the Year.2022 Reviewers of the YearAnnamaria Pau — Università di Roma La Sapienza, ItalyJie Zhou — Northwestern Polytechnical University, ChinaThe Reviewers of the Year Award is given to reviewers who have made an outstanding contribution to the journal in terms of the quantity, quality, and turnaround time of reviews completed during the past 12 months. The prize includes a Wall Plaque, 50 free downloads from the ASME Digital Collection, and a one year free subscription to the journal.
美国机械工程师协会振动与声学杂志的主编和编辑委员会感谢所有的审稿人在2022年自愿贡献他们的专业知识和时间来审稿。作为期刊的审稿人是一项至关重要的服务，它可以保持我们的出版质量，并为作者的工作提供有价值的同行评议。以下是2022年的完整审稿人名单。我们还要感谢两位杰出的年度审稿人。2022年度审稿人annamaria Pau -意大利罗马大学(universitiondi Roma La Sapienza)周杰-中国西北工业大学(Northwestern industrial University)年度审稿人奖授予在过去12个月内完成的审稿数量、质量和周期方面对期刊做出杰出贡献的审稿人。奖品包括一块墙上的牌匾，50个免费下载的ASME数字合集，以及一年免费订阅杂志。
{"title":"Reviewer's Recognition","authors":"","doi":"10.1115/1.4056743","DOIUrl":"https://doi.org/10.1115/1.4056743","url":null,"abstract":"The Editor-in-Chief and Editorial Board of the ASME Journal of Vibration and Acoustics would like to thank all of the reviewers for volunteering their expertise and time reviewing manuscripts in 2022. Serving as reviewers for the journal is a critical service necessary to maintain the quality of our publication and to provide the authors with a valuable peer review of their work. Below is a complete list of reviewers for 2022. We would also like to acknowledge two outstanding Reviewers of the Year.2022 Reviewers of the YearAnnamaria Pau — Università di Roma La Sapienza, ItalyJie Zhou — Northwestern Polytechnical University, ChinaThe Reviewers of the Year Award is given to reviewers who have made an outstanding contribution to the journal in terms of the quantity, quality, and turnaround time of reviews completed during the past 12 months. The prize includes a Wall Plaque, 50 free downloads from the ASME Digital Collection, and a one year free subscription to the journal.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136156734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Structural damage occurs in a variety of civil, mechanical, and aerospace engineering systems, and it is critical to effectively identify such damage in order to prevent catastrophic failures. When cracks are present in a structure, the breathing phenomenon that occurs between crack surfaces typically triggers nonlinearity in the dynamic response. In this work, in order to thoroughly understand the nonlinear effect of cracks on structural dynamics, two modeling approaches are integrated to investigate the crack-induced nonlinear dynamics of cantilever beams. First, a modeling method referred to as the discrete element (DE) method is employed to construct a model of a cracked beam. The DE model is able to characterize the breathing phenomenon of cracks. Next, a simulation technique referred to as the hybrid symbolic-numeric computational (HSNC) method is used to analyze the nonlinear response of the cracked beam. The HSNC method provides an efficient way to evaluate both stationary and nonstationary dynamics of cracked systems since it combines efficient linear techniques with an optimization tool to capture the system’s nonlinear response. The proposed computational platform thus enables efficient multiparametric analysis of cracked structures. The effects of crack location, crack depth, and excitation frequency on the cantilever beam are parametrically investigated using the proposed method. Nonlinear features such as subharmonic resonance, nonstationary motion, multistability, and frequency shift are also discussed in this paper.
{"title":"Parametric Analysis of the Nonlinear Dynamics of a Cracked Cantilever Beam","authors":"Chia-Ling Hsu, Meng-Hsuan Tien","doi":"10.1115/1.4056644","DOIUrl":"https://doi.org/10.1115/1.4056644","url":null,"abstract":"Abstract Structural damage occurs in a variety of civil, mechanical, and aerospace engineering systems, and it is critical to effectively identify such damage in order to prevent catastrophic failures. When cracks are present in a structure, the breathing phenomenon that occurs between crack surfaces typically triggers nonlinearity in the dynamic response. In this work, in order to thoroughly understand the nonlinear effect of cracks on structural dynamics, two modeling approaches are integrated to investigate the crack-induced nonlinear dynamics of cantilever beams. First, a modeling method referred to as the discrete element (DE) method is employed to construct a model of a cracked beam. The DE model is able to characterize the breathing phenomenon of cracks. Next, a simulation technique referred to as the hybrid symbolic-numeric computational (HSNC) method is used to analyze the nonlinear response of the cracked beam. The HSNC method provides an efficient way to evaluate both stationary and nonstationary dynamics of cracked systems since it combines efficient linear techniques with an optimization tool to capture the system’s nonlinear response. The proposed computational platform thus enables efficient multiparametric analysis of cracked structures. The effects of crack location, crack depth, and excitation frequency on the cantilever beam are parametrically investigated using the proposed method. Nonlinear features such as subharmonic resonance, nonstationary motion, multistability, and frequency shift are also discussed in this paper.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135200967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Many oscillatory systems of engineering and scientific interest (e.g., mechanical metastructures) exhibit non-proportional damping, wherein the mass-normalized damping and stiffness matrices do not commute. A new modal analysis technique for non-proportionally damped systems, referred to as the “dual-oscillator approach to complex-stiffness damping,” was recently proposed as an alternative to the current standard method originally developed by Foss and Traill-Nash. This paper presents a critical comparison of the two approaches, with particular emphasis on the time required to compute the resonant frequencies of non-proportionally damped linear systems. It is shown that, for degrees of freedom greater than or equal to nine, the dual-oscillator approach is significantly faster (on average) than the conventional approach, and that the relative computation speed actually improves with the system's degree of freedom. With 145 degrees of freedom, for example, the dual-oscillator approach is about 25% faster than the traditional approach. The difference between the two approaches is statistically significant, with attained significance levels less than machine precision. To the authors' knowledge, this establishes the dual-oscillator approach as the fastest existing algorithm for computing resonant frequencies of non-proportionally damped linear systems with large degrees of freedom. The approach is illustrated by application to a model system representative of a mechanical metastructure.
{"title":"Rapid computation of resonant frequencies for non-proportionally damped systems using dual oscillators","authors":"J. W. Sanders, D. Inman","doi":"10.1115/1.4056796","DOIUrl":"https://doi.org/10.1115/1.4056796","url":null,"abstract":"\u0000 Many oscillatory systems of engineering and scientific interest (e.g., mechanical metastructures) exhibit non-proportional damping, wherein the mass-normalized damping and stiffness matrices do not commute. A new modal analysis technique for non-proportionally damped systems, referred to as the “dual-oscillator approach to complex-stiffness damping,” was recently proposed as an alternative to the current standard method originally developed by Foss and Traill-Nash. This paper presents a critical comparison of the two approaches, with particular emphasis on the time required to compute the resonant frequencies of non-proportionally damped linear systems. It is shown that, for degrees of freedom greater than or equal to nine, the dual-oscillator approach is significantly faster (on average) than the conventional approach, and that the relative computation speed actually improves with the system's degree of freedom. With 145 degrees of freedom, for example, the dual-oscillator approach is about 25% faster than the traditional approach. The difference between the two approaches is statistically significant, with attained significance levels less than machine precision. To the authors' knowledge, this establishes the dual-oscillator approach as the fastest existing algorithm for computing resonant frequencies of non-proportionally damped linear systems with large degrees of freedom. The approach is illustrated by application to a model system representative of a mechanical metastructure.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82438620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Through creating slow waves in structures, Acoustic Black Hole (ABH) shows promise for potential vibration control applications. However, it remains unclear whether such phenomena can still occur in a structure undergoing high-speed spinning, and if so, what is the interplay among various system parameters and what are the underpinning physical mechanisms. To address this issue, this work establishes a semi-analytical model for a spinning ABH beam based on Euler-Bernoulli beam theory under the energy framework. After its validation, the model is used to reveal a few important vibration features pertinent to the spinning ABH beam through examining its dynamics, modal properties and energy flow. It is shown that the spinning-induced centrifugal effects generate hardening effects inside the structure, thus increasing the overall structural stiffness and stretching the wavelength of the modal deformation of flexural waves as compared with its counterpart at still. Meanwhile, energy flow to the ABH portion of the beam is also adversely affected. As a result, the ABH-induced overall damping enhancement effect of the viscoelastic coating, as observed in conventional ABH beam at still, is impaired. Nevertheless, the study confirms that typical ABH features, in terms of wave compression, energy trapping and dissipation, though affected by the spinning effects, are still persistent in a high-speed spinning structure. This paves the way forward for the embodiment of ABH phenomena in the design of high performance rotating mechanical components such as turbine blades.
{"title":"Acoustic Black Holes in a Spinning Beam","authors":"Yuhang Wang, Li Cheng, J. Du, Yang Liu","doi":"10.1115/1.4056791","DOIUrl":"https://doi.org/10.1115/1.4056791","url":null,"abstract":"\u0000 Through creating slow waves in structures, Acoustic Black Hole (ABH) shows promise for potential vibration control applications. However, it remains unclear whether such phenomena can still occur in a structure undergoing high-speed spinning, and if so, what is the interplay among various system parameters and what are the underpinning physical mechanisms. To address this issue, this work establishes a semi-analytical model for a spinning ABH beam based on Euler-Bernoulli beam theory under the energy framework. After its validation, the model is used to reveal a few important vibration features pertinent to the spinning ABH beam through examining its dynamics, modal properties and energy flow. It is shown that the spinning-induced centrifugal effects generate hardening effects inside the structure, thus increasing the overall structural stiffness and stretching the wavelength of the modal deformation of flexural waves as compared with its counterpart at still. Meanwhile, energy flow to the ABH portion of the beam is also adversely affected. As a result, the ABH-induced overall damping enhancement effect of the viscoelastic coating, as observed in conventional ABH beam at still, is impaired. Nevertheless, the study confirms that typical ABH features, in terms of wave compression, energy trapping and dissipation, though affected by the spinning effects, are still persistent in a high-speed spinning structure. This paves the way forward for the embodiment of ABH phenomena in the design of high performance rotating mechanical components such as turbine blades.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84584814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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