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}
Pub Date : 2024-11-20DOI: 10.1016/j.ijnonlinmec.2024.104952
Özgül Ilhan
{"title":"Corrigendum to “Slip with friction boundary conditions for the Navier–Stokes-α turbulence model and the effects of the friction on the reattachment point” [Int. J. Non–Linear Mech. 159 (2024) 104614]","authors":"Özgül Ilhan","doi":"10.1016/j.ijnonlinmec.2024.104952","DOIUrl":"10.1016/j.ijnonlinmec.2024.104952","url":null,"abstract":"","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"169 ","pages":"Article 104952"},"PeriodicalIF":2.8,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142699379","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 : 2024-11-20DOI: 10.1016/j.ijnonlinmec.2024.104955
Vivek Anand , N. Hamza , H. Murthy
Singular integral equations solved to obtain a closed-form shear distribution under partial reverse slip conditions involve the integration of contact pressure over a sub-domain of the contact region. Pressure distribution for a nominal flat contact contains logarithmic terms, which pose difficulty in solving these integral equations. This paper provides a simpler approximation to the pressure distribution for a symmetrical nominally flat punch in contact with an elastic half-space to overcome this difficulty. Taylor series approximation has been used in the central flat and curved regions to approximate the nominally flat contact pressure distribution to a square flat (with sharp corners) and Hertzian pressure forms, respectively. The approximation is valid over the entire domain and for any ratio of contact length to flat length. The approximated pressure is used to evaluate the necessary singular integrals for the analytical solution for shear traction under partial reverse slip conditions while being subjected to bulk stress.
{"title":"An approximate analytical solution for shear traction in partial reverse slip contacts","authors":"Vivek Anand , N. Hamza , H. Murthy","doi":"10.1016/j.ijnonlinmec.2024.104955","DOIUrl":"10.1016/j.ijnonlinmec.2024.104955","url":null,"abstract":"<div><div>Singular integral equations solved to obtain a closed-form shear distribution under partial reverse slip conditions involve the integration of contact pressure over a sub-domain of the contact region. Pressure distribution for a nominal flat contact contains logarithmic terms, which pose difficulty in solving these integral equations. This paper provides a simpler approximation to the pressure distribution for a symmetrical nominally flat punch in contact with an elastic half-space to overcome this difficulty. Taylor series approximation has been used in the central flat and curved regions to approximate the nominally flat contact pressure distribution to a <em>square flat</em> (with sharp corners) and <em>Hertzian</em> pressure forms, respectively. The approximation is valid over the entire domain and for any ratio of contact length to flat length. The approximated pressure is used to evaluate the necessary singular integrals for the analytical solution for shear traction under partial reverse slip conditions while being subjected to bulk stress.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"169 ","pages":"Article 104955"},"PeriodicalIF":2.8,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142699378","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 : 2024-11-19DOI: 10.1016/j.ijnonlinmec.2024.104960
N. Antoni
Bifurcation and stability of irreversible systems in plasticity have widely been studied in the literature devoted to Solid Mechanics and are now well understood. The same criteria are of great importance in frictional contact problems as they define the allowable limits of the service domain for frictional contact interfaces prior to their failure due to those mechanisms. In this paper, it is shown that uniqueness, bifurcation and stability in the sense of Hill can be obtained for associated friction, via the established asymptotic equivalence with elastic-perfect plasticity, when the intermediate elastic-plastic layer tends towards the contact interface. The problem formulation and its discretization by the finite element method then lead to the solving of an eigenvalue problem in the vicinity of the limit state for which a static condensation can be performed on the discrete contact interface. The application of the derived stability and non-bifurcation criterion is finally illustrated through two worked examples.
{"title":"Derivation of a stability and non-bifurcation criterion for frictional contact problems","authors":"N. Antoni","doi":"10.1016/j.ijnonlinmec.2024.104960","DOIUrl":"10.1016/j.ijnonlinmec.2024.104960","url":null,"abstract":"<div><div>Bifurcation and stability of irreversible systems in plasticity have widely been studied in the literature devoted to Solid Mechanics and are now well understood. The same criteria are of great importance in frictional contact problems as they define the allowable limits of the service domain for frictional contact interfaces prior to their failure due to those mechanisms. In this paper, it is shown that uniqueness, bifurcation and stability in the sense of Hill can be obtained for associated friction, via the established asymptotic equivalence with elastic-perfect plasticity, when the intermediate elastic-plastic layer tends towards the contact interface. The problem formulation and its discretization by the finite element method then lead to the solving of an eigenvalue problem in the vicinity of the limit state for which a static condensation can be performed on the discrete contact interface. The application of the derived stability and non-bifurcation criterion is finally illustrated through two worked examples.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"169 ","pages":"Article 104960"},"PeriodicalIF":2.8,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142748391","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 : 2024-11-19DOI: 10.1016/j.ijnonlinmec.2024.104954
K.R. Rajagopal , A. Wineman
In this article we establish universal relations for a cube of a nonlinear elastic isotropic electroactive solid that undergoes a homogeneous deformation due to shear tractions but no normal tractions. When there is no electric field, in addition to a shearing deformation, the cube’s dimensions change because of the Poynting effect. In this work, we study the influence of the electric field vector on these dimensional changes using a previously developed constitutive equation for nonlinear electroactive solids. Expressions are obtained for these dimensional changes that depend the amount of shear for different directions of the electric field vector relative to the shearing direction. In addition, universal relations are obtained when there is no electric field and are extended for different electric field directions.
{"title":"Universal relations for electroactive solids undergoing shear and triaxial extension","authors":"K.R. Rajagopal , A. Wineman","doi":"10.1016/j.ijnonlinmec.2024.104954","DOIUrl":"10.1016/j.ijnonlinmec.2024.104954","url":null,"abstract":"<div><div>In this article we establish universal relations for a cube of a nonlinear elastic isotropic electroactive solid that undergoes a homogeneous deformation due to shear tractions but no normal tractions. When there is no electric field, in addition to a shearing deformation, the cube’s dimensions change because of the Poynting effect. In this work, we study the influence of the electric field vector on these dimensional changes using a previously developed constitutive equation for nonlinear electroactive solids. Expressions are obtained for these dimensional changes that depend the amount of shear for different directions of the electric field vector relative to the shearing direction. In addition, universal relations are obtained when there is no electric field and are extended for different electric field directions.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"169 ","pages":"Article 104954"},"PeriodicalIF":2.8,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142699377","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 : 2024-11-19DOI: 10.1016/j.ijnonlinmec.2024.104936
Davood Shahsavari, Prashant Saxena
Magnetorheological elastomers (MREs) are soft solids that can undergo large and reversible deformation in the presence of an externally applied magnetic field. This coupled magneto-mechanical response can be used for active control of surface roughness and actuation in engineering applications by exploiting the reversible instabilities in these materials. In this work, we develop a general mathematical formulation to analyse the surface instabilities of a finitely deformed and magnetised MRE half-space and find the critical stretch that causes bifurcation of the solution of the resulting partial differential equations. The equations are derived using a variational approach in the reference configuration and the null-space relating the incremental solutions is presented to provide a basis for post-bifurcation analysis. Details of the numerical calculations are presented to clearly identify and discount non-physical solutions. Stability phase diagrams are presented to analyse the effect of material parameters and strength/direction of magnetic field.
{"title":"Surface instability of a finitely deformed magnetoelastic half-space","authors":"Davood Shahsavari, Prashant Saxena","doi":"10.1016/j.ijnonlinmec.2024.104936","DOIUrl":"10.1016/j.ijnonlinmec.2024.104936","url":null,"abstract":"<div><div>Magnetorheological elastomers (MREs) are soft solids that can undergo large and reversible deformation in the presence of an externally applied magnetic field. This coupled magneto-mechanical response can be used for active control of surface roughness and actuation in engineering applications by exploiting the reversible instabilities in these materials. In this work, we develop a general mathematical formulation to analyse the surface instabilities of a finitely deformed and magnetised MRE half-space and find the critical stretch that causes bifurcation of the solution of the resulting partial differential equations. The equations are derived using a variational approach in the reference configuration and the null-space relating the incremental solutions is presented to provide a basis for post-bifurcation analysis. Details of the numerical calculations are presented to clearly identify and discount non-physical solutions. Stability phase diagrams are presented to analyse the effect of material parameters and strength/direction of magnetic field.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"169 ","pages":"Article 104936"},"PeriodicalIF":2.8,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142699375","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 : 2024-11-17DOI: 10.1016/j.ijnonlinmec.2024.104957
Bo Meng , Qian Yin , Xinxin Nie , Hongwen Jing , Jingkui Long , Xiaozhao Li , Kai Zhong , Dongfeng Bai
This study is devoted to revealing the vibration responses of anchored fractured rock structure subjected to external excitation disturbances. By utilizing a self-constructed vibration testing platform, a series of vibration tests were conducted regarding various anchoring parameters (bolt spacing D, pre-tightening torque Pt and types of bottom support) and lateral forces Fl. Modal analysis was employed to propose modal parameters including natural frequency ωr and damping ratio ξr, extracted from the vibration signals, as sensitive indicators for assessing structural stability. The test results reveal that a smaller D and higher Pt can effectively enhance the reinforcement effect provided by bolts, as indicated by an increase in ωr and a decrease in ξr in self-stabilized state of the anchored structure. As Fl increases, the restraining effect supported by constrained frame intensifies, the increasing ωr and decreasing ξr can be observed during lateral loading. When the anchored structure is subjected to a large Fl, the weak support areas between adjacent steel belts are susceptible to concentrate as zones of rock collapse, resulting in the formation of circular cavities and a corresponding sharp reduction in Fl, alongside a pronounced decrease in ωr and a significant increase in ξr. Compared to the steel belts, the steel mesh acting as bottom support structure has more advantages in providing effective restraint to achieve self-stability of the anchored structure, as the steel mesh is able to distribute the internal stress more uniformly and reduce localized stress concentrations between rock blocks. As the mining face advances, the stress concentration and redistribution caused by mining activities lead to an increase in fragmentation degree of the roadway roof and a decrease in ωr. The findings of this study provide a scientific basis for understanding the relationship between vibration signals and the stability of anchored fractured surrounding rocks in roadway.
{"title":"Vibration responses and stability assessment of anchored extremely fractured rock mass based on modal analysis","authors":"Bo Meng , Qian Yin , Xinxin Nie , Hongwen Jing , Jingkui Long , Xiaozhao Li , Kai Zhong , Dongfeng Bai","doi":"10.1016/j.ijnonlinmec.2024.104957","DOIUrl":"10.1016/j.ijnonlinmec.2024.104957","url":null,"abstract":"<div><div>This study is devoted to revealing the vibration responses of anchored fractured rock structure subjected to external excitation disturbances. By utilizing a self-constructed vibration testing platform, a series of vibration tests were conducted regarding various anchoring parameters (bolt spacing <em>D</em>, pre-tightening torque <em>P</em><sub>t</sub> and types of bottom support) and lateral forces <em>F</em><sub>l</sub>. Modal analysis was employed to propose modal parameters including natural frequency <em>ω</em><sub>r</sub> and damping ratio <em>ξ</em><sub>r</sub>, extracted from the vibration signals, as sensitive indicators for assessing structural stability. The test results reveal that a smaller <em>D</em> and higher <em>P</em><sub>t</sub> can effectively enhance the reinforcement effect provided by bolts, as indicated by an increase in <em>ω</em><sub>r</sub> and a decrease in <em>ξ</em><sub>r</sub> in self-stabilized state of the anchored structure. As <em>F</em><sub>l</sub> increases, the restraining effect supported by constrained frame intensifies, the increasing <em>ω</em><sub>r</sub> and decreasing <em>ξ</em><sub>r</sub> can be observed during lateral loading. When the anchored structure is subjected to a large <em>F</em><sub>l</sub>, the weak support areas between adjacent steel belts are susceptible to concentrate as zones of rock collapse, resulting in the formation of circular cavities and a corresponding sharp reduction in <em>F</em><sub>l</sub>, alongside a pronounced decrease in <em>ω</em><sub>r</sub> and a significant increase in <em>ξ</em><sub>r</sub>. Compared to the steel belts, the steel mesh acting as bottom support structure has more advantages in providing effective restraint to achieve self-stability of the anchored structure, as the steel mesh is able to distribute the internal stress more uniformly and reduce localized stress concentrations between rock blocks. As the mining face advances, the stress concentration and redistribution caused by mining activities lead to an increase in fragmentation degree of the roadway roof and a decrease in <em>ω</em><sub>r</sub>. The findings of this study provide a scientific basis for understanding the relationship between vibration signals and the stability of anchored fractured surrounding rocks in roadway.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"168 ","pages":"Article 104957"},"PeriodicalIF":2.8,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655233","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 : 2024-11-17DOI: 10.1016/j.ijnonlinmec.2024.104958
W.S. Ma , F.H. Liu , S.F. Lu , X.J. Song , S. Huang , Y.K. Zhu , X. Jiang
In this study, we analyze the nonlinear dynamic characteristics of a 12-pole variable stiffness rotor active magnetic bearings (rotor-AMBs) under intricate resonance conditions. Using the principles of electromagnetic bearings, a model for the 12-pole variable stiffness rotor-AMBs system is developed. Next, the dynamic equations for a two-degree-of-freedom 12-pole variable stiffness rotor-AMBs system are derived, incorporating both quadratic and cubic nonlinearities, through Newton's second law. Considering the primary parametric resonance, 1:1 internal resonance, and 1/2 subharmonic resonance, the multiple time scale perturbation method is applied to derive the average equation of the system. Based on these averaged equations, the characteristics and complex dynamics of the system are analyzed. Finally, MATLAB software is employed for numerical simulations of the 12-pole variable stiffness rotor-AMBs system. The simulation results indicate that the nonlinear control parameters can modify the system's softening and hardening spring behaviors. Varying the parametric excitation amplitude leads to diverse dynamic behaviors, including single-periodic motion, double-periodic motion, and chaotic vibrations.
{"title":"Nonlinear dynamics and motion bifurcations of 12-pole variable stiffness rotor active magnetic bearings system under complex resonance","authors":"W.S. Ma , F.H. Liu , S.F. Lu , X.J. Song , S. Huang , Y.K. Zhu , X. Jiang","doi":"10.1016/j.ijnonlinmec.2024.104958","DOIUrl":"10.1016/j.ijnonlinmec.2024.104958","url":null,"abstract":"<div><div>In this study, we analyze the nonlinear dynamic characteristics of a 12-pole variable stiffness rotor active magnetic bearings (rotor-AMBs) under intricate resonance conditions. Using the principles of electromagnetic bearings, a model for the 12-pole variable stiffness rotor-AMBs system is developed. Next, the dynamic equations for a two-degree-of-freedom 12-pole variable stiffness rotor-AMBs system are derived, incorporating both quadratic and cubic nonlinearities, through Newton's second law. Considering the primary parametric resonance, 1:1 internal resonance, and 1/2 subharmonic resonance, the multiple time scale perturbation method is applied to derive the average equation of the system. Based on these averaged equations, the characteristics and complex dynamics of the system are analyzed. Finally, MATLAB software is employed for numerical simulations of the 12-pole variable stiffness rotor-AMBs system. The simulation results indicate that the nonlinear control parameters can modify the system's softening and hardening spring behaviors. Varying the parametric excitation amplitude leads to diverse dynamic behaviors, including single-periodic motion, double-periodic motion, and chaotic vibrations.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"169 ","pages":"Article 104958"},"PeriodicalIF":2.8,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142699374","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 : 2024-11-15DOI: 10.1016/j.ijnonlinmec.2024.104959
Pingchao Yu , Zihan Jiang , Xuanjun Tao , Shuang Li , Ke Jiang
Substantial imbalance is a real possibility in aero–engines and is usually caused by blade off, bird strikes, etc. A substantially unbalanced rotor system will exhibit extremely complicated nonlinear lateral–torsional behavior, and the related dynamics are critical to the safe design of a rotor system. In this paper, a comprehensive nonlinear model of an imbalanced flexible rotor system is proposed, in which translational–torsional coupling and angular–torsional coupling are introduced simultaneously. Based on the model, the lateral–torsional coupling features are discussed, and the lateral as well as the torsional vibration behaviors are further analyzed in detail. The results show that the lateral–torsional coupling factors only exist under the nonsynchronous whirl condition. Thus, if the imbalance is small, the lateral vibration exhibits the linear feature of a traditional unbalanced response, and the torsional vibration does not occur in steady state. However, under substantially unbalanced conditions, the vibration responses are significantly changed. In lateral vibration, many combined frequency components between rotation frequency (fu) and torsional natural frequency (ft1 and ft2) such as fu-ft1, fu-2ft1 and fu-ft2 can be induced, which can lead to combined resonance phenomena and many additional resonance peaks. The lateral–torsional coupling effect is strong at that time. Both the lateral translational–torsional coupling excitation and lateral angular–torsional coupling excitation exhibits the multiple harmonics whose frequencies are closely related to ft1 and ft2. Consequently, the torsional vibration in those combined resonance regions can be very high. The corresponding vibration exhibits the steady harmonic feature with vibration frequency being ft1 or ft2.
{"title":"Research on lateral–torsional coupled vibration induced by substantial imbalance in an overhung flexible rotor","authors":"Pingchao Yu , Zihan Jiang , Xuanjun Tao , Shuang Li , Ke Jiang","doi":"10.1016/j.ijnonlinmec.2024.104959","DOIUrl":"10.1016/j.ijnonlinmec.2024.104959","url":null,"abstract":"<div><div>Substantial imbalance is a real possibility in aero–engines and is usually caused by blade off, bird strikes, etc. A substantially unbalanced rotor system will exhibit extremely complicated nonlinear lateral–torsional behavior, and the related dynamics are critical to the safe design of a rotor system. In this paper, a comprehensive nonlinear model of an imbalanced flexible rotor system is proposed, in which translational–torsional coupling and angular–torsional coupling are introduced simultaneously. Based on the model, the lateral–torsional coupling features are discussed, and the lateral as well as the torsional vibration behaviors are further analyzed in detail. The results show that the lateral–torsional coupling factors only exist under the nonsynchronous whirl condition. Thus, if the imbalance is small, the lateral vibration exhibits the linear feature of a traditional unbalanced response, and the torsional vibration does not occur in steady state. However, under substantially unbalanced conditions, the vibration responses are significantly changed. In lateral vibration, many combined frequency components between rotation frequency (<em>f</em><sub>u</sub>) and torsional natural frequency (<em>f</em><sub>t1</sub> and <em>f</em><sub>t2</sub>) such as <em>f</em><sub>u</sub>-<em>f</em><sub>t1</sub>, <em>f</em><sub>u</sub>-2<em>f</em><sub>t1</sub> and <em>f</em><sub>u</sub>-<em>f</em><sub>t2</sub> can be induced, which can lead to combined resonance phenomena and many additional resonance peaks. The lateral–torsional coupling effect is strong at that time. Both the lateral translational–torsional coupling excitation and lateral angular–torsional coupling excitation exhibits the multiple harmonics whose frequencies are closely related to <em>f</em><sub>t1</sub> and <em>f</em><sub>t2</sub>. Consequently, the torsional vibration in those combined resonance regions can be very high. The corresponding vibration exhibits the steady harmonic feature with vibration frequency being <em>f</em><sub>t1</sub> or <em>f</em><sub>t2</sub>.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"169 ","pages":"Article 104959"},"PeriodicalIF":2.8,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142721150","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号