The focus of this investigation is first on assessing the validity to structures close to or past buckling of the reduced order modeling approach for nonlinear geometric response that has been extensively developed in the last two decades. This focus is motivated by a class of piezoelectric energy harvesters that rely on strongly nonlinear behavior, such as large amplitude responses, to achieve broadband energy harvesting. A simple, two rigid bars linkage that approximates a buckling beam is first considered to discover the features of the nonlinear force-displacement relation induced by an in plane loading. It is observed that the corresponding form of this relation is not consistent with the one derived from a reduced order model (ROM) but can be closely approximated by it over a large displacement range. This analysis emphasizes in particular the role of a group of ROM coefficients that are usually considered unimportant. A similar study is performed next for the buckled harvester modeled within Nastran and it is again found that a close match of the force-displacement relationship can be achieved. Based on that positive outlook, a 6 basis functions ROM of this beam harvester that includes piezoelectric effects is built and identified. It is found to provide a close match of Nastran nonlinear predictions over a broad range of transverse and in plane loading in static and dynamic conditions. The ROM usefulness in predicting the open-circuit voltage is demonstrated.
{"title":"NONLINEAR REDUCED ORDER MODELING OF STRUCTURES NEAR BUCKLING AND APPLICATION TO AN ENERGY HARVESTER","authors":"X. Q. Wang, M. Mignolet, Yabin Liao","doi":"10.1115/1.4055784","DOIUrl":"https://doi.org/10.1115/1.4055784","url":null,"abstract":"\u0000 The focus of this investigation is first on assessing the validity to structures close to or past buckling of the reduced order modeling approach for nonlinear geometric response that has been extensively developed in the last two decades. This focus is motivated by a class of piezoelectric energy harvesters that rely on strongly nonlinear behavior, such as large amplitude responses, to achieve broadband energy harvesting. A simple, two rigid bars linkage that approximates a buckling beam is first considered to discover the features of the nonlinear force-displacement relation induced by an in plane loading. It is observed that the corresponding form of this relation is not consistent with the one derived from a reduced order model (ROM) but can be closely approximated by it over a large displacement range. This analysis emphasizes in particular the role of a group of ROM coefficients that are usually considered unimportant. A similar study is performed next for the buckled harvester modeled within Nastran and it is again found that a close match of the force-displacement relationship can be achieved. Based on that positive outlook, a 6 basis functions ROM of this beam harvester that includes piezoelectric effects is built and identified. It is found to provide a close match of Nastran nonlinear predictions over a broad range of transverse and in plane loading in static and dynamic conditions. The ROM usefulness in predicting the open-circuit voltage is demonstrated.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79311925","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}
By exchanging the internal energy between coupled vibration modes, internal-resonance-based energy harvesters may provide an effective solution to broadening and enhancing bandwidth and power performance in dealing with natural vibration sources. With the development of piezoelectric-based transducers, thickness and face shear coefficients in proper piezoelectric elements can also generate the power output from shear deformation on the core vibrating elements. However, in most cantilever-based energy harvesters that focused on bending modes, the shear responses were neglected. In this paper, we present an internal-resonance-based piezoelectric energy harvester with three-dimensional coupled bending and torsional modes, for the first time. The fine-tuned system leverages a two-to-one internal resonance between its first torsion and second bending modes to enhance the power output with piezoelectric effects. The dynamic behaviour implies the coexistence of in-plane and out-of-plane motions under a single excitation frequency, and the corresponding strain changes in the bending and shear directions are captured by bonded piezoelectric transducers. Dependence between excitation levels and the internal-resonance phenomenon is justified as a critical system parameter study; the results also indicate that an intriguing non-periodic region exists near the centre frequency. The outcomes of this study feature a multi-directional and multi-modal energy harvester that displays rich dynamic behaviors. The operational bandwidth is promising for broadband energy harvesting, and the output voltage is enhanced by capturing both in-plane and out-of-plane motions at the same time.
{"title":"A proof-of-concept study on an internal-resonance-based piezoelectric energy harvester with coupled three-dimensional bending-torsion motions","authors":"Yimin Fan, M. Ghayesh, Tien-Fu Lu","doi":"10.1115/1.4055720","DOIUrl":"https://doi.org/10.1115/1.4055720","url":null,"abstract":"\u0000 By exchanging the internal energy between coupled vibration modes, internal-resonance-based energy harvesters may provide an effective solution to broadening and enhancing bandwidth and power performance in dealing with natural vibration sources. With the development of piezoelectric-based transducers, thickness and face shear coefficients in proper piezoelectric elements can also generate the power output from shear deformation on the core vibrating elements. However, in most cantilever-based energy harvesters that focused on bending modes, the shear responses were neglected. In this paper, we present an internal-resonance-based piezoelectric energy harvester with three-dimensional coupled bending and torsional modes, for the first time. The fine-tuned system leverages a two-to-one internal resonance between its first torsion and second bending modes to enhance the power output with piezoelectric effects. The dynamic behaviour implies the coexistence of in-plane and out-of-plane motions under a single excitation frequency, and the corresponding strain changes in the bending and shear directions are captured by bonded piezoelectric transducers. Dependence between excitation levels and the internal-resonance phenomenon is justified as a critical system parameter study; the results also indicate that an intriguing non-periodic region exists near the centre frequency. The outcomes of this study feature a multi-directional and multi-modal energy harvester that displays rich dynamic behaviors. The operational bandwidth is promising for broadband energy harvesting, and the output voltage is enhanced by capturing both in-plane and out-of-plane motions at the same time.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81844777","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 minimum sound pressure is an important aspect of noise control. This means that minimal or no noise at a location will be experienced at a certain frequency. In many engineering applications, it is desirable to compute and assign the frequency corresponding to the minimum sound pressure. This paper presents three novel methods for the prediction of frequencies corresponding to the minima of radiated sound pressure. Two of them are developed for determining zero sound pressure frequencies, which correspond to a response close to zero. They are based on the application of linear matrix algebra methods in conjunction with the fundamental definitions for the existence of local minima. The other is developed to solve for frequencies of the minimum response points corresponding to a zero slope in the frequency response function curve by using the dichotomy method. In addition, an inverse structural modification for the assignment of the zero sound pressure frequency and antiresonant frequencies is presented. At these frequencies, the modification causes the selected location to experience the minimum sound pressure, while the other selected locations do not vibrate. Numerical examples of a simply supported plate in air and water are analyzed to demonstrate the effectiveness and accuracy of the proposed approaches.
{"title":"Computation and Assignment of the Minima of Structurally Radiated Sound Pressure","authors":"Yingsha Shi, Sheng Li","doi":"10.1115/1.4055615","DOIUrl":"https://doi.org/10.1115/1.4055615","url":null,"abstract":"\u0000 The minimum sound pressure is an important aspect of noise control. This means that minimal or no noise at a location will be experienced at a certain frequency. In many engineering applications, it is desirable to compute and assign the frequency corresponding to the minimum sound pressure. This paper presents three novel methods for the prediction of frequencies corresponding to the minima of radiated sound pressure. Two of them are developed for determining zero sound pressure frequencies, which correspond to a response close to zero. They are based on the application of linear matrix algebra methods in conjunction with the fundamental definitions for the existence of local minima. The other is developed to solve for frequencies of the minimum response points corresponding to a zero slope in the frequency response function curve by using the dichotomy method. In addition, an inverse structural modification for the assignment of the zero sound pressure frequency and antiresonant frequencies is presented. At these frequencies, the modification causes the selected location to experience the minimum sound pressure, while the other selected locations do not vibrate. Numerical examples of a simply supported plate in air and water are analyzed to demonstrate the effectiveness and accuracy of the proposed approaches.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87540416","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}
Topological acoustics has recently witnessed a spurt in research activity, owing to their unprecedented properties transcending typical wave phenomena. In recent years, the use of coupled arrays of acoustic chambers has gained popularity in designing topological acoustic systems. In their common form, an array of acoustic chambers with relatively large volume is coupled via narrow channels. Such configuration is generally modeled as a full three-dimensional system, requiring extended computational time for simulating its harmonic response. To this end, this paper establishes a comprehensive mathematical treatment of the use of electroacoustic analogies for designing topological acoustic lattices. The potential of such analytical approach is demonstrated via two types of topological systems: (1) edge states with quantized winding numbers in an acoustic diatomic lattice and (2) valley Hall transition in an acoustic honeycomb lattice that leads to robust waveguiding. In both cases, the established analytical approach exhibits an excellent agreement with the full three-dimensional model, whether in dispersion analyses or the response of an acoustic system with a finite number of cells. The established analytical framework is invaluable for designing a variety of acoustic topological insulators with minimal computational cost.
{"title":"Designing topological acoustic lattices via electroacoustic analogies","authors":"H. A. Ba'ba'a, Kyung Hoon Lee, Qiming Wang","doi":"10.1115/1.4062360","DOIUrl":"https://doi.org/10.1115/1.4062360","url":null,"abstract":"\u0000 Topological acoustics has recently witnessed a spurt in research activity, owing to their unprecedented properties transcending typical wave phenomena. In recent years, the use of coupled arrays of acoustic chambers has gained popularity in designing topological acoustic systems. In their common form, an array of acoustic chambers with relatively large volume is coupled via narrow channels. Such configuration is generally modeled as a full three-dimensional system, requiring extended computational time for simulating its harmonic response. To this end, this paper establishes a comprehensive mathematical treatment of the use of electroacoustic analogies for designing topological acoustic lattices. The potential of such analytical approach is demonstrated via two types of topological systems: (1) edge states with quantized winding numbers in an acoustic diatomic lattice and (2) valley Hall transition in an acoustic honeycomb lattice that leads to robust waveguiding. In both cases, the established analytical approach exhibits an excellent agreement with the full three-dimensional model, whether in dispersion analyses or the response of an acoustic system with a finite number of cells. The established analytical framework is invaluable for designing a variety of acoustic topological insulators with minimal computational cost.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78365092","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}
Rotors are used to transfer power from one component to the other component in various rotor dynamics applications like steam turbines, aerospace systems, and power generators. In certain applications, the seal is an important and inevitable component of the rotor dynamic system. The linear dynamics of the rotor is converted into nonlinear in the presence of a seal. The presence of a seal, can sometimes, trigger self-excited vibrations in rotor/seal systems. Generally, the amplitude of vibration during such vibrations is several times higher than normal steady-state vibrations. Due to this, other faults like transverse crack initialization and rotor/stator rub get accelerated. The rotating machinery working at high spinning speeds is more prone to this type of instability. Hence, the stability limits of the rotor/seal system must be known in advance for the safe operation of the rotating machinery. The dynamic behaviour of such a system qualitatively varies corresponding to different system parameters of the rotating machinery. Combursome analytical methods have been used in the past for bifurcation analysis of rotor/seal system. In the present work, system bifurcations have been investigated using a sub-harmonic sampling rate strategy. The proposed method is easy to implement and numerically efficient. The effect of various parameters like spinning speed of the rotor, unstable mass, and seal clearance is investigated for the stability of the rotor/seal system. Experimental testing is done to verify the simulation results.
{"title":"Modeling, nonlinear dynamics, and bifurcation analysis of the rotor-seal system using a sub-harmonic sampling strategy","authors":"R. Vashisht","doi":"10.1115/1.4055616","DOIUrl":"https://doi.org/10.1115/1.4055616","url":null,"abstract":"\u0000 Rotors are used to transfer power from one component to the other component in various rotor dynamics applications like steam turbines, aerospace systems, and power generators. In certain applications, the seal is an important and inevitable component of the rotor dynamic system. The linear dynamics of the rotor is converted into nonlinear in the presence of a seal. The presence of a seal, can sometimes, trigger self-excited vibrations in rotor/seal systems. Generally, the amplitude of vibration during such vibrations is several times higher than normal steady-state vibrations. Due to this, other faults like transverse crack initialization and rotor/stator rub get accelerated. The rotating machinery working at high spinning speeds is more prone to this type of instability. Hence, the stability limits of the rotor/seal system must be known in advance for the safe operation of the rotating machinery. The dynamic behaviour of such a system qualitatively varies corresponding to different system parameters of the rotating machinery. Combursome analytical methods have been used in the past for bifurcation analysis of rotor/seal system. In the present work, system bifurcations have been investigated using a sub-harmonic sampling rate strategy. The proposed method is easy to implement and numerically efficient. The effect of various parameters like spinning speed of the rotor, unstable mass, and seal clearance is investigated for the stability of the rotor/seal system. Experimental testing is done to verify the simulation results.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86745395","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 delayed resonator (DR) is an active vibration absorber, which yields ideal vibration suppression at its resonance frequency. In this study, we further complement the DR design in a distinctive mechanical path by introducing an amplifying mechanism (AM), so the creation of DRA. Very different from the existing works that focus more on how to enhance the ideal vibration suppression of the DR, we are interested in how the DR behaves under uncertainties and how can the newly proposed DRA abate the arising negative effects. First, we study the effects of such uncertainties in detecting the excitation frequency on the quality of vibration suppression, working space of the absorber, and energy cost. Then, we discuss how the control parameter perturbation affects the system stability. A comparative study between the classic DR and the proposed DRA is presented throughout the text, showing that the enhanced performance and robustness characteristics enabled by the AM are almost all-around while posing no additional controller complexity. We also show using spectral analysis that the AM can also enhance the transient behavior of the system. Finally, three numerical simulations included as core studies vividly exhibit DRA’s practical strength.
{"title":"A Robust Delayed Resonator Construction using Amplifying Mechanism","authors":"Yifan Liu, Jiazhi Cai, N. Olgaç, Qingbin Gao","doi":"10.1115/1.4055559","DOIUrl":"https://doi.org/10.1115/1.4055559","url":null,"abstract":"\u0000 The delayed resonator (DR) is an active vibration absorber, which yields ideal vibration suppression at its resonance frequency. In this study, we further complement the DR design in a distinctive mechanical path by introducing an amplifying mechanism (AM), so the creation of DRA. Very different from the existing works that focus more on how to enhance the ideal vibration suppression of the DR, we are interested in how the DR behaves under uncertainties and how can the newly proposed DRA abate the arising negative effects. First, we study the effects of such uncertainties in detecting the excitation frequency on the quality of vibration suppression, working space of the absorber, and energy cost. Then, we discuss how the control parameter perturbation affects the system stability. A comparative study between the classic DR and the proposed DRA is presented throughout the text, showing that the enhanced performance and robustness characteristics enabled by the AM are almost all-around while posing no additional controller complexity. We also show using spectral analysis that the AM can also enhance the transient behavior of the system. Finally, three numerical simulations included as core studies vividly exhibit DRA’s practical strength.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85370288","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 study modeled an elliptical diaphragm in a push-pull electrostatic speaker using the average displacement, specific impedance and equivalent radius to predict the frequency response in terms of sound pressure level (SPL). We also fabricated a prototype of an electrostatic speaker based on an elliptical diaphragm with fixed rim measuring 32 mm (semi-major axis) by 30 mm (semi-minor axis). The speaker was then used to analyze the frequency-response characteristics associated with resonance modes and displacement curves using the optical measurement, and obtain the SPL curves in an anechoic chamber using the acoustic measurements. The experiment results revealed that the predicted curves were in good agreement with the measured displacement and SPL curves. These curves of the electrostatic speaker were strongly affected by air radiation impedance. When our speaker was implemented in an over-ear electrostatic headphone, we obtained solid bass response and a frequency response typical of high-fidelity headphones.
{"title":"Resonance Mode and Sound Pressure of a Push-Pull Electrostatic Speaker Based on Elliptical Diaphragm","authors":"Hsin-Yuan Chiang, Yu-Hsi Huang","doi":"10.1115/1.4055561","DOIUrl":"https://doi.org/10.1115/1.4055561","url":null,"abstract":"\u0000 This study modeled an elliptical diaphragm in a push-pull electrostatic speaker using the average displacement, specific impedance and equivalent radius to predict the frequency response in terms of sound pressure level (SPL). We also fabricated a prototype of an electrostatic speaker based on an elliptical diaphragm with fixed rim measuring 32 mm (semi-major axis) by 30 mm (semi-minor axis). The speaker was then used to analyze the frequency-response characteristics associated with resonance modes and displacement curves using the optical measurement, and obtain the SPL curves in an anechoic chamber using the acoustic measurements. The experiment results revealed that the predicted curves were in good agreement with the measured displacement and SPL curves. These curves of the electrostatic speaker were strongly affected by air radiation impedance. When our speaker was implemented in an over-ear electrostatic headphone, we obtained solid bass response and a frequency response typical of high-fidelity headphones.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78971715","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 article, an energy-based statistical linearization method (SL) is proposed to simulate a nonlinear dynamic model of spur gear pair. The gear pair operates under combined deterministic and random loads, and both backlash and time-varying mesh stiffness are considered in the dynamic model. The equivalent linear function approximates the teeth backlash nonlinearity in the gear model. The energy-based linearization, which minimizes the error in potential energy between the original and equivalent linear systems, is used. Simulations are conducted on a gear-pair, and the effect of the input torque on the dynamic response of the gear pair is then examined. The results demonstrate that for high input torque, the system operates in the linear range. For low input torque, the results are not similar to the original because the system became strongly nonlinear. Monte Carlo simulations were carried out to verify the accuracy of the presented method.
{"title":"Develop and verify Energy-Based Statistical Linearization Technique to Analysis Nonlinear Stochastic Vibration of A Spur Gear Pair","authors":"J. Taheri Kahnamouei, Jianming Yang","doi":"10.1115/1.4055560","DOIUrl":"https://doi.org/10.1115/1.4055560","url":null,"abstract":"\u0000 In this article, an energy-based statistical linearization method (SL) is proposed to simulate a nonlinear dynamic model of spur gear pair. The gear pair operates under combined deterministic and random loads, and both backlash and time-varying mesh stiffness are considered in the dynamic model. The equivalent linear function approximates the teeth backlash nonlinearity in the gear model. The energy-based linearization, which minimizes the error in potential energy between the original and equivalent linear systems, is used. Simulations are conducted on a gear-pair, and the effect of the input torque on the dynamic response of the gear pair is then examined. The results demonstrate that for high input torque, the system operates in the linear range. For low input torque, the results are not similar to the original because the system became strongly nonlinear. Monte Carlo simulations were carried out to verify the accuracy of the presented method.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79205710","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}
V. Cool, L. Van Belle, C. Claeys, E. Deckers, W. Desmet
In the original publication, the captions of Figures 4 and 5 are correct, but the graphs have been erroneously switched between both figures. In the corrected version below, Figure 4 correctly shows the result of the lattice-based UC in which the computation times of the ROMs exceed the computation time of the FOM, while Figure 5 correctly shows the results of the shifted UC in which the computation times of the ROMs are significantly smaller than the computation time of the FOM.
{"title":"Erratum: “Impact of the unit cell choice on the efficiency of dispersion curve calculations using GBMS” [ASME J. Vibr. Acoust., 2022, 144(2), p. 024501; DOI: 10.1115/1.4051817]","authors":"V. Cool, L. Van Belle, C. Claeys, E. Deckers, W. Desmet","doi":"10.1115/1.4055410","DOIUrl":"https://doi.org/10.1115/1.4055410","url":null,"abstract":"\u0000 In the original publication, the captions of Figures 4 and 5 are correct, but the graphs have been erroneously switched between both figures. In the corrected version below, Figure 4 correctly shows the result of the lattice-based UC in which the computation times of the ROMs exceed the computation time of the FOM, while Figure 5 correctly shows the results of the shifted UC in which the computation times of the ROMs are significantly smaller than the computation time of the FOM.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73452475","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}
Beam structures are widely used in various engineering occasions to model various structures. Numerous researchers have studied dynamic responses of beam structures with nonlinear supports or nonlinear foundations. In engineering, nonlinear supports were subjected to the beam structure through the surface contact rather than the point connection. Few works studied the dynamic behavior of the beam structure with local uniform cubic nonlinear stiffness foundations. Additionally, the boundary rotational restraints of the beam structure are ignored. To improve the engineering acceptance of the beam structure with nonlinearity, it is of great significance to study the dynamic behavior of the generally restrained axially loaded beam structure with a local uniform nonlinear foundation. This work establishes a nonlinear dynamic model of the beam structure with a local uniform nonlinear foundation. Dynamic responses of the beam structure are predicted through the Galerkin truncated method. In Galerkin truncated method, mode functions of the axially loaded beam structure without the local uniform nonlinear foundation are selected as the trail and weight functions. The harmonic balance method is employed to verify the correctness of the Galerkin truncated method. The influence of the sweeping ways and local uniform nonlinear foundation on dynamic responses of the generally restrained axially loaded beam structure is investigated. Dynamic responses of the generally restrained axially loaded beam structure with a local uniform nonlinear foundation are sensitive to its calculation initial values. Suitable parameters of the local uniform nonlinear foundation can suppress the vibration response and transform the vibration state of the beam structure.
{"title":"Nonlinear vibration analysis of a generally restrained axially loaded beam structure with a local uniform nonlinear foundation","authors":"J. Du, Yuhao Zhao, Yilin Chen, Yang Liu","doi":"10.1115/1.4055303","DOIUrl":"https://doi.org/10.1115/1.4055303","url":null,"abstract":"\u0000 Beam structures are widely used in various engineering occasions to model various structures. Numerous researchers have studied dynamic responses of beam structures with nonlinear supports or nonlinear foundations. In engineering, nonlinear supports were subjected to the beam structure through the surface contact rather than the point connection. Few works studied the dynamic behavior of the beam structure with local uniform cubic nonlinear stiffness foundations. Additionally, the boundary rotational restraints of the beam structure are ignored. To improve the engineering acceptance of the beam structure with nonlinearity, it is of great significance to study the dynamic behavior of the generally restrained axially loaded beam structure with a local uniform nonlinear foundation. This work establishes a nonlinear dynamic model of the beam structure with a local uniform nonlinear foundation. Dynamic responses of the beam structure are predicted through the Galerkin truncated method. In Galerkin truncated method, mode functions of the axially loaded beam structure without the local uniform nonlinear foundation are selected as the trail and weight functions. The harmonic balance method is employed to verify the correctness of the Galerkin truncated method. The influence of the sweeping ways and local uniform nonlinear foundation on dynamic responses of the generally restrained axially loaded beam structure is investigated. Dynamic responses of the generally restrained axially loaded beam structure with a local uniform nonlinear foundation are sensitive to its calculation initial values. Suitable parameters of the local uniform nonlinear foundation can suppress the vibration response and transform the vibration state of the beam structure.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73024425","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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