Pub Date : 2026-01-01Epub Date: 2025-09-22DOI: 10.1016/j.ijnonlinmec.2025.105262
Hari Om Jangid , Subhankar Sil , T. Raja Sekhar
In this article, we obtain some exact solutions to a new hyperbolic system of quasilinear partial differential equations which describes the two-phase thin film model of a perfectly soluble antisurfactant by using symmetry analysis. Lie’s method provides a group of transformations for which the set of solutions remains invariant and through the help of push-forward actions, optimal classes are constructed. The aid of optimal classes facilitates exact solutions of the system. Additionally, we compute some traveling wave solutions of the governing system with the help of special transformations. For each phase, the evolution of the film thickness and concentration gradient is characterized by geometric representation of the solutions. The weak discontinuity behavior across a solution curve is analyzed as time progresses. In addition, the propagation of characteristic shock and the corresponding collision between the characteristic shock and the weak discontinuity are discussed. The reflected and transmitted wave amplitudes, along with the jump in shock acceleration influenced by the incident wave after interaction, are computed.
{"title":"Exact solutions and wave interactions for one-dimensional two-phase thin film model of a perfectly soluble antisurfactant","authors":"Hari Om Jangid , Subhankar Sil , T. Raja Sekhar","doi":"10.1016/j.ijnonlinmec.2025.105262","DOIUrl":"10.1016/j.ijnonlinmec.2025.105262","url":null,"abstract":"<div><div>In this article, we obtain some exact solutions to a new hyperbolic system of quasilinear partial differential equations which describes the two-phase thin film model of a perfectly soluble antisurfactant by using symmetry analysis. Lie’s method provides a group of transformations for which the set of solutions remains invariant and through the help of push-forward actions, optimal classes are constructed. The aid of optimal classes facilitates exact solutions of the system. Additionally, we compute some traveling wave solutions of the governing system with the help of special transformations. For each phase, the evolution of the film thickness and concentration gradient is characterized by geometric representation of the solutions. The weak discontinuity behavior across a solution curve is analyzed as time progresses. In addition, the propagation of characteristic shock and the corresponding collision between the characteristic shock and the weak discontinuity are discussed. The reflected and transmitted wave amplitudes, along with the jump in shock acceleration influenced by the incident wave after interaction, are computed.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"180 ","pages":"Article 105262"},"PeriodicalIF":3.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145158543","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 : 2026-01-01Epub Date: 2025-09-12DOI: 10.1016/j.ijnonlinmec.2025.105248
Harikrishnan Venugopal, Mia Loccufier, Kevin Dekemele
Torsional vibrations are undesirable in rotating machinery, and demands for better performance and material savings to reduce weight exacerbate this issue by triggering resonance conditions. The Nonlinear Energy Sink (NES) offers a robust and effective vibration attenuation solution. In this research, a 2 Degree-Of-Freedom torsionally vibrating host structure is equipped with a NES having piecewise-linear stiffness approximating a cubic nonlinearity. The first-order Complexification-Averaging (CxA) method is used to analyse the Slow Flow dynamics on the response envelope, and a NES tuning methodology based on the Slow Invariant Manifold is proposed for 1:1 resonance attenuation for two resonance frequencies of the host system. The mechanical design of the NES is optimised for minimal stresses and fatigue while avoiding local resonances of the individual components. Experiments and numerical simulations validate the CxA method, and indicate the presence of Strongly Modulated Response regime and an Isolated Resonance Curve in the vicinity of resonance. Significant resonant response attenuation is achieved for both the first mode () and the second mode () over a wide range of forcing amplitudes, with possibility of further improvements. In this regard, design modifications that allow for effective multi-modal attenuation are presented. As such, a complete toolchain has been developed to obtain an NES design which can be applied to a wide range of torsional vibration applications.
{"title":"Design of a piecewise-stiffening Nonlinear Energy Sink for torsional vibration attenuation","authors":"Harikrishnan Venugopal, Mia Loccufier, Kevin Dekemele","doi":"10.1016/j.ijnonlinmec.2025.105248","DOIUrl":"10.1016/j.ijnonlinmec.2025.105248","url":null,"abstract":"<div><div>Torsional vibrations are undesirable in rotating machinery, and demands for better performance and material savings to reduce weight exacerbate this issue by triggering resonance conditions. The Nonlinear Energy Sink (NES) offers a robust and effective vibration attenuation solution. In this research, a 2 Degree-Of-Freedom torsionally vibrating host structure is equipped with a NES having piecewise-linear stiffness approximating a cubic nonlinearity. The first-order Complexification-Averaging (CxA) method is used to analyse the Slow Flow dynamics on the response envelope, and a NES tuning methodology based on the Slow Invariant Manifold is proposed for 1:1 resonance attenuation for two resonance frequencies of the host system. The mechanical design of the NES is optimised for minimal stresses and fatigue while avoiding local resonances of the individual components. Experiments and numerical simulations validate the CxA method, and indicate the presence of Strongly Modulated Response regime and an Isolated Resonance Curve in the vicinity of resonance. Significant resonant response attenuation is achieved for both the first mode (<span><math><mrow><mo>></mo><mn>80</mn><mtext>%</mtext></mrow></math></span>) and the second mode (<span><math><mrow><mo>></mo><mn>65</mn><mtext>%</mtext></mrow></math></span>) over a wide range of forcing amplitudes, with possibility of further improvements. In this regard, design modifications that allow for effective multi-modal attenuation are presented. As such, a complete toolchain has been developed to obtain an NES design which can be applied to a wide range of torsional vibration applications.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"180 ","pages":"Article 105248"},"PeriodicalIF":3.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145158546","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 : 2026-01-01Epub Date: 2025-09-22DOI: 10.1016/j.ijnonlinmec.2025.105267
Tousheng Huang , Zihan Gu , Zitong Wang , Haotian Yang , Zhaoxiong Yu , Lin Sun , Jingyu Li , Hengshan Xu
This research investigates the relationship between complex dynamical transitions and average output power (AOP) in a hybrid galloping energy harvester (HGEH) featuring a vertically aligned D-shaped bluff body. The model of the HGEH is developed using Hamilton's principle. Based on the derived equations, the nonlinear dynamical behaviors and AOP variations are systematically analyzed with respect to four parameters associated with base excitation and wind energy. Nine distinct patterns of dynamical transitions between periodicity, quasiperiodicity, and chaos are identified, playing a crucial role in inducing jumps in periodic frequencies. Between two transitions, the HGEH remains in periodic vibration with a stable frequency over a broad parameter range, determining an upper limit for AOP growth. In most cases, the occurrence of quasiperiodic and/or chaotic vibrations in transitional regions causes abrupt, often opposing shifts or zigzags in the AOP curve. As a result, while the overall trend of the AOP curve shows a rise with varying parameters, the emergence of dynamical transitions makes the curve go like “resting between climbing stairs”. Furthermore, when wind speed varies, the maximum AOP is frequently achieved at peak points corresponding to period-3 vibrations. This study may provide valuable insights for optimizing HGEHs with D-shaped bluff bodies to enhance broadband concurrent energy harvesting.
{"title":"Dynamical transitions between periodicity, quasiperiodicity, and chaos drive performance changes in a hybrid galloping energy harvester","authors":"Tousheng Huang , Zihan Gu , Zitong Wang , Haotian Yang , Zhaoxiong Yu , Lin Sun , Jingyu Li , Hengshan Xu","doi":"10.1016/j.ijnonlinmec.2025.105267","DOIUrl":"10.1016/j.ijnonlinmec.2025.105267","url":null,"abstract":"<div><div>This research investigates the relationship between complex dynamical transitions and average output power (AOP) in a hybrid galloping energy harvester (HGEH) featuring a vertically aligned D-shaped bluff body. The model of the HGEH is developed using Hamilton's principle. Based on the derived equations, the nonlinear dynamical behaviors and AOP variations are systematically analyzed with respect to four parameters associated with base excitation and wind energy. Nine distinct patterns of dynamical transitions between periodicity, quasiperiodicity, and chaos are identified, playing a crucial role in inducing jumps in periodic frequencies. Between two transitions, the HGEH remains in periodic vibration with a stable frequency over a broad parameter range, determining an upper limit for AOP growth. In most cases, the occurrence of quasiperiodic and/or chaotic vibrations in transitional regions causes abrupt, often opposing shifts or zigzags in the AOP curve. As a result, while the overall trend of the AOP curve shows a rise with varying parameters, the emergence of dynamical transitions makes the curve go like “resting between climbing stairs”. Furthermore, when wind speed varies, the maximum AOP is frequently achieved at peak points corresponding to period-3 vibrations. This study may provide valuable insights for optimizing HGEHs with D-shaped bluff bodies to enhance broadband concurrent energy harvesting.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"180 ","pages":"Article 105267"},"PeriodicalIF":3.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145158542","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 : 2026-01-01Epub Date: 2025-09-20DOI: 10.1016/j.ijnonlinmec.2025.105266
Xin-Yao Wang , Tian-Chen Yuan , Zhe-hui Li , Jian Yang , Ruigang Song , Li-qun Chen
Electromagnetic vibration energy harvesters (EVEHs) present a sustainable power solution for sensor networks in the Internet of Things. Most of the EVEHs commonly adopt the axial magnetization structure. Notably, when the magnet moves to the coil's center, the axially radiated magnetic flux lines become nearly parallel to the coil, reducing flux variation and weakening the induced current. Maintaining an effective operating area requires a significant gap between the magnet and coil, which diminishes magnetic field strength and limits device compactness. To address the problem, a radially magnetized electromechanical energy conversion unit is proposed. The magnetic flux lines radially radiated by the magnet remain highly orthogonal to the surrounding coils, increasing flux variation and enhancing electromagnetic induction. The finite element method is used to optimize the coil parameters of the radial magnetized structure, and the induced current is significantly higher than that of the axial magnetized structure. We developed a single-degree-of-freedom (SDoF-MLVEH) and a two-degree-of-freedom (TDoF-MLVEH) magnetic-levitation vibration energy harvester based on the radial magnetization structure. Two types of MLVEHs are validated using a semi-analytical approach based on harmonic balance. Simulations show that TDoF-MLVEH collects about six times more energy than SDoF-MLVEH under rail vehicle axle box excitation. Experimental results verify that the TDoF-MLVEH maintains stable output within the 0.5–1.5 g excitation range, achieving a peak power of 48.76 mW. Compared to the SDoF-MLVEH, the TDoF-MLVEH attains 66.10 % and 88.75 % higher peak power at the first and second resonant frequencies, respectively.
{"title":"Design and experimentation of radial magnetic field vibration energy harvester based on magnetic levitation","authors":"Xin-Yao Wang , Tian-Chen Yuan , Zhe-hui Li , Jian Yang , Ruigang Song , Li-qun Chen","doi":"10.1016/j.ijnonlinmec.2025.105266","DOIUrl":"10.1016/j.ijnonlinmec.2025.105266","url":null,"abstract":"<div><div>Electromagnetic vibration energy harvesters (EVEHs) present a sustainable power solution for sensor networks in the Internet of Things. Most of the EVEHs commonly adopt the axial magnetization structure. Notably, when the magnet moves to the coil's center, the axially radiated magnetic flux lines become nearly parallel to the coil, reducing flux variation and weakening the induced current. Maintaining an effective operating area requires a significant gap between the magnet and coil, which diminishes magnetic field strength and limits device compactness. To address the problem, a radially magnetized electromechanical energy conversion unit is proposed. The magnetic flux lines radially radiated by the magnet remain highly orthogonal to the surrounding coils, increasing flux variation and enhancing electromagnetic induction. The finite element method is used to optimize the coil parameters of the radial magnetized structure, and the induced current is significantly higher than that of the axial magnetized structure. We developed a single-degree-of-freedom (SDoF-MLVEH) and a two-degree-of-freedom (TDoF-MLVEH) magnetic-levitation vibration energy harvester based on the radial magnetization structure. Two types of MLVEHs are validated using a semi-analytical approach based on harmonic balance. Simulations show that TDoF-MLVEH collects about six times more energy than SDoF-MLVEH under rail vehicle axle box excitation. Experimental results verify that the TDoF-MLVEH maintains stable output within the 0.5–1.5 g excitation range, achieving a peak power of 48.76 mW. Compared to the SDoF-MLVEH, the TDoF-MLVEH attains 66.10 % and 88.75 % higher peak power at the first and second resonant frequencies, respectively.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"180 ","pages":"Article 105266"},"PeriodicalIF":3.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145158545","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 : 2026-01-01Epub Date: 2025-10-03DOI: 10.1016/j.ijnonlinmec.2025.105268
Giovanni Migliaccio , Francesco D’Annibale , Haitao Li , Zigang Deng , Francesco dell’Isola , Gino D’Ovidio
This paper investigates the nonlinear dynamics of the High-Temperature Superconducting (HTS) pinning magnetic levitation (MAGLEV) transit system under development at the University of L’Aquila. Due to its inherently weak damping characteristics, the MAGLEV system is particularly susceptible to external disturbances, such as mechanical or magnetic irregularities along the guideway. To analytically characterize its complex nonlinear dynamics, a simplified nonlinear single-degree-of-freedom model is developed, and the Multiple Scales Method (MSM) is employed as a solution technique. This approach enables the evaluation of how key design parameters influence the system’s dynamic response. The analysis highlights the emergence of both primary and secondary resonances, which arise depending on system parameters and the nonlinear nature of the levitation force, potentially impacting not only performance but also stability. Finally, the analytical findings are validated against benchmark solutions obtained through direct numerical integration of the system’s nonlinear equation of motion.
{"title":"A multiple scales approach to analyze the nonlinear dynamics of the high-temperature superconducting magnetic levitation train","authors":"Giovanni Migliaccio , Francesco D’Annibale , Haitao Li , Zigang Deng , Francesco dell’Isola , Gino D’Ovidio","doi":"10.1016/j.ijnonlinmec.2025.105268","DOIUrl":"10.1016/j.ijnonlinmec.2025.105268","url":null,"abstract":"<div><div>This paper investigates the nonlinear dynamics of the High-Temperature Superconducting (HTS) pinning magnetic levitation (MAGLEV) transit system under development at the University of L’Aquila. Due to its inherently weak damping characteristics, the MAGLEV system is particularly susceptible to external disturbances, such as mechanical or magnetic irregularities along the guideway. To analytically characterize its complex nonlinear dynamics, a simplified nonlinear single-degree-of-freedom model is developed, and the Multiple Scales Method (MSM) is employed as a solution technique. This approach enables the evaluation of how key design parameters influence the system’s dynamic response. The analysis highlights the emergence of both primary and secondary resonances, which arise depending on system parameters and the nonlinear nature of the levitation force, potentially impacting not only performance but also stability. Finally, the analytical findings are validated against benchmark solutions obtained through direct numerical integration of the system’s nonlinear equation of motion.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"180 ","pages":"Article 105268"},"PeriodicalIF":3.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266068","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 : 2026-01-01Epub Date: 2025-09-06DOI: 10.1016/j.ijnonlinmec.2025.105256
Guofang Li , Xiaoli Ji , Shaopei Wu , Deyang Li , Jiqi Wang , Wangcai Ding
Metamaterials play a significant role in controlling wave propagation, and locally resonant metamaterial structures are widely used for vibration isolation. Therefore, this study considers discontinuous external environmental resistance and internal non-smooth collisions, and adopts a physical-to-mathematical modeling approach to build the physical model from a single-unit system to a multi-unit system. A locally resonant metamaterial structure consisting of a mass-spring-mass system with collisions and stick-slip effects is designed. Under a three-unit system, the switching mechanism is incorporated to validate and demonstrate the rationality and effectiveness of the motion behavior of the system. The wave transmission rate in the chain is obtained to reveal the wave propagation effects under different inter-unit parameter ratios. After optimizing the parameters, the number of units is varied to investigate the influence of unit quantity on wave transmission and vibration isolation performance. The research shows that increasing the inter-unit damping ratio, decreasing the inter-unit stiffness ratio, increasing the base mass ratio, decreasing the intra-unit stiffness ratio, and higher friction contribute to broadening the vibration isolation region and maintaining stable isolation. Parameter optimization and an increase in the number of units help achieve effective vibration isolation at lower frequencies, expand the isolation range, and promote wave attenuation. The research results provide a feasible approach for wave attenuation by adjusting inter-unit parameter ratios and the number of units.
{"title":"Design and vibration isolation analysis of locally resonant metamaterial structures considering collision and stick-slip","authors":"Guofang Li , Xiaoli Ji , Shaopei Wu , Deyang Li , Jiqi Wang , Wangcai Ding","doi":"10.1016/j.ijnonlinmec.2025.105256","DOIUrl":"10.1016/j.ijnonlinmec.2025.105256","url":null,"abstract":"<div><div>Metamaterials play a significant role in controlling wave propagation, and locally resonant metamaterial structures are widely used for vibration isolation. Therefore, this study considers discontinuous external environmental resistance and internal non-smooth collisions, and adopts a physical-to-mathematical modeling approach to build the physical model from a single-unit system to a multi-unit system. A locally resonant metamaterial structure consisting of a mass-spring-mass system with collisions and stick-slip effects is designed. Under a three-unit system, the switching mechanism is incorporated to validate and demonstrate the rationality and effectiveness of the motion behavior of the system. The wave transmission rate in the chain is obtained to reveal the wave propagation effects under different inter-unit parameter ratios. After optimizing the parameters, the number of units is varied to investigate the influence of unit quantity on wave transmission and vibration isolation performance. The research shows that increasing the inter-unit damping ratio, decreasing the inter-unit stiffness ratio, increasing the base mass ratio, decreasing the intra-unit stiffness ratio, and higher friction contribute to broadening the vibration isolation region and maintaining stable isolation. Parameter optimization and an increase in the number of units help achieve effective vibration isolation at lower frequencies, expand the isolation range, and promote wave attenuation. The research results provide a feasible approach for wave attenuation by adjusting inter-unit parameter ratios and the number of units.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"180 ","pages":"Article 105256"},"PeriodicalIF":3.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145061107","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 : 2026-01-01Epub Date: 2025-09-06DOI: 10.1016/j.ijnonlinmec.2025.105233
Shishu Zhang , Canlin Li , Congyan Ran , Zhanglei Wu , Weidong Deng , Haizhu Qu , Zhen Liu , Cuiying Zhou
The nonlinear evolution of rock mass shear strength and its coupling with structural plane morphology represent a critical scientific challenge in geotechnical stability analysis. Existing shear strength models based on in-situ direct shear tests lack universality for both soft and hard rock masses, failing to meet rapid stability assessment needs in engineering practice. To address this gap, the study improves the Mohr-Coulomb criterion by incorporating a normal stress modulation coefficient (κ) and a shear plane undulation coupling coefficient (λ). A unified shear strength model for soft-hard rock masses, accounting for normal stress effects, is proposed. The model's validity is confirmed using in-situ direct shear test data from engineering sites. The results demonstrate excellent fitting of experimental data. Hard rocks exhibit characteristics of normal stress suppression coupled with undulation enhancement, while soft rocks display normal stress strengthening and undulation weakening. Structural plane specimens exhibit normal stress inhibition resulting from plastic deformation, while residual interlocking maintains positive contributions from undulations. The model reveals the differential governing mechanisms of normal stress and shear plane undulation on shear strength in soft-hard interbedded rock masses, providing a theoretical foundation for rapid stability assessments in rock mass engineering.
{"title":"Unified model for shear strength of soft and hard rock masses based on in-Situ direct shear test parameters","authors":"Shishu Zhang , Canlin Li , Congyan Ran , Zhanglei Wu , Weidong Deng , Haizhu Qu , Zhen Liu , Cuiying Zhou","doi":"10.1016/j.ijnonlinmec.2025.105233","DOIUrl":"10.1016/j.ijnonlinmec.2025.105233","url":null,"abstract":"<div><div>The nonlinear evolution of rock mass shear strength and its coupling with structural plane morphology represent a critical scientific challenge in geotechnical stability analysis. Existing shear strength models based on in-situ direct shear tests lack universality for both soft and hard rock masses, failing to meet rapid stability assessment needs in engineering practice. To address this gap, the study improves the Mohr-Coulomb criterion by incorporating a normal stress modulation coefficient (<em>κ</em>) and a shear plane undulation coupling coefficient (<em>λ</em>). A unified shear strength model for soft-hard rock masses, accounting for normal stress effects, is proposed. The model's validity is confirmed using in-situ direct shear test data from engineering sites. The results demonstrate excellent fitting of experimental data. Hard rocks exhibit characteristics of normal stress suppression coupled with undulation enhancement, while soft rocks display normal stress strengthening and undulation weakening. Structural plane specimens exhibit normal stress inhibition resulting from plastic deformation, while residual interlocking maintains positive contributions from undulations. The model reveals the differential governing mechanisms of normal stress and shear plane undulation on shear strength in soft-hard interbedded rock masses, providing a theoretical foundation for rapid stability assessments in rock mass engineering.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"180 ","pages":"Article 105233"},"PeriodicalIF":3.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049699","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 : 2026-01-01Epub Date: 2025-09-11DOI: 10.1016/j.ijnonlinmec.2025.105253
Yuanyuan Bai, Liang Wang, Wei Xu
This study proposes a path integration framework to investigate the periodic response evolution of nonlinear dynamical systems subjected to combined harmonic and Poisson white noise excitations. To address the problem of sharp transition probability density functions induced by Poisson white noise, the variable substitution and mapping techniques are introduced to enhance the accuracy of the probability density function. For the periodic response analysis, a decomposition strategy is developed to reconstruct the multi-step transition probability density functions within a full period, deviating from the traditional single-step approach. These functions are subsequently incorporated into the Chapman–Kolmogorov equation for numerical iteration, enabling the derivation of time-dependent probability density functions for different period phases. The methodology is validated through two representative stochastic systems: one under external harmonic excitation and the other under parametric harmonic excitation. The underlying mechanism of two different excitation modes on the system response is discussed, and the correctness of the results is verified by comparing them with Monte Carlo simulation results.
{"title":"Periodic stochastic responses of nonlinear systems under combined harmonic and Poisson white noise excitations","authors":"Yuanyuan Bai, Liang Wang, Wei Xu","doi":"10.1016/j.ijnonlinmec.2025.105253","DOIUrl":"10.1016/j.ijnonlinmec.2025.105253","url":null,"abstract":"<div><div>This study proposes a path integration framework to investigate the periodic response evolution of nonlinear dynamical systems subjected to combined harmonic and Poisson white noise excitations. To address the problem of sharp transition probability density functions induced by Poisson white noise, the variable substitution and mapping techniques are introduced to enhance the accuracy of the probability density function. For the periodic response analysis, a decomposition strategy is developed to reconstruct the multi-step transition probability density functions within a full period, deviating from the traditional single-step approach. These functions are subsequently incorporated into the Chapman–Kolmogorov equation for numerical iteration, enabling the derivation of time-dependent probability density functions for different period phases. The methodology is validated through two representative stochastic systems: one under external harmonic excitation and the other under parametric harmonic excitation. The underlying mechanism of two different excitation modes on the system response is discussed, and the correctness of the results is verified by comparing them with Monte Carlo simulation results.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"180 ","pages":"Article 105253"},"PeriodicalIF":3.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046679","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 : 2026-01-01Epub Date: 2025-09-13DOI: 10.1016/j.ijnonlinmec.2025.105261
Xin Jiang, Qiang Zhang, Wenhan Cao, Xuqiang Dou
Interval uncertainty quantification for multibody systems has gained increasing attention due to complex requirements in the dynamic analysis of virtual prototypes. It is important to carefully consider the correlation between input interval parameters to avoid overestimating predictions, which can happen in traditional interval analysis that assumes parameters are mutually independent. This study introduced a new method that propagates multiple interval parameters with large uncertainty levels in multibody systems. The method combines local mean decomposition and bivariate function decomposition with Chebyshev polynomials to create a coupled surrogate model. This model can envelope the examined interval response and calculate response correlation coefficients. Numerical examples are provided to demonstrate the effectiveness of the method. The results showed that the proposed approach efficiently handles multiple interval parameters with significant uncertainty in the dynamic analysis of a multibody system.
{"title":"Dynamic analysis and correlation propagation of the multibody system considering correlated interval parameters","authors":"Xin Jiang, Qiang Zhang, Wenhan Cao, Xuqiang Dou","doi":"10.1016/j.ijnonlinmec.2025.105261","DOIUrl":"10.1016/j.ijnonlinmec.2025.105261","url":null,"abstract":"<div><div>Interval uncertainty quantification for multibody systems has gained increasing attention due to complex requirements in the dynamic analysis of virtual prototypes. It is important to carefully consider the correlation between input interval parameters to avoid overestimating predictions, which can happen in traditional interval analysis that assumes parameters are mutually independent. This study introduced a new method that propagates multiple interval parameters with large uncertainty levels in multibody systems. The method combines local mean decomposition and bivariate function decomposition with Chebyshev polynomials to create a coupled surrogate model. This model can envelope the examined interval response and calculate response correlation coefficients. Numerical examples are provided to demonstrate the effectiveness of the method. The results showed that the proposed approach efficiently handles multiple interval parameters with significant uncertainty in the dynamic analysis of a multibody system.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"180 ","pages":"Article 105261"},"PeriodicalIF":3.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145061106","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 : 2026-01-01Epub Date: 2025-09-19DOI: 10.1016/j.ijnonlinmec.2025.105265
Manoj Kumar , Ashok Kumar Pal , Ravi Kumar Verma , Sergey Ershkov , Elbaz I. Abouelmagd
This study explores the existence and characteristics of libration points, as well as their linear stability, in the ring-body problem while accounting for additional perturbations from radiation pressure and the albedo effect. Our analysis reveals that even minor variations in the number of peripheral primaries, can lead to significant changes in the system’s dynamics. The mass parameter plays a crucial role in determining the regions associated with libration points. To deepen our understanding, we compare the results of our proposed model with those of the classical ring-body problem. This comparison highlights substantial differences in the locations of the libration points and their respective linear stability. Notably, our findings indicate that the libration point , positioned at the center alongside the peripheral primary , remains unaffected by the considered perturbations. However, with a few exceptions, most identified libration points exhibit unstable behavior. We emphasize that the conducted study is crucial in astrophysics and orbital mechanics, as it helps model planetary ring systems (such as Saturn’s rings), protoplanetary disks, and even certain galactic formations.
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