In this paper, the nonlinear response of indenter-foam dampers is characterized. Those dampers consist of indenters pressed on open-cell foams swollen with wetting liquids. Recently, the authors identified the dominant mechanism of damping in those dampers as poro-viscoelastic (PVE) relaxations as in articular cartilage, one of nature's best solutions to vibration attenuation. Those previous works by the authors included dynamic mechanical analyses of the indenter-foam dampers under small vibrations, i.e., linear regime. The current study features the dynamic response of similar dampers under larger strains to investigate the nonlinear regime. In particular, the indenter-foam dampers tested in this paper consist of an open-cell polyurethane foam swollen with castor oil. Harmonic displacements are applied on the swollen and pre-compressed foam using a flat-ended cylindrical indenter. Measured forces and corresponding hysteresis (force-displacement) loops are then analyzed to quantify damping performance (via specific damping capacity) and nonlinearities (via harmonic ratio). The effects of strain and strain rates on the damping capacity and harmonic ratio are investigated experimentally. The dominant source of the non-linearity is identified as peeling at the indenter-foam interface (and quantified via peeling index). A representative model consisting of a linear viscoelastic foam and rate-dependent adhesive interface (slider element with limiting adhesive strength) explains the observed trends in peeling and thus nonlinear dynamic response. Possible remedies to suppress those nonlinearities in future designs of indenter-foam dampers are also discussed.
{"title":"Contact Nonlinearity in Indenter-Foam Dampers","authors":"Lejie Liu, K. Yerrapragada, C. Henak, M. Eriten","doi":"10.1115/1.4054054","DOIUrl":"https://doi.org/10.1115/1.4054054","url":null,"abstract":"\u0000 In this paper, the nonlinear response of indenter-foam dampers is characterized. Those dampers consist of indenters pressed on open-cell foams swollen with wetting liquids. Recently, the authors identified the dominant mechanism of damping in those dampers as poro-viscoelastic (PVE) relaxations as in articular cartilage, one of nature's best solutions to vibration attenuation. Those previous works by the authors included dynamic mechanical analyses of the indenter-foam dampers under small vibrations, i.e., linear regime. The current study features the dynamic response of similar dampers under larger strains to investigate the nonlinear regime. In particular, the indenter-foam dampers tested in this paper consist of an open-cell polyurethane foam swollen with castor oil. Harmonic displacements are applied on the swollen and pre-compressed foam using a flat-ended cylindrical indenter. Measured forces and corresponding hysteresis (force-displacement) loops are then analyzed to quantify damping performance (via specific damping capacity) and nonlinearities (via harmonic ratio). The effects of strain and strain rates on the damping capacity and harmonic ratio are investigated experimentally. The dominant source of the non-linearity is identified as peeling at the indenter-foam interface (and quantified via peeling index). A representative model consisting of a linear viscoelastic foam and rate-dependent adhesive interface (slider element with limiting adhesive strength) explains the observed trends in peeling and thus nonlinear dynamic response. Possible remedies to suppress those nonlinearities in future designs of indenter-foam dampers are also discussed.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81949754","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 paper proposes a new computationally efficient methodology for random vibrations of nonlinear vibratory systems using a time-dependent second-order adjoint variable (AV2) method, and a second-order projected differentiation (PD2) method. The proposed approach is called AV2-PD2. The vibratory system can be excited by stationary Gaussian or non-Gaussian random processes following the traditional translation process model. A Karhunen-Loeve (KL) expansion expresses each input random process in terms of standard normal random variables. A second-order adjoint approach is used to obtain the required first and second-order output derivatives accurately by solving as many sets of equations of motion (EOMs) as the number of KL random variables. These derivatives are used to compute the marginal CDF of the output process with second-order accuracy. Then, a second-order projected differentiation method calculates the autocorrelation function of each output process with second-order accuracy, at an additional cost of solving as many sets of equations of motion (EOMs) as the number of outputs of interest, independently of the time horizon (simulation time). The total number of solutions of the EOM scales linearly with the number of input KL random variables and the number of output processes. The efficiency and accuracy of the proposed approach is demonstrated using a nonlinear Duffing oscillator problem under a quadratic random excitation and a nonlinear half-car suspension example.
{"title":"Nonlinear Random Vibrations using Second-Order Adjoint and Projected Differentiation Methods","authors":"D. Papadimitriou, Z. Mourelatos, Zhen Hu","doi":"10.1115/1.4054033","DOIUrl":"https://doi.org/10.1115/1.4054033","url":null,"abstract":"\u0000 This paper proposes a new computationally efficient methodology for random vibrations of nonlinear vibratory systems using a time-dependent second-order adjoint variable (AV2) method, and a second-order projected differentiation (PD2) method. The proposed approach is called AV2-PD2. The vibratory system can be excited by stationary Gaussian or non-Gaussian random processes following the traditional translation process model. A Karhunen-Loeve (KL) expansion expresses each input random process in terms of standard normal random variables. A second-order adjoint approach is used to obtain the required first and second-order output derivatives accurately by solving as many sets of equations of motion (EOMs) as the number of KL random variables. These derivatives are used to compute the marginal CDF of the output process with second-order accuracy. Then, a second-order projected differentiation method calculates the autocorrelation function of each output process with second-order accuracy, at an additional cost of solving as many sets of equations of motion (EOMs) as the number of outputs of interest, independently of the time horizon (simulation time). The total number of solutions of the EOM scales linearly with the number of input KL random variables and the number of output processes. The efficiency and accuracy of the proposed approach is demonstrated using a nonlinear Duffing oscillator problem under a quadratic random excitation and a nonlinear half-car suspension example.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89153255","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 mode shapes of beam-type structures, such as aircraft wings and wind turbine blades, involve a high degree of coupling between bending and torsional deformation. In the case of wind turbine blades, different types of deformation are typically easily recognized by visual observation. However, this visual approach is sometimes challenging for high-order mode shapes, which involve coupling of both bending and torsional deformations. This work proposes a novel mode shape recognition algorithm, called Finite Cross-Section Method (FCSM), for application to highly coupled beam-type structures not only to identify the deformation components of the complex beam mode shapes, but more importantly, to quantify their respective relative contribution. In the application case study for the FCSM method, the entire structure is discretized into multiple cross-sections. The flap-wise, edge-wise, and torsional deformation components of the entire structure are determined at the cross-section level. The deformation components of the entire structure and their respective contribution is obtained from assembling all cross-sections. To validate the mode shape recognition performance, FCSM is applied to and demonstrated on four test cases: (1) numerical mode shapes of a simple cantilever beam, (2) numerical mode shapes from a straight wind turbine blade, (3) numerical mode shapes of a swept wind turbine blade, and (4) experimental mode shapes from a high spatial resolution 3D SLDV modal test. Both numerical and experimental studies demonstrate that FCSM can successfully recognize the quantitative contribution of flap-wise, edge-wise, and torsional deformation.
{"title":"Finite Cross-Section Method (FCSM) for Mode Shape Recognition of Highly Coupled Beam-Type Structures","authors":"Yuanchang Chen, T. Griffith","doi":"10.1115/1.4053977","DOIUrl":"https://doi.org/10.1115/1.4053977","url":null,"abstract":"\u0000 The mode shapes of beam-type structures, such as aircraft wings and wind turbine blades, involve a high degree of coupling between bending and torsional deformation. In the case of wind turbine blades, different types of deformation are typically easily recognized by visual observation. However, this visual approach is sometimes challenging for high-order mode shapes, which involve coupling of both bending and torsional deformations. This work proposes a novel mode shape recognition algorithm, called Finite Cross-Section Method (FCSM), for application to highly coupled beam-type structures not only to identify the deformation components of the complex beam mode shapes, but more importantly, to quantify their respective relative contribution. In the application case study for the FCSM method, the entire structure is discretized into multiple cross-sections. The flap-wise, edge-wise, and torsional deformation components of the entire structure are determined at the cross-section level. The deformation components of the entire structure and their respective contribution is obtained from assembling all cross-sections. To validate the mode shape recognition performance, FCSM is applied to and demonstrated on four test cases: (1) numerical mode shapes of a simple cantilever beam, (2) numerical mode shapes from a straight wind turbine blade, (3) numerical mode shapes of a swept wind turbine blade, and (4) experimental mode shapes from a high spatial resolution 3D SLDV modal test. Both numerical and experimental studies demonstrate that FCSM can successfully recognize the quantitative contribution of flap-wise, edge-wise, and torsional deformation.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89166814","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 inerter has been integrated into various vibration mitigation devices, whose mass amplification effect could enhance the suppression capabilities of these devices. In the current study, the inerter is integrated with a pendulum vibration absorber, referred to as inerter pendulum vibration absorber (IPVA). To demonstrate its efficacy, the IPVA is integrated with a linear, harmonically forced oscillator seeking vibration mitigation. A theoretical investigation is conducted to understand the nonlinear response of the IPVA. It is shown that the IPVA operates based on a nonlinear energy transfer phenomenon wherein the energy of the linear oscillator transfers to the pendulum vibration absorber as a result of parametric resonance of the pendulum. The parametric instability is predicted by the harmonic balance method along with Floquet theory. A perturbation analysis shows that a pitchfork bifurcation and period doubling bifurcation are necessary and sufficient conditions for the parametric resonance to occur. An arc-length continuation scheme is used to predict the boundary of parametric instability in the parameter space and verify the perturbation analysis. The effects of various system parameters on the parametric instability are examined. Finally, the IPVA is compared with a linear benchmark and an autoparametric vibration absorber, and shows more efficacious vibration suppression.
{"title":"The response of an inerter-based dynamic vibration absorber with a parametrically excited centrifugal pendulum","authors":"Aakash Gupta, Wei-Che Tai","doi":"10.1115/1.4053789","DOIUrl":"https://doi.org/10.1115/1.4053789","url":null,"abstract":"\u0000 The inerter has been integrated into various vibration mitigation devices, whose mass amplification effect could enhance the suppression capabilities of these devices. In the current study, the inerter is integrated with a pendulum vibration absorber, referred to as inerter pendulum vibration absorber (IPVA). To demonstrate its efficacy, the IPVA is integrated with a linear, harmonically forced oscillator seeking vibration mitigation. A theoretical investigation is conducted to understand the nonlinear response of the IPVA. It is shown that the IPVA operates based on a nonlinear energy transfer phenomenon wherein the energy of the linear oscillator transfers to the pendulum vibration absorber as a result of parametric resonance of the pendulum. The parametric instability is predicted by the harmonic balance method along with Floquet theory. A perturbation analysis shows that a pitchfork bifurcation and period doubling bifurcation are necessary and sufficient conditions for the parametric resonance to occur. An arc-length continuation scheme is used to predict the boundary of parametric instability in the parameter space and verify the perturbation analysis. The effects of various system parameters on the parametric instability are examined. Finally, the IPVA is compared with a linear benchmark and an autoparametric vibration absorber, and shows more efficacious vibration suppression.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87833923","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}
Mechanical shock events experienced by electronic systems can be reproduced in the laboratory using Hopkinson bar tests. In such tests a projectile strikes a rod, creating a pulse which then travels into the electronic system. The quality of these tests depends on the closeness of the shape of the incident pulse to a desired shape specified for each test. This paper introduces a new approach for controlling the shape of the incident pulse through the use of phononic material concepts, thereby improving the test procedure. Two dispersion-modifying concepts, phononic crystals and local resonators, are examined for their wave shaping capabilities in one-dimensional elastic waveguides. They are evaluated using a transfer matrix method to determine the output pulse shape in the time domain. Parametric studies show that no single parameter allows for precise-enough control to achieve the possible desired output pulse shapes. Instead, the parameters of an approximate, discrete model for a combined phononic crystal/locally resonant system are optimized together to achieve the desired pulse shape. A sensitivity analysis documents that the pulse shape is relatively insensitive to errors in the optimized parameter values. The optimized discrete model is then translated into a physical design, which when analyzed using the finite element method shows that desired pulse shapes are indeed produced.
{"title":"Phononic Materials for Pulse Shaping in Elastic Waveguides Motivated by Shock Testing","authors":"William Johnson, M. Leamy, W. Delima, M. Ruzzene","doi":"10.1115/1.4053778","DOIUrl":"https://doi.org/10.1115/1.4053778","url":null,"abstract":"\u0000 Mechanical shock events experienced by electronic systems can be reproduced in the laboratory using Hopkinson bar tests. In such tests a projectile strikes a rod, creating a pulse which then travels into the electronic system. The quality of these tests depends on the closeness of the shape of the incident pulse to a desired shape specified for each test. This paper introduces a new approach for controlling the shape of the incident pulse through the use of phononic material concepts, thereby improving the test procedure. Two dispersion-modifying concepts, phononic crystals and local resonators, are examined for their wave shaping capabilities in one-dimensional elastic waveguides. They are evaluated using a transfer matrix method to determine the output pulse shape in the time domain. Parametric studies show that no single parameter allows for precise-enough control to achieve the possible desired output pulse shapes. Instead, the parameters of an approximate, discrete model for a combined phononic crystal/locally resonant system are optimized together to achieve the desired pulse shape. A sensitivity analysis documents that the pulse shape is relatively insensitive to errors in the optimized parameter values. The optimized discrete model is then translated into a physical design, which when analyzed using the finite element method shows that desired pulse shapes are indeed produced.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75030810","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}
In this paper, the forced coupled flexural-torsional vibration of a piezoelectrically-actuated double-cantilever structure is investigated. The double-cantilever structure is composed of two uniform and identical Euler-Bernoulli cantilever beams connected by a rigid tip connection at their free ends. There is also a piezoelectric layer on the top surface of each cantilever beam. The characteristic equation for the coupled flexural-torsional vibrations of the structure is derived and solved to determine the natural frequencies. The time response to the forced vibrations of the structure is studied using the Galerkin approximation method. The effects of dimensional parameters, including the length of the cantilever beams and the length of the tip connection, and the piezoelectric input voltage on the coupled flexural-torsional natural frequencies and amplitude of the vibrations of the structure are investigated analytically and experimentally. The results show that the coupled flexural-torsional fundamental frequency of the piezoelectrically-actuated double-cantilever structure decreases as either the length of the cantilever beams or the tip connection is increased. Moreover, the amplitude of the coupled flexural-torsional vibrations of the structure is proportional to the piezoelectric input voltage, however, the slope of the curves depends on dimensional parameters. For a given voltage, the effect of either of the aforementioned dimensional parameter on the amplitude of vibrations depends on the other dimensional parameter such that there is a turning point in all the curves, whose location depends on the configuration of the structure.
{"title":"COUPLED FLEXURAL-TORSIONAL FORCED VIBRATION ANALYSIS OF A PIEZOELECTRICALLY-ACTUATED DOUBLE-CANTILEVER STRUCTURE","authors":"A. Zargarani, John O'Donnell, Nima Mahmoodi","doi":"10.1115/1.4053714","DOIUrl":"https://doi.org/10.1115/1.4053714","url":null,"abstract":"\u0000 In this paper, the forced coupled flexural-torsional vibration of a piezoelectrically-actuated double-cantilever structure is investigated. The double-cantilever structure is composed of two uniform and identical Euler-Bernoulli cantilever beams connected by a rigid tip connection at their free ends. There is also a piezoelectric layer on the top surface of each cantilever beam. The characteristic equation for the coupled flexural-torsional vibrations of the structure is derived and solved to determine the natural frequencies. The time response to the forced vibrations of the structure is studied using the Galerkin approximation method. The effects of dimensional parameters, including the length of the cantilever beams and the length of the tip connection, and the piezoelectric input voltage on the coupled flexural-torsional natural frequencies and amplitude of the vibrations of the structure are investigated analytically and experimentally. The results show that the coupled flexural-torsional fundamental frequency of the piezoelectrically-actuated double-cantilever structure decreases as either the length of the cantilever beams or the tip connection is increased. Moreover, the amplitude of the coupled flexural-torsional vibrations of the structure is proportional to the piezoelectric input voltage, however, the slope of the curves depends on dimensional parameters. For a given voltage, the effect of either of the aforementioned dimensional parameter on the amplitude of vibrations depends on the other dimensional parameter such that there is a turning point in all the curves, whose location depends on the configuration of the structure.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78834129","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}
Acoustic metasurfaces use the phase gradient of a single layer to reflect/refract waves in any direction. This study shows that other than wave steering, acoustic metasurfaces can exhibit wave splitting or trapping through the geometry design. Previous studies focused on the generalized Snell's law when developing metasurfaces and attempted to prevent wave leakages. On the contrary, this study exploits the periodicity of metasurfaces to accomplish acoustic wave splitting, which leads to a similar concept to metagrating. For acoustic wave trapping, we show that through proper arrangements, an acoustic wave can be localized in a specific region without using any boundaries based on the generalized Snell's law. A design formula is provided to trap waves from any incident angle or at any frequency. The analytical and numerical results are in good agreement, verifying the effectiveness of the proposed concept for wave splitting and trapping. This study shows the versatile applications of acoustic metasurfaces and is useful for interferometry and energy harvesting.
{"title":"Acoustic Wave Splitting and Wave Trapping Designs","authors":"Yu-Chi Su, Liwen Ko","doi":"10.1115/1.4053713","DOIUrl":"https://doi.org/10.1115/1.4053713","url":null,"abstract":"\u0000 Acoustic metasurfaces use the phase gradient of a single layer to reflect/refract waves in any direction. This study shows that other than wave steering, acoustic metasurfaces can exhibit wave splitting or trapping through the geometry design. Previous studies focused on the generalized Snell's law when developing metasurfaces and attempted to prevent wave leakages. On the contrary, this study exploits the periodicity of metasurfaces to accomplish acoustic wave splitting, which leads to a similar concept to metagrating. For acoustic wave trapping, we show that through proper arrangements, an acoustic wave can be localized in a specific region without using any boundaries based on the generalized Snell's law. A design formula is provided to trap waves from any incident angle or at any frequency. The analytical and numerical results are in good agreement, verifying the effectiveness of the proposed concept for wave splitting and trapping. This study shows the versatile applications of acoustic metasurfaces and is useful for interferometry and energy harvesting.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83181998","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 nonlinear response of a series-type pendulum tuned mass damper-tuned liquid damper (TMD-TLD) system is investigated in this study. The TLD is mounted on the pendulum TMD in series to remove the need for costly viscous damping elements. Since the response of the TMD is greater than that of the primary structure, the TLD experiences a significant base motion, leading to a highly nonlinear response that is difficult to model. The nonlinear pendulum TMD equation of motion is modelled without linearizing assumptions. The TLD is represented by an incompressible smoothed particle hydrodynamics (SPH) model that can capture large sloshing responses. The nonlinear model results are compared to shake table testing for a TMD-TLD system and a linear equivalent mechanical model. Four system configurations are considered. The nonlinear model shows good agreement with the experimental data for the TMD displacement and TLD wave heights in both time and frequency domains. The nonlinear model shows improved agreement compared to the linear model for all cases studied, especially for the TLD wave heights. The impact of simplifying the pendulum TMD equation of motion by the small angle assumption is investigated for two cases. The results indicate that the simplified pendulum equation does not properly capture the frequency of the TMD in the TMD-TLD system, and results in a reduction in calculated TLD wave heights compared to the fully nonlinear equation. It is therefore critical to consider the fully nonlinear pendulum TMD response to capture the TMD-TLD behavior.
{"title":"Nonlinear modelling of series-type pendulum tuned mass damper-tuned liquid damper","authors":"K. McNamara, J. Love, M. Tait","doi":"10.1115/1.4053636","DOIUrl":"https://doi.org/10.1115/1.4053636","url":null,"abstract":"\u0000 The nonlinear response of a series-type pendulum tuned mass damper-tuned liquid damper (TMD-TLD) system is investigated in this study. The TLD is mounted on the pendulum TMD in series to remove the need for costly viscous damping elements. Since the response of the TMD is greater than that of the primary structure, the TLD experiences a significant base motion, leading to a highly nonlinear response that is difficult to model. The nonlinear pendulum TMD equation of motion is modelled without linearizing assumptions. The TLD is represented by an incompressible smoothed particle hydrodynamics (SPH) model that can capture large sloshing responses. The nonlinear model results are compared to shake table testing for a TMD-TLD system and a linear equivalent mechanical model. Four system configurations are considered. The nonlinear model shows good agreement with the experimental data for the TMD displacement and TLD wave heights in both time and frequency domains. The nonlinear model shows improved agreement compared to the linear model for all cases studied, especially for the TLD wave heights. The impact of simplifying the pendulum TMD equation of motion by the small angle assumption is investigated for two cases. The results indicate that the simplified pendulum equation does not properly capture the frequency of the TMD in the TMD-TLD system, and results in a reduction in calculated TLD wave heights compared to the fully nonlinear equation. It is therefore critical to consider the fully nonlinear pendulum TMD response to capture the TMD-TLD behavior.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91199031","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}
Zhaobin Zhan, Hui Liu, B. Feeny, Z. Wang, Yunkun Xie
Gear manufacturing errors are key parameters in planetary gear trains, which have effects on the load sharing, tooth stress and so on. Accurate estimation of manufacturing errors can help monitoring the conditions of planetary gear system. This study investigates the dynamic response sensitivity to model parameters for a nonlinear single-stage planetary gear set with coupled lateral and torsional motions. Power flow theory is introduced to assess the gear vibration and the parameter sensitivity. The response sensitivity equations are deduced with the direct method (DM). The influence of the rotating speed is considered in the sensitivity analysis. Then, the identifiability of the parameter estimation is investigated based on the sensitivity results. The Gauss-Newton method is applied to estimate the manufacturing errors. Gear meshing is a primary factor in gear vibration, so the sensitivities of its vibration power to the parameters are analysed in this paper. The estimated results are accurate when the collected data contain lower noise signal. The sensitivity and parameter estimation make it possible to provide support for the design and diagnosis of a planetary gear set.
{"title":"Prognostics of gear manufacturing errors for planetary gear systems based on power flow theory","authors":"Zhaobin Zhan, Hui Liu, B. Feeny, Z. Wang, Yunkun Xie","doi":"10.1115/1.4053630","DOIUrl":"https://doi.org/10.1115/1.4053630","url":null,"abstract":"\u0000 Gear manufacturing errors are key parameters in planetary gear trains, which have effects on the load sharing, tooth stress and so on. Accurate estimation of manufacturing errors can help monitoring the conditions of planetary gear system. This study investigates the dynamic response sensitivity to model parameters for a nonlinear single-stage planetary gear set with coupled lateral and torsional motions. Power flow theory is introduced to assess the gear vibration and the parameter sensitivity. The response sensitivity equations are deduced with the direct method (DM). The influence of the rotating speed is considered in the sensitivity analysis. Then, the identifiability of the parameter estimation is investigated based on the sensitivity results. The Gauss-Newton method is applied to estimate the manufacturing errors. Gear meshing is a primary factor in gear vibration, so the sensitivities of its vibration power to the parameters are analysed in this paper. The estimated results are accurate when the collected data contain lower noise signal. The sensitivity and parameter estimation make it possible to provide support for the design and diagnosis of a planetary gear set.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75364349","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 forced Mathieu equation with damping, with weak harmonic direct excitation at the same frequency as the parametric excitation. A second-order perturbation analysis using the method of multiple scales unfolds parametric amplification at primary resonance. The parametric effect on the primary resonance behavior occurs with a slow time scale of second order, although the effect on the steady-state response is of order one. As the parametric excitation level increases, the response at primary resonance stretches before becoming unbounded and unstable. Analytical expressions for predicting the response amplitudes are presented and compared with numerical results for a specific set of system parameters. Dependence of the amplification behavior, and indeed possible deamplification, on parameters is examined. The effect of parametric excitation on the response phase behavior is also presented.
{"title":"Primary parametric amplification in a weakly forced Mathieu equation","authors":"V. Ramakrishnan, B. Feeny","doi":"10.1115/1.4053635","DOIUrl":"https://doi.org/10.1115/1.4053635","url":null,"abstract":"\u0000 The present study deals with the response of a forced Mathieu equation with damping, with weak harmonic direct excitation at the same frequency as the parametric excitation. A second-order perturbation analysis using the method of multiple scales unfolds parametric amplification at primary resonance. The parametric effect on the primary resonance behavior occurs with a slow time scale of second order, although the effect on the steady-state response is of order one. As the parametric excitation level increases, the response at primary resonance stretches before becoming unbounded and unstable. Analytical expressions for predicting the response amplitudes are presented and compared with numerical results for a specific set of system parameters. Dependence of the amplification behavior, and indeed possible deamplification, on parameters is examined. The effect of parametric excitation on the response phase behavior is also presented.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82624002","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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