Pub Date : 2024-10-09DOI: 10.1016/j.ijnonlinmec.2024.104922
A.V. Porubov, N.M. Bessonov
A non-linear modulation of bending waves in a metamaterial mass-in-mass lattice model is studied. Various kinds of non-linear wave modulation are obtained using a harmonic boundary excitation. It is shown, that these waves can be described by an asymptotic simplification of the equations of motion resulting in a non-linear modulation equation for the displacements. Exact periodic traveling wave solutions to the equation demonstrate a dependence on the sign of the equation coefficients or the elastic parameters of the original model. Dispersion relation for the carrier part of the solution is obtained as a function of wave number versus frequency, it is found how its solutions relate to the acoustic and optic branches and the band gap. This form of the dispersion relation is further used for a description of numerical results on the wave modulation by a harmonic boundary excitation.
{"title":"Boundary excitation of nonlinearly modulated bending strain waves in a metamaterial","authors":"A.V. Porubov, N.M. Bessonov","doi":"10.1016/j.ijnonlinmec.2024.104922","DOIUrl":"10.1016/j.ijnonlinmec.2024.104922","url":null,"abstract":"<div><div>A non-linear modulation of bending waves in a metamaterial mass-in-mass lattice model is studied. Various kinds of non-linear wave modulation are obtained using a harmonic boundary excitation. It is shown, that these waves can be described by an asymptotic simplification of the equations of motion resulting in a non-linear modulation equation for the displacements. Exact periodic traveling wave solutions to the equation demonstrate a dependence on the sign of the equation coefficients or the elastic parameters of the original model. Dispersion relation for the carrier part of the solution is obtained as a function of wave number versus frequency, it is found how its solutions relate to the acoustic and optic branches and the band gap. This form of the dispersion relation is further used for a description of numerical results on the wave modulation by a harmonic boundary excitation.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104922"},"PeriodicalIF":2.8,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142431935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-09DOI: 10.1016/j.ijnonlinmec.2024.104923
Nazmul Sharif, Helal Uddin Molla, M.S. Alam
In this paper, a novel homotopy perturbation method is employed to estimate the approximate angular frequencies of highly nonlinear oscillators. This innovative methodology is extended to generate periodic solutions for the nonlinear free vibration observed in a conservative couple-mass-spring system. The system is characterized by both linear and nonlinear stiffness, specifically incorporating cubic nonlinearity. The application of this technique involves a detailed analysis of two practical instances of such systems. The validation process, comparing the results against published findings and exact solutions, reveals a notable alignment in the approximated angular frequencies and the corresponding periodic solutions. Noteworthy for its precision and easy to use application, this approach proves suitable for addressing a diverse range of nonlinear oscillatory problems encountered in both scientific and engineering domains.
{"title":"Analytical solution of couple-mass-spring systems by novel homotopy perturbation method","authors":"Nazmul Sharif, Helal Uddin Molla, M.S. Alam","doi":"10.1016/j.ijnonlinmec.2024.104923","DOIUrl":"10.1016/j.ijnonlinmec.2024.104923","url":null,"abstract":"<div><div>In this paper, a novel homotopy perturbation method is employed to estimate the approximate angular frequencies of highly nonlinear oscillators. This innovative methodology is extended to generate periodic solutions for the nonlinear free vibration observed in a conservative couple-mass-spring system. The system is characterized by both linear and nonlinear stiffness, specifically incorporating cubic nonlinearity. The application of this technique involves a detailed analysis of two practical instances of such systems. The validation process, comparing the results against published findings and exact solutions, reveals a notable alignment in the approximated angular frequencies and the corresponding periodic solutions. Noteworthy for its precision and easy to use application, this approach proves suitable for addressing a diverse range of nonlinear oscillatory problems encountered in both scientific and engineering domains.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104923"},"PeriodicalIF":2.8,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142431934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-03DOI: 10.1016/j.ijnonlinmec.2024.104920
Angelo Luongo, Manuel Ferretti
The phenomenon of buckling disappearance, occurring in a parameter-dependent family of systems admitting a nontrivial fundamental path, is studied. Two different forms of disappearance are detected, namely: (i) the divergence, in which the critical load continuously tends to infinity, and (ii) the merging, in which two critical loads approach each other, coalesce, and then disappear at a finite value of the critical load. It is shown that the two phenomena can be exhibited by the same mechanical system, when a suitable elasto-geometric parameter is varied. More importantly, it is proved that merging continuously changes into divergence when a second parameter is changed. A paradigmatic system is chosen to illustrate the two forms of buckling, i.e., a three degree-of-freedom spherical pendulum, elastically constrained at the ground, loaded by a transverse force and/or a conservative couple, made of two longitudinal potential forces. The springs are taken elastically linear, to stress the fact that divergence not necessarily calls for introducing a nonlinear constitutive law, as also mentioned in literature. Only a linear bifurcation analysis is carried out here, aimed to find the bifurcation points along the nonlinear fundamental path. However, due to the presence of non-negligible prestrains, such a bifurcation problem is governed by nonlinear algebraic equations, whose number of roots cannot be predicted in advance.
{"title":"Buckling disappearance via merging/divergence in a nonlinear three-d.o.f. system with linear constitutive law","authors":"Angelo Luongo, Manuel Ferretti","doi":"10.1016/j.ijnonlinmec.2024.104920","DOIUrl":"10.1016/j.ijnonlinmec.2024.104920","url":null,"abstract":"<div><div>The phenomenon of buckling disappearance, occurring in a parameter-dependent family of systems admitting a nontrivial fundamental path, is studied. Two different forms of disappearance are detected, namely: (i) the <em>divergence</em>, in which the critical load continuously tends to infinity, and (ii) the <em>merging</em>, in which two critical loads approach each other, coalesce, and then disappear at a finite value of the critical load. It is shown that the two phenomena can be exhibited by the same mechanical system, when a suitable elasto-geometric parameter is varied. More importantly, it is proved that merging continuously changes into divergence when a second parameter is changed. A paradigmatic system is chosen to illustrate the two forms of buckling, <em>i.e.</em>, a three degree-of-freedom spherical pendulum, elastically constrained at the ground, loaded by a transverse force and/or a conservative couple, made of two longitudinal potential forces. The springs are taken elastically linear, to stress the fact that divergence not necessarily calls for introducing a nonlinear constitutive law, as also mentioned in literature. Only a linear bifurcation analysis is carried out here, aimed to find the bifurcation points along the nonlinear fundamental path. However, due to the presence of non-negligible prestrains, such a bifurcation problem is governed by nonlinear algebraic equations, whose number of roots cannot be predicted in advance.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104920"},"PeriodicalIF":2.8,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142420071","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-02DOI: 10.1016/j.ijnonlinmec.2024.104919
Junchao Li , Xiaofang Zhang , Wenan Jiang , Qinsheng Bi , Liqun Chen
In this paper, we proposed a novel cut-out piezoelectric beam with two pairs of motion limiter for broadband operation. By means of the finite element simulation, a superior geometric structure of the corresponding linear model is designed and the model parameters are determined, then the simulation results are verified by experiments. The subsequent experiments mainly investigate the effect of the position of the limiter on the beam and the size of the limiting gap on the amplitude–frequency response of the system. The experimental results show that the frequency bandwidth of the first resonance peak can be significantly expanded from 2.45Hz to 6.28Hz by selecting suitable limiter parameters, which can increase of 256.33% compared with no limiter. Meanwhile, limiters also cause a maximum 171.79% increase in the primary resonance voltage amplitude, and the level of anti-resonance valley can be increased up to 5.35 times. Finally, the influence of external resistance load on the output power of the system is discussed through detailed parametric study, and the maximum power output of 370W is achieved.
{"title":"A novel cut-out piezoelectric beam with limiters for broadband energy harvesting","authors":"Junchao Li , Xiaofang Zhang , Wenan Jiang , Qinsheng Bi , Liqun Chen","doi":"10.1016/j.ijnonlinmec.2024.104919","DOIUrl":"10.1016/j.ijnonlinmec.2024.104919","url":null,"abstract":"<div><div>In this paper, we proposed a novel cut-out piezoelectric beam with two pairs of motion limiter for broadband operation. By means of the finite element simulation, a superior geometric structure of the corresponding linear model is designed and the model parameters are determined, then the simulation results are verified by experiments. The subsequent experiments mainly investigate the effect of the position of the limiter on the beam and the size of the limiting gap on the amplitude–frequency response of the system. The experimental results show that the frequency bandwidth of the first resonance peak can be significantly expanded from 2.45Hz to 6.28Hz by selecting suitable limiter parameters, which can increase of 256.33% compared with no limiter. Meanwhile, limiters also cause a maximum 171.79% increase in the primary resonance voltage amplitude, and the level of anti-resonance valley can be increased up to 5.35 times. Finally, the influence of external resistance load on the output power of the system is discussed through detailed parametric study, and the maximum power output of 370<span><math><mi>μ</mi></math></span>W is achieved.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104919"},"PeriodicalIF":2.8,"publicationDate":"2024-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142420072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-30DOI: 10.1016/j.ijnonlinmec.2024.104915
Junaid Ali , Douglas Hansel , Jezrah Horen , John Evans , Anil Bajaj , Gregory Shaver
Torsional oscillations can pose a significant challenge in automatic transmissions, including those stemming from instabilities induced by friction in the clutch system during shifts. Examples include chatter, squeal, shudder, judder and squawk. Transmission squawk is more than just an annoying noise; it is a symptom of underlying issues that, if left unaddressed, can lead to significant structural failures. Squawk is a high-frequency torsional oscillation, predominantly induced due to a negative friction slope and the presence of a weakly damped oscillating mode in the transmission system. Although numerous passive methods are available to prevent the squawking of the clutch in automotive transmission, the significant drawback of passive methods is the limited duration of effectiveness. This paper particularly focuses on the mitigation of squawk using active control techniques. Since squawk occurs in clutch output, therefore, the output speed is used as the measured signal and clutch clamping force as the control action. The primary objective is to develop a control strategy that effectively dampens squawk oscillations while also minimizing control effort, a crucial aspect that has been overlooked in previous research on robust control of friction-induced vibrations (FIV) in context of automatic transmissions. The effectiveness of the designed controller is tested on an experimentally validated non-linear vehicle-level simulation model of a 9-speed automatic transmission. With the designed controller, the squawk oscillations are successfully suppressed. Comparisons with industrial routine PI controller are made to demonstrate the performance of -optimal controller in terms of minimal control effort and smoother clutch engagement.
{"title":"On robust control of transmission squawk in a medium-duty vehicle","authors":"Junaid Ali , Douglas Hansel , Jezrah Horen , John Evans , Anil Bajaj , Gregory Shaver","doi":"10.1016/j.ijnonlinmec.2024.104915","DOIUrl":"10.1016/j.ijnonlinmec.2024.104915","url":null,"abstract":"<div><div>Torsional oscillations can pose a significant challenge in automatic transmissions, including those stemming from instabilities induced by friction in the clutch system during shifts. Examples include chatter, squeal, shudder, judder and squawk. Transmission squawk is more than just an annoying noise; it is a symptom of underlying issues that, if left unaddressed, can lead to significant structural failures. Squawk is a high-frequency torsional oscillation, predominantly induced due to a negative friction slope and the presence of a weakly damped oscillating mode in the transmission system. Although numerous passive methods are available to prevent the squawking of the clutch in automotive transmission, the significant drawback of passive methods is the limited duration of effectiveness. This paper particularly focuses on the mitigation of squawk using active control techniques. Since squawk occurs in clutch output, therefore, the output speed is used as the measured signal and clutch clamping force as the control action. The primary objective is to develop a control strategy that effectively dampens squawk oscillations while also minimizing control effort, a crucial aspect that has been overlooked in previous research on robust control of friction-induced vibrations (FIV) in context of automatic transmissions. The effectiveness of the designed controller is tested on an experimentally validated non-linear vehicle-level simulation model of a 9-speed automatic transmission. With the designed controller, the squawk oscillations are successfully suppressed. Comparisons with industrial routine PI controller are made to demonstrate the performance of <span><math><mi>μ</mi></math></span>-optimal controller in terms of minimal control effort and smoother clutch engagement.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104915"},"PeriodicalIF":2.8,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142420074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-28DOI: 10.1016/j.ijnonlinmec.2024.104914
Qijia Yao , Hadi Jahanshahi
In this paper, an anti-disturbance control strategy is exploited for the attitude reorientation and vibration damping of flexible satellite under disturbances and output constraints. The flexible satellite is formulated by partial differential equations (PDEs) and the exploited controller extends the existing results from the following two aspects. (1) The exploited controller is capable of handling the time-varying output constraints by incorporating the barrier Lyapunov function (BLF) with a coupling-based item through Lyapunov analysis. (2) The exploited controller possesses the excellent disturbance rejection property by introducing two disturbance observers to separately identify the disturbance torque and force. The asymptotic stability of the closed-loop system is strictly evaluated. The exploited controller can restrain the attitude reorientation error and the tip deformation always in the predefined output constraints. Lastly, comparative simulations validate and highlight the main results.
{"title":"PDE-based anti-disturbance attitude and vibration control of flexible satellite under output constraints","authors":"Qijia Yao , Hadi Jahanshahi","doi":"10.1016/j.ijnonlinmec.2024.104914","DOIUrl":"10.1016/j.ijnonlinmec.2024.104914","url":null,"abstract":"<div><div>In this paper, an anti-disturbance control strategy is exploited for the attitude reorientation and vibration damping of flexible satellite under disturbances and output constraints. The flexible satellite is formulated by partial differential equations (PDEs) and the exploited controller extends the existing results from the following two aspects. (1) The exploited controller is capable of handling the time-varying output constraints by incorporating the barrier Lyapunov function (BLF) with a coupling-based item through Lyapunov analysis. (2) The exploited controller possesses the excellent disturbance rejection property by introducing two disturbance observers to separately identify the disturbance torque and force. The asymptotic stability of the closed-loop system is strictly evaluated. The exploited controller can restrain the attitude reorientation error and the tip deformation always in the predefined output constraints. Lastly, comparative simulations validate and highlight the main results.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104914"},"PeriodicalIF":2.8,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142420073","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-27DOI: 10.1016/j.ijnonlinmec.2024.104918
Zilu Wang, Cong Wang, Yingjie Wei
Morphogenesis, which is a complex interplay of biological, chemical, and physical processes, facilitates differential growth in various biological systems, particularly in plant organs, such as petals and leaves. Although recent studies have increasingly delved into the mechanical aspects of these biological structures, there remains a lack of a comprehensive quantitative understanding of shape formation induced by differential growth in plant organs. Thus, this study addressed this gap by employing a multifaceted approach encompassing theoretical analyses and comprehensive finite element analysis of the effect of differential growth on the shape of a cylinder into a flower shape. Based on the derivation of the strain energy expressions for the axisymmetric and asymmetric configurations, the shape function of the growing flower-like structures were calculated through mathematical optimization. The findings of this study shed light on the influence of the growth function, geometric characteristics, and material properties. As the wave number increased, the final configuration tended to have smaller waves, whereas a longer cylinder buckled more easily and the thickness had a minimal effect. This study offers insights that can pave the way for innovative geometrical designs, thereby providing inspiration for applications on both micro-and macroscales, such as in the realms of self-assembly of soft robotics and flexible electronics.
{"title":"Differential growth and shape formation of a flower-shaped structure","authors":"Zilu Wang, Cong Wang, Yingjie Wei","doi":"10.1016/j.ijnonlinmec.2024.104918","DOIUrl":"10.1016/j.ijnonlinmec.2024.104918","url":null,"abstract":"<div><div>Morphogenesis, which is a complex interplay of biological, chemical, and physical processes, facilitates differential growth in various biological systems, particularly in plant organs, such as petals and leaves. Although recent studies have increasingly delved into the mechanical aspects of these biological structures, there remains a lack of a comprehensive quantitative understanding of shape formation induced by differential growth in plant organs. Thus, this study addressed this gap by employing a multifaceted approach encompassing theoretical analyses and comprehensive finite element analysis of the effect of differential growth on the shape of a cylinder into a flower shape. Based on the derivation of the strain energy expressions for the axisymmetric and asymmetric configurations, the shape function of the growing flower-like structures were calculated through mathematical optimization. The findings of this study shed light on the influence of the growth function, geometric characteristics, and material properties. As the wave number increased, the final configuration tended to have smaller waves, whereas a longer cylinder buckled more easily and the thickness had a minimal effect. This study offers insights that can pave the way for innovative geometrical designs, thereby providing inspiration for applications on both micro-and macroscales, such as in the realms of self-assembly of soft robotics and flexible electronics.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104918"},"PeriodicalIF":2.8,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 we present experimental investigation of the frequency dependence of nonlinear elastic (Murnaghan) moduli of polystyrene samples by the ultrasonic method based on the acousto-elastic effect. Measurements were performed in a wide frequency range, from 250 kHz to 2.5 MHz. The absolute values of the Murnaghan moduli demonstrated considerably nonlinear dependencies on the ultrasound frequency. While at higher frequencies above 600 kHz no significant variations of the moduli occurred, at lower frequencies a drastic rise of absolute values in several orders of magnitude has been observed. The values obtained at lower frequencies were utilized for theoretical estimation of parameters of a strain solitary wave in this material. The data obtained correlated well with the parameters obtained experimentally and allowed for explaining the long-lasting discrepancy between theoretical estimations and experimental results.
{"title":"Frequency dependence of nonlinear elastic moduli of polystyrene","authors":"A.V. Belashov, A.A. Zhikhoreva, Y.M. Beltukov, I.V. Semenova","doi":"10.1016/j.ijnonlinmec.2024.104913","DOIUrl":"10.1016/j.ijnonlinmec.2024.104913","url":null,"abstract":"<div><div>In this paper we present experimental investigation of the frequency dependence of nonlinear elastic (Murnaghan) moduli of polystyrene samples by the ultrasonic method based on the acousto-elastic effect. Measurements were performed in a wide frequency range, from 250 kHz to 2.5 MHz. The absolute values of the Murnaghan moduli demonstrated considerably nonlinear dependencies on the ultrasound frequency. While at higher frequencies above <span><math><mo>∼</mo></math></span>600 kHz no significant variations of the moduli occurred, at lower frequencies a drastic rise of absolute values in several orders of magnitude has been observed. The values obtained at lower frequencies were utilized for theoretical estimation of parameters of a strain solitary wave in this material. The data obtained correlated well with the parameters obtained experimentally and allowed for explaining the long-lasting discrepancy between theoretical estimations and experimental results.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104913"},"PeriodicalIF":2.8,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142420070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-25DOI: 10.1016/j.ijnonlinmec.2024.104917
Xiaozhe Chen, Chengbin Zhang, Weiye Shi, Mutian Ban
The engineering application of vibration synchronization of multiple eccentric rotors (ERs) with the same rotational plane in far resonance is limited due to the constraints of motion characteristics and resultant force cancellation. Therefore, a dynamic model of four ERs distributed in two orthogonal planes is proposed in this paper, which is designed to increase the excitation force and drive the vibrating body to achieve the motion in a straight line. Based on the governing equation corresponding to the dynamic model firstly, the synchronous condition of four ERs and its stability condition are deduced. Then, the phase relationship of four ERs is obtained by numerical analysis, and the resultant force of four ERs in each phase difference is further studied to determine the motion trajectory of the vibrating body. Lastly, theoretical results are verified by four sets of experiments, which show that there are two stable motion states of the system. In each motion state, the resultant force of four ERs is increased compared to two ERs, and the system also moves in a straight line. Therefore, the model presented in this paper can provide a theoretical basis for designing large vibration machinery.
由于受到运动特性和结果力抵消的限制，多个具有相同旋转平面的偏心转子（ER）远共振振动同步的工程应用受到了限制。因此，本文提出了分布在两个正交平面上的四个 ER 的动力学模型，旨在增加激振力，驱动振动体实现直线运动。首先，根据动态模型对应的控制方程，推导出四个 ER 的同步条件及其稳定条件。然后，通过数值分析获得四个 ER 的相位关系，并进一步研究四个 ER 在每个相位差中的结果力，从而确定振动体的运动轨迹。最后，通过四组实验验证了理论结果，结果表明系统存在两种稳定的运动状态。在每种运动状态下，四个 ER 的结果力都比两个 ER 的结果力大，而且系统还做直线运动。因此，本文提出的模型可为大型振动机械的设计提供理论依据。
{"title":"Synchronization phenomenon in a vibrating system driven by four eccentric rotors mounted in the orthogonal plane","authors":"Xiaozhe Chen, Chengbin Zhang, Weiye Shi, Mutian Ban","doi":"10.1016/j.ijnonlinmec.2024.104917","DOIUrl":"10.1016/j.ijnonlinmec.2024.104917","url":null,"abstract":"<div><div>The engineering application of vibration synchronization of multiple eccentric rotors (ERs) with the same rotational plane in far resonance is limited due to the constraints of motion characteristics and resultant force cancellation. Therefore, a dynamic model of four ERs distributed in two orthogonal planes is proposed in this paper, which is designed to increase the excitation force and drive the vibrating body to achieve the motion in a straight line. Based on the governing equation corresponding to the dynamic model firstly, the synchronous condition of four ERs and its stability condition are deduced. Then, the phase relationship of four ERs is obtained by numerical analysis, and the resultant force of four ERs in each phase difference is further studied to determine the motion trajectory of the vibrating body. Lastly, theoretical results are verified by four sets of experiments, which show that there are two stable motion states of the system. In each motion state, the resultant force of four ERs is increased compared to two ERs, and the system also moves in a straight line. Therefore, the model presented in this paper can provide a theoretical basis for designing large vibration machinery.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104917"},"PeriodicalIF":2.8,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tyres are the sole vehicle components in direct contact with the ground, so making an accurate description of their ground pressure distribution is crucial for studying tyres and vehicles mechanical characteristics. The incorporation of an insert body on the rim leads to a significant divergence in the ground pressure distribution of inserts supporting run-flat tyre (ISRFT) under zero-pressure conditions compared to radial tyres. To elucidate the ground pressure distribution law of ISRFT, this study first develops a theoretical model of ISRFT-ground contact and proposes a modified non-linear ground pressure distribution. Subsequently, the verification and estimation of the parameters related to the modified non-linear ground pressure distribution were conducted. The lateral and longitudinal forces of ISRFT under various load and pressure conditions were then examined in conjunction with the brush tyre model. The results demonstrate that the modified non-linear ground pressure distribution exhibits a high degree of fitting accuracy, with a maximum error of 5.27% between theoretical and simulation. The lateral force increases rapidly when the slip angle is less than 3°, and slows down when it exceeds 3°. Furthermore, the slip angle at which the maximum lateral force occurs under zero-pressure conditions is 3–5° greater than that under standard pressure. The longitudinal force exhibits a rapid increase when the slip rate exceeds −0.2, and then plateaus as the slip rate further increases. It is noteworthy that the maximum longitudinal force under zero-pressure conditions is 23.33% lower than that under standard pressure. This research lays a theoretical foundation for the mathematical modelling of ground pressure distribution of ISRFT and provides a reference for analysing tyres and vehicles mechanical characteristics.
{"title":"Investigation on dynamic characteristics of inserts supporting run-flat tyre based on the modified non-linear ground pressure distribution","authors":"Liguo Zang , Cheng Xue , Xinlei Peng , Jing Jiao , Yuxin Feng , Yulin Mao","doi":"10.1016/j.ijnonlinmec.2024.104916","DOIUrl":"10.1016/j.ijnonlinmec.2024.104916","url":null,"abstract":"<div><div>Tyres are the sole vehicle components in direct contact with the ground, so making an accurate description of their ground pressure distribution is crucial for studying tyres and vehicles mechanical characteristics. The incorporation of an insert body on the rim leads to a significant divergence in the ground pressure distribution of inserts supporting run-flat tyre (ISRFT) under zero-pressure conditions compared to radial tyres. To elucidate the ground pressure distribution law of ISRFT, this study first develops a theoretical model of ISRFT-ground contact and proposes a modified non-linear ground pressure distribution. Subsequently, the verification and estimation of the parameters related to the modified non-linear ground pressure distribution were conducted. The lateral and longitudinal forces of ISRFT under various load and pressure conditions were then examined in conjunction with the brush tyre model. The results demonstrate that the modified non-linear ground pressure distribution exhibits a high degree of fitting accuracy, with a maximum error of 5.27% between theoretical and simulation. The lateral force increases rapidly when the slip angle is less than 3°, and slows down when it exceeds 3°. Furthermore, the slip angle at which the maximum lateral force occurs under zero-pressure conditions is 3–5° greater than that under standard pressure. The longitudinal force exhibits a rapid increase when the slip rate exceeds −0.2, and then plateaus as the slip rate further increases. It is noteworthy that the maximum longitudinal force under zero-pressure conditions is 23.33% lower than that under standard pressure. This research lays a theoretical foundation for the mathematical modelling of ground pressure distribution of ISRFT and provides a reference for analysing tyres and vehicles mechanical characteristics.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104916"},"PeriodicalIF":2.8,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142323367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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