Pub Date : 2024-12-06DOI: 10.1016/j.ijnonlinmec.2024.104983
W.X. Qian , Y. Ni , L.H. He
A geometrically nonlinear model is developed to explore photo-induced wrinkling of a patterned liquid crystal network (LCN) coating consisting of striped domains with orthogonal director alignments. The inhomogeneous coating is replaced by an equivalent homogeneous plate with distributed eigenstrains, and the large deflections activated by linearly polarized UV light are solved numerically via a kinetic approach. It is found that substantially different wrinkling modes can be formed when the intensity and polarization direction of the light as well as the width of the domains are changed. The results demonstrate a contactless way to create reconfigurable surface topographies.
{"title":"Reconfigurable wrinkles of a patterned liquid crystal network coating activated by polarized light","authors":"W.X. Qian , Y. Ni , L.H. He","doi":"10.1016/j.ijnonlinmec.2024.104983","DOIUrl":"10.1016/j.ijnonlinmec.2024.104983","url":null,"abstract":"<div><div>A geometrically nonlinear model is developed to explore photo-induced wrinkling of a patterned liquid crystal network (LCN) coating consisting of striped domains with orthogonal director alignments. The inhomogeneous coating is replaced by an equivalent homogeneous plate with distributed eigenstrains, and the large deflections activated by linearly polarized UV light are solved numerically via a kinetic approach. It is found that substantially different wrinkling modes can be formed when the intensity and polarization direction of the light as well as the width of the domains are changed. The results demonstrate a contactless way to create reconfigurable surface topographies.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"170 ","pages":"Article 104983"},"PeriodicalIF":2.8,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136696","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 : 2024-12-04DOI: 10.1016/j.ijnonlinmec.2024.104982
Oleg V. Gendelman , Mohammad Bukhari , Alexander F. Vakakis
Hysteresis loops are ubiquitous in harmonically (and not only) forced nonlinear oscillators. These loops result due to the well-known nonlinear bi-stability phenomenon, i.e., the co-existence of steady state responses, with the initial conditions dictating the attraction of a specific orbit by either of these steady states. This introduces an element of uncertainty in the forced dynamics. Hence, if one targets the excitation of a higher-amplitude co-existing steady state solution, e.g., to maximize the energy input into the forced oscillator, this sensitivity on initial conditions introduces uncertainty. Moreover, the role of such hysteresis loops in terms of nonlinear physics is not entirely clear; this contrasts with similar hysteresis loops appearing in, e.g., in cyclically loaded viscoelastic materials, which denote the energy dissipated per excitation cycle. Here a methodology is presented for removing the uncertainty of the forced dynamics on initial conditions, and, in the process, for better understanding and exploiting nonlinear hysteresis loops. Considering the forced Duffing oscillator, as an example, harmonic excitations with super-slowly modulated amplitudes are considered as a means of “tracking” the hysteresis loop during a super-slow cycle of the applied modulated force. For either single or repetitive cycles of super-slow force modulations one may tune the modulations to predictively maximize or minimize the energy intake into the forced oscillator depending on which regions of the hysteresis loop are tracked. Importantly, computational studies indicate that the forced dynamics become independent of the specific initial conditions, thus removing the uncertainty in the response due to bi-stability. These findings elucidate the physical significance of nonlinear hysteresis in terms of energy transfer in forced oscillators, and are applicable to a broad class of forced dynamical systems exhibiting nonlinear hysteresis.
{"title":"Super-slow nonlinear hysteresis loop “tracking” for managing energy intake in the forced Duffing oscillator","authors":"Oleg V. Gendelman , Mohammad Bukhari , Alexander F. Vakakis","doi":"10.1016/j.ijnonlinmec.2024.104982","DOIUrl":"10.1016/j.ijnonlinmec.2024.104982","url":null,"abstract":"<div><div>Hysteresis loops are ubiquitous in harmonically (and not only) forced nonlinear oscillators. These loops result due to the well-known nonlinear bi-stability phenomenon, i.e., the co-existence of steady state responses, with the initial conditions dictating the attraction of a specific orbit by either of these steady states. This introduces an element of uncertainty in the forced dynamics. Hence, if one targets the excitation of a higher-amplitude co-existing steady state solution, e.g., to maximize the energy input into the forced oscillator, this sensitivity on initial conditions introduces uncertainty. Moreover, the role of such hysteresis loops in terms of nonlinear physics is not entirely clear; this contrasts with similar hysteresis loops appearing in, e.g., in cyclically loaded viscoelastic materials, which denote the energy dissipated per excitation cycle. Here a methodology is presented for removing the uncertainty of the forced dynamics on initial conditions, and, in the process, for better understanding and exploiting nonlinear hysteresis loops. Considering the forced Duffing oscillator, as an example, harmonic excitations with super-slowly modulated amplitudes are considered as a means of “tracking” the hysteresis loop during a super-slow cycle of the applied modulated force. For either single or repetitive cycles of super-slow force modulations one may tune the modulations to predictively maximize or minimize the energy intake into the forced oscillator depending on which regions of the hysteresis loop are tracked. Importantly, computational studies indicate that the forced dynamics become independent of the specific initial conditions, thus removing the uncertainty in the response due to bi-stability. These findings elucidate the physical significance of nonlinear hysteresis in terms of energy transfer in forced oscillators, and are applicable to a broad class of forced dynamical systems exhibiting nonlinear hysteresis.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"170 ","pages":"Article 104982"},"PeriodicalIF":2.8,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136695","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 engineering, controlling the vibration of suspended cables is crucial and urgent. Notably, prolonged exposure to varying temperatures alters the vibration characteristics of suspended cables, impacting the selection and effectiveness of control strategies. Given the advancements in temperature-sensitive materials and refined engineering needs, researching temperature effects on cable vibration control is essential. Consequently, this study explores the nonlinear vibration control of suspended cables under temperature variations using a time-delay velocity feedback strategy. A nonlinear dynamic model of time-delay vibration considering temperature effects is established based on Hamilton’s principle. Comparative analysis quantitatively characterizes how temperature variations affect the inherent properties, nonlinear dynamics, and control strategies of suspended cables. Using the method of multiple scales, this study obtains analytical solutions for the primary resonance response. Analysis of three critical variables, sag-to-span ratio, control gain, and time delay under temperatures of C, C and C led to an optimal control parameter design that achieves a vibration control efficiency of 93.6, underscoring the effectiveness of the time-delay feedback strategy.
{"title":"Nonlinear time-delay feedback control of a suspended cable under temperature effect","authors":"Jian Peng , Hui Xia , Stefano Lenci , Xianzhong Xie , Lianhua Wang","doi":"10.1016/j.ijnonlinmec.2024.104975","DOIUrl":"10.1016/j.ijnonlinmec.2024.104975","url":null,"abstract":"<div><div>In engineering, controlling the vibration of suspended cables is crucial and urgent. Notably, prolonged exposure to varying temperatures alters the vibration characteristics of suspended cables, impacting the selection and effectiveness of control strategies. Given the advancements in temperature-sensitive materials and refined engineering needs, researching temperature effects on cable vibration control is essential. Consequently, this study explores the nonlinear vibration control of suspended cables under temperature variations using a time-delay velocity feedback strategy. A nonlinear dynamic model of time-delay vibration considering temperature effects is established based on Hamilton’s principle. Comparative analysis quantitatively characterizes how temperature variations affect the inherent properties, nonlinear dynamics, and control strategies of suspended cables. Using the method of multiple scales, this study obtains analytical solutions for the primary resonance response. Analysis of three critical variables, sag-to-span ratio, control gain, and time delay under temperatures of <span><math><mrow><mo>−</mo><mn>40</mn><msup><mrow><mspace></mspace></mrow><mrow><mo>∘</mo></mrow></msup></mrow></math></span>C, <span><math><mrow><mn>0</mn><mi>‘</mi><msup><mrow><mspace></mspace></mrow><mrow><mo>∘</mo></mrow></msup></mrow></math></span>C and <span><math><mrow><mo>+</mo><mn>40</mn><msup><mrow><mspace></mspace></mrow><mrow><mo>∘</mo></mrow></msup></mrow></math></span>C led to an optimal control parameter design that achieves a vibration control efficiency of 93.6<span><math><mtext>%</mtext></math></span>, underscoring the effectiveness of the time-delay feedback strategy.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"170 ","pages":"Article 104975"},"PeriodicalIF":2.8,"publicationDate":"2024-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136620","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 : 2024-11-30DOI: 10.1016/j.ijnonlinmec.2024.104971
K.R. Rajagopal , A. Wineman
In his pioneering work in nonlinear elasticity, Rivlin studied the tension–torsion of a solid isotropic homogeneous elastic cylinder and obtained expressions for the twisting moment as well as the normal force for all bodies belonging to that class in terms of the angle of twist and the stretch. The deformation considered by Rivlin was a universal controllable deformation in that it can be engendered by just the application of the appropriate surface tractions. In this short note we consider the tension–torsion of a solid electroelastic cylinder under the action of an electric field along the axis of the cylinder, and determine expressions for the twisting moment and normal force that depend on the angle of twist, stretch and the applied electric field. We obtain an expression for the torsional rigidity of the electroelastic solid cylinder that depends on the electric field, thereby implying its torsional rigidity can be “tuned” by varying the electrical field. While within the context of classical Cauchy elasticity one observes the compression of the isotropic solid cylinder, namely the POYNTING effect, we show that the cylinder can be made shorter or longer by controlling the electrical field.
{"title":"Tension/torsion of electroactive solid cylinders","authors":"K.R. Rajagopal , A. Wineman","doi":"10.1016/j.ijnonlinmec.2024.104971","DOIUrl":"10.1016/j.ijnonlinmec.2024.104971","url":null,"abstract":"<div><div>In his pioneering work in nonlinear elasticity, Rivlin studied the tension–torsion of a solid isotropic homogeneous elastic cylinder and obtained expressions for the twisting moment as well as the normal force for all bodies belonging to that class in terms of the angle of twist and the stretch. The deformation considered by Rivlin was a universal controllable deformation in that it can be engendered by just the application of the appropriate surface tractions. In this short note we consider the tension–torsion of a solid electroelastic cylinder under the action of an electric field along the axis of the cylinder, and determine expressions for the twisting moment and normal force that depend on the angle of twist, stretch and the applied electric field. We obtain an expression for the torsional rigidity of the electroelastic solid cylinder that depends on the electric field, thereby implying its torsional rigidity can be “tuned” by varying the electrical field. While within the context of classical Cauchy elasticity one observes the compression of the isotropic solid cylinder, namely the POYNTING effect, we show that the cylinder can be made shorter or longer by controlling the electrical field.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"170 ","pages":"Article 104971"},"PeriodicalIF":2.8,"publicationDate":"2024-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136621","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 : 2024-11-26DOI: 10.1016/j.ijnonlinmec.2024.104974
Ali Kandil , Abraham C. Francis , Ahmed Elsaid , Waheed K. Zahra
Magnetic levitation (MAGLEV) technology over the years has attracted significant attention, not just for transportation purposes – as in MAGLEV trains and vehicles, but also for energy harvesting purposes. This paper presents a detailed study of a non-ideal magnetic levitation system, emphasizing the potential for energy harvesting while taking into account the weight of the oscillating suspended block in the middle. Geometry of axis translation is used to account for the new consideration of the middle block's weight. Both numerical simulations using Runge-Kutta method and analytical solution through the method of multiple scales are utilized to study the system's behavior. Numerical results confirm resonance behaviors of the middle block and electrodynamic shaker, supported by phase plane and Poincare maps describing system stability under varying conditions. Through the analytical findings, the study considers the system's response to mechanical-electrical damping variations and center magnet mass changes. Parametric variations reveal subtle effects on system dynamics, showing the relationship between damping, mass, and the oscillation amplitude. Moreover, power output analyses indicate that, at the presence of internal resonance, the power is approximately three times more than the case of absence of internal resonance. Overall, incorporating weight yields better power output, making the way for future research development in system design and application.
{"title":"Effect of the suspended block's weight on the nonlinear dynamics of a non-ideal magnetic levitation model connected to an energy harvester","authors":"Ali Kandil , Abraham C. Francis , Ahmed Elsaid , Waheed K. Zahra","doi":"10.1016/j.ijnonlinmec.2024.104974","DOIUrl":"10.1016/j.ijnonlinmec.2024.104974","url":null,"abstract":"<div><div>Magnetic levitation (MAGLEV) technology over the years has attracted significant attention, not just for transportation purposes – as in MAGLEV trains and vehicles, but also for energy harvesting purposes. This paper presents a detailed study of a non-ideal magnetic levitation system, emphasizing the potential for energy harvesting while taking into account the weight of the oscillating suspended block in the middle. Geometry of axis translation is used to account for the new consideration of the middle block's weight. Both numerical simulations using Runge-Kutta method and analytical solution through the method of multiple scales are utilized to study the system's behavior. Numerical results confirm resonance behaviors of the middle block and electrodynamic shaker, supported by phase plane and Poincare maps describing system stability under varying conditions. Through the analytical findings, the study considers the system's response to mechanical-electrical damping variations and center magnet mass changes. Parametric variations reveal subtle effects on system dynamics, showing the relationship between damping, mass, and the oscillation amplitude. Moreover, power output analyses indicate that, at the presence of internal resonance, the power is approximately three times more than the case of absence of internal resonance. Overall, incorporating weight yields better power output, making the way for future research development in system design and application.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"170 ","pages":"Article 104974"},"PeriodicalIF":2.8,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136584","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 : 2024-11-26DOI: 10.1016/j.ijnonlinmec.2024.104972
Hailun Zhou , Jinhao Yu , Cun Wang , An Ke
The contact behavior between the boss of the elastic ring and the bearing outer ring, as well as the bearing housing, results in significant nonlinear characteristics in its stiffness. By analyzing the existing mathematical model for calculating elastic ring stiffness and considering engineering practice, a finite element model was established to incorporate the contact behavior of the elastic ring boss. This study deeply investigates the nonlinear stiffness characteristics of the elastic ring. The findings indicate that under ideal conditions, when there is full contact between the elastic ring boss and both inner and outer rings, no obvious nonlinear characteristics are observed in its stiffness. However, when ellipticity occurs in the elastic ring or if there is insufficient boss contact, an increase in load leads to evident nonlinear changes in its stiffness. Furthermore, it is noted that these nonlinear characteristics vary at different circumferential positions within the elastic ring. To further investigate these stiffness characteristics and validate numerical results accurately, an experimental test rig specifically designed for measuring elastic ring stiffness was constructed. This study reveals how contact behavior between the elastic ring boss and both bearing components influences its overall stiffness while elucidating its inherent nonlinear properties. These findings provide valuable insights for designing and utilizing elastic rings.
{"title":"Study on the influence of contact behavior on nonlinear stiffness characteristics of elastic rings","authors":"Hailun Zhou , Jinhao Yu , Cun Wang , An Ke","doi":"10.1016/j.ijnonlinmec.2024.104972","DOIUrl":"10.1016/j.ijnonlinmec.2024.104972","url":null,"abstract":"<div><div>The contact behavior between the boss of the elastic ring and the bearing outer ring, as well as the bearing housing, results in significant nonlinear characteristics in its stiffness. By analyzing the existing mathematical model for calculating elastic ring stiffness and considering engineering practice, a finite element model was established to incorporate the contact behavior of the elastic ring boss. This study deeply investigates the nonlinear stiffness characteristics of the elastic ring. The findings indicate that under ideal conditions, when there is full contact between the elastic ring boss and both inner and outer rings, no obvious nonlinear characteristics are observed in its stiffness. However, when ellipticity occurs in the elastic ring or if there is insufficient boss contact, an increase in load leads to evident nonlinear changes in its stiffness. Furthermore, it is noted that these nonlinear characteristics vary at different circumferential positions within the elastic ring. To further investigate these stiffness characteristics and validate numerical results accurately, an experimental test rig specifically designed for measuring elastic ring stiffness was constructed. This study reveals how contact behavior between the elastic ring boss and both bearing components influences its overall stiffness while elucidating its inherent nonlinear properties. These findings provide valuable insights for designing and utilizing elastic rings.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"170 ","pages":"Article 104972"},"PeriodicalIF":2.8,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136582","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 : 2024-11-26DOI: 10.1016/j.ijnonlinmec.2024.104968
Diego Grandi, Arianna Passerini, Manuela Trullo
In an Oberbeck–Boussinesq model, rigorously derived, which includes compressibility, one could expect that the onset of convection for Bénard’s problem occurs at a higher critical Rayleigh number with respect to the classic O–B solutions. The new partial differential equations exhibit non constant coefficients and the unknown velocity field is not divergence-free. By considering these equations, the critical Rayleigh number for the instability of the rest state in Lorenz approximation system is shown to be higher than the classical value, so proving increased stability of the rest state as expected.
{"title":"A Lorenz model for an anelastic Oberbeck-Boussinesq system","authors":"Diego Grandi, Arianna Passerini, Manuela Trullo","doi":"10.1016/j.ijnonlinmec.2024.104968","DOIUrl":"10.1016/j.ijnonlinmec.2024.104968","url":null,"abstract":"<div><div>In an Oberbeck–Boussinesq model, rigorously derived, which includes compressibility, one could expect that the onset of convection for Bénard’s problem occurs at a higher critical Rayleigh number with respect to the classic O–B solutions. The new partial differential equations exhibit non constant coefficients and the unknown velocity field is not divergence-free. By considering these equations, the critical Rayleigh number for the instability of the rest state in Lorenz approximation system is shown to be higher than the classical value, so proving increased stability of the rest state as expected.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"169 ","pages":"Article 104968"},"PeriodicalIF":2.8,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142748390","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 : 2024-11-26DOI: 10.1016/j.ijnonlinmec.2024.104973
Zhan Wang, Xuhui Liang, Zinan Wang, Ke Zhang, Peng Zhou
The high rigidity and small deformation of full-ceramic bearings make them essential components in high-end rotating machinery. However, at high speeds, the lubricant in the contact area between the ball and the raceway is constantly forced out, causing the full ceramic bearing to run out of oil. This leads to increased friction between the ball and the cage, accelerating cage wear. Using the lumped mass approach, a dimensionless model with ten DOFs is constructed to study the effects of cage wear on the dynamic properties of a bearing–rotor system with starved lubrication. The model accounts for the phenomenon of starved lubrication occurring when the ball and raceway come into contact, as well as the interaction between the worn-out cage and the bearing components. An analysis is conducted on the impact of the cage on the dynamic characteristics of the system at varying levels of wear. An analysis of the nonlinear vibration is conducted using a bifurcation diagram and a Poincare section. Ultimately, a comparison is made between the experimental data and the simulation results. The findings indicate that as rotational speed rises, the distribution of lubricating oil becomes uneven, and there is a noticeable decrease in both the volume fraction and thickness of the lubricating oil. After the cage wear is aggravated, the frequency component mfs±nfc becomes more abundant in the frequency diagram, and the concentration of vibration energy is primarily in the low-frequency range. The experimental results are largely congruent with the computational results, with a maximum frequency domain error of 5.88%. The model precisely characterizes the frequency features of cage defects resulting from wear due to starved lubrication in full-ceramic bearings. It provides important information for fault detection and health status monitoring of full-ceramic bearings.
{"title":"Effect of cage pocket wear on the nonlinear dynamics of a full-ceramic bearing–rotor system under starved conditions","authors":"Zhan Wang, Xuhui Liang, Zinan Wang, Ke Zhang, Peng Zhou","doi":"10.1016/j.ijnonlinmec.2024.104973","DOIUrl":"10.1016/j.ijnonlinmec.2024.104973","url":null,"abstract":"<div><div>The high rigidity and small deformation of full-ceramic bearings make them essential components in high-end rotating machinery. However, at high speeds, the lubricant in the contact area between the ball and the raceway is constantly forced out, causing the full ceramic bearing to run out of oil. This leads to increased friction between the ball and the cage, accelerating cage wear. Using the lumped mass approach, a dimensionless model with ten DOFs is constructed to study the effects of cage wear on the dynamic properties of a bearing–rotor system with starved lubrication. The model accounts for the phenomenon of starved lubrication occurring when the ball and raceway come into contact, as well as the interaction between the worn-out cage and the bearing components. An analysis is conducted on the impact of the cage on the dynamic characteristics of the system at varying levels of wear. An analysis of the nonlinear vibration is conducted using a bifurcation diagram and a Poincare section. Ultimately, a comparison is made between the experimental data and the simulation results. The findings indicate that as rotational speed rises, the distribution of lubricating oil becomes uneven, and there is a noticeable decrease in both the volume fraction and thickness of the lubricating oil. After the cage wear is aggravated, the frequency component <em>mf</em><sub><em>s</em></sub> <em>±</em> <em>nf</em><sub><em>c</em></sub> becomes more abundant in the frequency diagram, and the concentration of vibration energy is primarily in the low-frequency range. The experimental results are largely congruent with the computational results, with a maximum frequency domain error of 5.88%. The model precisely characterizes the frequency features of cage defects resulting from wear due to starved lubrication in full-ceramic bearings. It provides important information for fault detection and health status monitoring of full-ceramic bearings.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"170 ","pages":"Article 104973"},"PeriodicalIF":2.8,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136619","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 : 2024-11-26DOI: 10.1016/j.ijnonlinmec.2024.104966
Bengi Yıldız , Sümeyye Sınır , Berra Gültekin Sınır
This paper considers oscillations of systems with a single-degree-of-freedom (SDOF) including fractional derivatives. The system is assumed to be an unforced condition. A general solution procedure that can be effectively applied to various types of fractionally damped models, where damping is defined by a fractional derivative, in engineering and physics is proposed. The nonlinearity of the mentioned models contains not only damping but can also consist of acceleration or displacement. This study proposed a new general model that includes but not limited to modified fractional versions of the well-known linear, quadratic, Coulomb and negative damped models. The method of multiple time scales is performed to obtain approximate analytical solutions. The solution, the amplitude, and the phase in the applications are plotted for various fractional derivative parameter values. In order to confirm their validity, our results for the case of the fractional derivative parameter equal to one are compared with others available in the literature.
{"title":"A general solution procedure for nonlinear single degree of freedom systems including fractional derivatives","authors":"Bengi Yıldız , Sümeyye Sınır , Berra Gültekin Sınır","doi":"10.1016/j.ijnonlinmec.2024.104966","DOIUrl":"10.1016/j.ijnonlinmec.2024.104966","url":null,"abstract":"<div><div>This paper considers oscillations of systems with a single-degree-of-freedom (SDOF) including fractional derivatives. The system is assumed to be an unforced condition. A general solution procedure that can be effectively applied to various types of fractionally damped models, where damping is defined by a fractional derivative, in engineering and physics is proposed. The nonlinearity of the mentioned models contains not only damping but can also consist of acceleration or displacement. This study proposed a new general model that includes but not limited to modified fractional versions of the well-known linear, quadratic, Coulomb and negative damped models. The method of multiple time scales is performed to obtain approximate analytical solutions. The solution, the amplitude, and the phase in the applications are plotted for various fractional derivative parameter values. In order to confirm their validity, our results for the case of the fractional derivative parameter equal to one are compared with others available in the literature.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"169 ","pages":"Article 104966"},"PeriodicalIF":2.8,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142748389","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 : 2024-11-25DOI: 10.1016/j.ijnonlinmec.2024.104967
An Ninh Thi Vu , Dinh Kien Nguyen
The size-dependent nonlinear dynamics of two-directional functionally graded (2D-FG) microbeams in a thermal environment under a moving mass is studied for the first time in the framework of the refined higher-order shear deformation theory (HSDT) and modified couple stress theory (MCST). The variation of the temperature-dependent material properties in the axial and thickness directions is estimated by the Mori–Tanaka homogenization scheme. Considering the rotary inertia and shear deformation, the nonlinear differential equations of motion, obtained from Hamilton’s principle, are discretized using an enriched beam element. Numerical results determined by the Newmark method in combination with Newton–Raphson iterative procedure confirm the efficiency of the derived beam formulation in predicting the nonlinear dynamics. The enriched beam element, which is derived herein by using hierarchical functions to enrich the conventional shape functions, is capable of furnishing accurate nonlinear dynamic characteristics with fewer elements compared to the conventional one. It is shown that the difference between the dynamic response predicted by the linear analysis and the nonlinear one increases by increasing the temperature, but it decreases by increasing the size scale parameter. The effects of the material gradation, temperature rise and micro-scale parameter on the nonlinear dynamic behavior of the 2D-FG microbeams are studied in detail and highlighted.
{"title":"Size-dependent nonlinear dynamics of two-directional functionally graded microbeams in thermal environment under a moving mass","authors":"An Ninh Thi Vu , Dinh Kien Nguyen","doi":"10.1016/j.ijnonlinmec.2024.104967","DOIUrl":"10.1016/j.ijnonlinmec.2024.104967","url":null,"abstract":"<div><div>The size-dependent nonlinear dynamics of two-directional functionally graded (2D-FG) microbeams in a thermal environment under a moving mass is studied for the first time in the framework of the refined higher-order shear deformation theory (HSDT) and modified couple stress theory (MCST). The variation of the temperature-dependent material properties in the axial and thickness directions is estimated by the Mori–Tanaka homogenization scheme. Considering the rotary inertia and shear deformation, the nonlinear differential equations of motion, obtained from Hamilton’s principle, are discretized using an enriched beam element. Numerical results determined by the Newmark method in combination with Newton–Raphson iterative procedure confirm the efficiency of the derived beam formulation in predicting the nonlinear dynamics. The enriched beam element, which is derived herein by using hierarchical functions to enrich the conventional shape functions, is capable of furnishing accurate nonlinear dynamic characteristics with fewer elements compared to the conventional one. It is shown that the difference between the dynamic response predicted by the linear analysis and the nonlinear one increases by increasing the temperature, but it decreases by increasing the size scale parameter. The effects of the material gradation, temperature rise and micro-scale parameter on the nonlinear dynamic behavior of the 2D-FG microbeams are studied in detail and highlighted.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"170 ","pages":"Article 104967"},"PeriodicalIF":2.8,"publicationDate":"2024-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136583","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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