Pub Date : 2026-01-10DOI: 10.1016/j.apm.2026.116747
Jian-Yu Liu, Xiao-Yong Wen
This work employs the modified complex short pulse equation to model the nonlinear propagation of ultrashort optical pulses in fibers. Based on the hodograph transformation and the generalized Darboux transformation, four types of position-controlled cuspon localized wave solutions are constructed, comprising cuspon semi-rational soliton, cuspon rogue wave, cuspon periodic wave, and their cuspon hybrid interaction solutions, all of which are illustrated graphically. Unlike traditional single-valued smooth structures, we demonstrate single-valued, non-smooth cuspon-type localized wave structures with sharp peaks. Furthermore, by adjusting specific parameters, we can effectively control the spatial positions and shapes of these localized wave solutions. These results not only enrich the understanding of cuspon localized wave structures but also offer valuable tools for interpreting ultrashort optical pulse propagation under nonlinear conditions.
{"title":"Hodograph transformation and cuspon localized wave solutions for the modified complex short pulse equation","authors":"Jian-Yu Liu, Xiao-Yong Wen","doi":"10.1016/j.apm.2026.116747","DOIUrl":"10.1016/j.apm.2026.116747","url":null,"abstract":"<div><div>This work employs the modified complex short pulse equation to model the nonlinear propagation of ultrashort optical pulses in fibers. Based on the hodograph transformation and the generalized Darboux transformation, four types of position-controlled cuspon localized wave solutions are constructed, comprising cuspon semi-rational soliton, cuspon rogue wave, cuspon periodic wave, and their cuspon hybrid interaction solutions, all of which are illustrated graphically. Unlike traditional single-valued smooth structures, we demonstrate single-valued, non-smooth cuspon-type localized wave structures with sharp peaks. Furthermore, by adjusting specific parameters, we can effectively control the spatial positions and shapes of these localized wave solutions. These results not only enrich the understanding of cuspon localized wave structures but also offer valuable tools for interpreting ultrashort optical pulse propagation under nonlinear conditions.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"155 ","pages":"Article 116747"},"PeriodicalIF":4.4,"publicationDate":"2026-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145956845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-01-10DOI: 10.1016/j.apm.2026.116751
Anuj Goel , Amit Kumar Manocha , Parveen Bajaj , George Uwadiegwu Alaneme
In the present work, a new framework is proposed to design controllers using model order reduction techniques for linear time invariant complex engineering systems. The proposed model order reduction methodology employs optimization-based techniques namely ant lion optimization and moth flame optimization for which boundary conditions are systematically procured from an interim model derived using balancing free square-root algorithm. An area control coefficient is introduced to adjust the exploration range of the optimization process around the coefficients of the interim reduced-order model. The numerator as well as denominator coefficients of the desired reduced-order models are optimized to retain the performance characteristics of the original high-order systems. The effectiveness of the proposed approach is assessed based on different error metrics and unit step response plots. To validate the performance, seven benchmark systems of different pole configurations have been considered from the literature. It has been found that proposed approach provides reduced-systems with significant improvement in error and transient performance when compared to the literature work. The suggested model order reduction approach is further extended to design proportional-integral-derivative controller and fractional-order proportional-integral-derivative controller for an 84th-order benchmark system and a mechanical ventilator system respectively. The results demonstrate that the proposed model order reduction-based controller design approach achieves high-performance control with lesser steady-state error, improved time-domain specifications and robust disturbance rejection capability.
{"title":"A new method of specifying parameter bounds for optimization of reduced-order models and application in design of controllers","authors":"Anuj Goel , Amit Kumar Manocha , Parveen Bajaj , George Uwadiegwu Alaneme","doi":"10.1016/j.apm.2026.116751","DOIUrl":"10.1016/j.apm.2026.116751","url":null,"abstract":"<div><div>In the present work, a new framework is proposed to design controllers using model order reduction techniques for linear time invariant complex engineering systems. The proposed model order reduction methodology employs optimization-based techniques namely ant lion optimization and moth flame optimization for which boundary conditions are systematically procured from an interim model derived using balancing free square-root algorithm. An area control coefficient is introduced to adjust the exploration range of the optimization process around the coefficients of the interim reduced-order model. The numerator as well as denominator coefficients of the desired reduced-order models are optimized to retain the performance characteristics of the original high-order systems. The effectiveness of the proposed approach is assessed based on different error metrics and unit step response plots. To validate the performance, seven benchmark systems of different pole configurations have been considered from the literature. It has been found that proposed approach provides reduced-systems with significant improvement in error and transient performance when compared to the literature work. The suggested model order reduction approach is further extended to design proportional-integral-derivative controller and fractional-order proportional-integral-derivative controller for an 84th-order benchmark system and a mechanical ventilator system respectively. The results demonstrate that the proposed model order reduction-based controller design approach achieves high-performance control with lesser steady-state error, improved time-domain specifications and robust disturbance rejection capability.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"155 ","pages":"Article 116751"},"PeriodicalIF":4.4,"publicationDate":"2026-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145956844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-01-10DOI: 10.1016/j.apm.2026.116746
Xiangqian Sheng , Kuahai Yu , Wenliang Fan , Baiwan Su
The translation process-based spectral representation method is widely used to simulate the non-stationary non-Gaussian stochastic ground motions. However, the computation of the underlying evolutionary power spectral density matrix and its decomposition require substantial computational effort at discrete time-frequency points. To address this problem, this paper proposes an adaptive interpolation strategy for selecting the time-frequency interpolation points to improve the simulation efficiency. Firstly, the correlation function equations between non-Gaussian stochastic processes and the underlying Gaussian stochastic processes are constructed using Mehler's formula. A fast calculation method for the evolutionary power spectral density of the underlying Gaussian processes is introduced based on the interpolation technique. Secondly, the discrete time-frequency interpolation points are determined based on the amplitude information of the evolutionary power spectral density of the underlying Gaussian stochastic processes. The evolutionary power spectral density matrix is decomposed at these time-frequency interpolation points. The decomposed spectrum is then expressed as a sum of products of various time and frequency components. Spline interpolation is applied to these components at the discrete time-frequency points to approximate the matrix decomposition required by the spectral representation method, improving the efficiency of the decomposition. Additionally, the Fast Fourier Transform further accelerates simulation efficiency. Finally, the accuracy and efficiency of the proposed method for simulating non-stationary non-Gaussian stochastic ground motions are verified by considering the real ground motion record, stochastic vector processes, different probability distribution types, different power spectrum density types, and the number of variates.
{"title":"Efficient simulation method of non-stationary non-Gaussian stochastic ground motions based on adaptive interpolation strategy","authors":"Xiangqian Sheng , Kuahai Yu , Wenliang Fan , Baiwan Su","doi":"10.1016/j.apm.2026.116746","DOIUrl":"10.1016/j.apm.2026.116746","url":null,"abstract":"<div><div>The translation process-based spectral representation method is widely used to simulate the non-stationary non-Gaussian stochastic ground motions. However, the computation of the underlying evolutionary power spectral density matrix and its decomposition require substantial computational effort at discrete time-frequency points. To address this problem, this paper proposes an adaptive interpolation strategy for selecting the time-frequency interpolation points to improve the simulation efficiency. Firstly, the correlation function equations between non-Gaussian stochastic processes and the underlying Gaussian stochastic processes are constructed using Mehler's formula. A fast calculation method for the evolutionary power spectral density of the underlying Gaussian processes is introduced based on the interpolation technique. Secondly, the discrete time-frequency interpolation points are determined based on the amplitude information of the evolutionary power spectral density of the underlying Gaussian stochastic processes. The evolutionary power spectral density matrix is decomposed at these time-frequency interpolation points. The decomposed spectrum is then expressed as a sum of products of various time and frequency components. Spline interpolation is applied to these components at the discrete time-frequency points to approximate the matrix decomposition required by the spectral representation method, improving the efficiency of the decomposition. Additionally, the Fast Fourier Transform further accelerates simulation efficiency. Finally, the accuracy and efficiency of the proposed method for simulating non-stationary non-Gaussian stochastic ground motions are verified by considering the real ground motion record, stochastic vector processes, different probability distribution types, different power spectrum density types, and the number of variates.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"155 ","pages":"Article 116746"},"PeriodicalIF":4.4,"publicationDate":"2026-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145956846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-01-09DOI: 10.1016/j.apm.2026.116740
Zhi Duan , Xiaohui Liu , Hongbing Guo , Chuan Wu , Zhongfei Ye , Zhongbin Lu
Achieving an optimal balance among computational efficiency, robustness, and accuracy is a central challenge in simulating second-order nonlinear dynamical systems. While the existing parameterized two-sub-step composite integrator provides rigorous nonlinear stability and controllable dissipation, its fixed-step formulation limits efficiency in simulations with strongly varying dynamics. This paper presents a novel adaptive time integration method that augments the second-order base scheme with an explicit auxiliary stage for efficient error estimation. Its key innovation is a cost-free, direct error estimator, constructed by rigorously deriving the embedding coefficients via order conditions and analytically combining the implicit base stages with an extrapolated explicit stage to derive a local error estimate based on a third-order embedding without additional nonlinear iterations or matrix operations. Combined with a proportional–integral–derivative-like step-size controller, systematic numerical tests show that the proposed method achieves a significantly better computational cost-to-accuracy trade-off than high-order algebraically stable singly diagonally implicit Runge–Kutta methods. The algorithm demonstrates strong robustness in stiff and large-scale nonlinear problems while preserving the unconditional nonlinear stability and controllable dissipation of the base scheme. In summary, the proposed adaptive method offers an efficient, reliable, and self-starting tool for simulating large-scale, long-duration, strongly nonlinear systems.
{"title":"An efficient adaptive time-integration method for second-order nonlinear dynamics","authors":"Zhi Duan , Xiaohui Liu , Hongbing Guo , Chuan Wu , Zhongfei Ye , Zhongbin Lu","doi":"10.1016/j.apm.2026.116740","DOIUrl":"10.1016/j.apm.2026.116740","url":null,"abstract":"<div><div>Achieving an optimal balance among computational efficiency, robustness, and accuracy is a central challenge in simulating second-order nonlinear dynamical systems. While the existing parameterized two-sub-step composite integrator provides rigorous nonlinear stability and controllable dissipation, its fixed-step formulation limits efficiency in simulations with strongly varying dynamics. This paper presents a novel adaptive time integration method that augments the second-order base scheme with an explicit auxiliary stage for efficient error estimation. Its key innovation is a cost-free, direct error estimator, constructed by rigorously deriving the embedding coefficients via order conditions and analytically combining the implicit base stages with an extrapolated explicit stage to derive a local error estimate based on a third-order embedding without additional nonlinear iterations or matrix operations. Combined with a proportional–integral–derivative-like step-size controller, systematic numerical tests show that the proposed method achieves a significantly better computational cost-to-accuracy trade-off than high-order algebraically stable singly diagonally implicit Runge–Kutta methods. The algorithm demonstrates strong robustness in stiff and large-scale nonlinear problems while preserving the unconditional nonlinear stability and controllable dissipation of the base scheme. In summary, the proposed adaptive method offers an efficient, reliable, and self-starting tool for simulating large-scale, long-duration, strongly nonlinear systems.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"155 ","pages":"Article 116740"},"PeriodicalIF":4.4,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145956848","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-01-09DOI: 10.1016/j.apm.2026.116743
Xin Qiang , Chong Wang , Huanyu Zhang
Since system parameters can reflect fluctuations in structural performance, identifying the thermo-elastic parameters based on measured responses is becoming increasingly important for health monitoring of thermo-mechanical systems. To avoid the drawback of traditional probabilistic methods in handling limited experimental samples, this paper proposes a novel interval theory-integrated computational framework for efficient and robust identification of uncertain thermo-elastic parameters. For the coupled thermo-mechanical problem, the thermo-elastic governing equation is derived and the thermal stress effect is discussed. In view of the limitation of extremum searching in capturing potential supplementary data, a confidence-based unbiased interval estimation method is introduced to quantify experimental response bounds of limited experimental samples. Subsequently, a gene expression programming support vector regression (GEP-SVR) metamodel is constructed to replace the full-scale finite element simulations, thereby alleviating the computational burden of the nested dual-loop optimization in interval parameter identification. The effectiveness of the proposed framework is demonstrated through three case studies. Numerical results show that the proposed method achieves identification errors below 3.0% while improving computational efficiency by 87.08% compared to full-scale finite element simulation, providing a practical and efficient tool for uncertainty-aware parameter identification of thermo-mechanical systems.
{"title":"Interval theory-embedded data-driven identification framework for uncertain thermo-elastic parameters","authors":"Xin Qiang , Chong Wang , Huanyu Zhang","doi":"10.1016/j.apm.2026.116743","DOIUrl":"10.1016/j.apm.2026.116743","url":null,"abstract":"<div><div>Since system parameters can reflect fluctuations in structural performance, identifying the thermo-elastic parameters based on measured responses is becoming increasingly important for health monitoring of thermo-mechanical systems. To avoid the drawback of traditional probabilistic methods in handling limited experimental samples, this paper proposes a novel interval theory-integrated computational framework for efficient and robust identification of uncertain thermo-elastic parameters. For the coupled thermo-mechanical problem, the thermo-elastic governing equation is derived and the thermal stress effect is discussed. In view of the limitation of extremum searching in capturing potential supplementary data, a confidence-based unbiased interval estimation method is introduced to quantify experimental response bounds of limited experimental samples. Subsequently, a gene expression programming support vector regression (GEP-SVR) metamodel is constructed to replace the full-scale finite element simulations, thereby alleviating the computational burden of the nested dual-loop optimization in interval parameter identification. The effectiveness of the proposed framework is demonstrated through three case studies. Numerical results show that the proposed method achieves identification errors below 3.0% while improving computational efficiency by 87.08% compared to full-scale finite element simulation, providing a practical and efficient tool for uncertainty-aware parameter identification of thermo-mechanical systems.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"155 ","pages":"Article 116743"},"PeriodicalIF":4.4,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145956847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-01-09DOI: 10.1016/j.apm.2026.116748
Taejeong Lim, Nur Indah Mukharromah, Hyun Woo Park
To date, no rigorous closed-form solutions can fully address the complexity of wave scattering phenomena, although such solutions are essential for fast and accurate assessment of edge cracks in beams. This study presents closed-form solutions for wave scattering coefficients when an incident bending wave encounters an edge crack in a Timoshenko beam, resulting in wave transmission, reflection, and mode conversion. Unlike its shallow counterpart, a deep edge crack produces complicated wave scattering phenomena due to axial–bending–shear coupling (ABSC) with increasing driving frequency. Herein, three compatibility equations for modes I and II crack in linear fracture mechanics are incorporated into the Timoshenko beam theory to account for ABSC. Closed-form solutions are derived by applying spectral solutions to the three compatibility equations and three equilibrium equations at the edge crack. The sole contribution of mode I crack and simultaneous contribution of modes I and II crack to wave scattering coefficients are thoroughly investigated with respect to the normalized frequency and crack depth ratio. Finally, the proposed closed-form solutions are validated via comparison with previously reported finite element analysis and experimental results. The findings of the study provide physical insights into complex wave scattering phenomena and are anticipated to enable faster inverse analysis in ultrasonic crack evaluation.
{"title":"Closed-form solutions for wave scattering coefficients of a Timoshenko beam with an edge crack considering axial–bending–shear coupling","authors":"Taejeong Lim, Nur Indah Mukharromah, Hyun Woo Park","doi":"10.1016/j.apm.2026.116748","DOIUrl":"10.1016/j.apm.2026.116748","url":null,"abstract":"<div><div>To date, no rigorous closed-form solutions can fully address the complexity of wave scattering phenomena, although such solutions are essential for fast and accurate assessment of edge cracks in beams. This study presents closed-form solutions for wave scattering coefficients when an incident bending wave encounters an edge crack in a Timoshenko beam, resulting in wave transmission, reflection, and mode conversion. Unlike its shallow counterpart, a deep edge crack produces complicated wave scattering phenomena due to axial–bending–shear coupling (ABSC) with increasing driving frequency. Herein, three compatibility equations for modes I and II crack in linear fracture mechanics are incorporated into the Timoshenko beam theory to account for ABSC. Closed-form solutions are derived by applying spectral solutions to the three compatibility equations and three equilibrium equations at the edge crack. The sole contribution of mode I crack and simultaneous contribution of modes I and II crack to wave scattering coefficients are thoroughly investigated with respect to the normalized frequency and crack depth ratio. Finally, the proposed closed-form solutions are validated via comparison with previously reported finite element analysis and experimental results. The findings of the study provide physical insights into complex wave scattering phenomena and are anticipated to enable faster inverse analysis in ultrasonic crack evaluation.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"155 ","pages":"Article 116748"},"PeriodicalIF":4.4,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145956905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-01-08DOI: 10.1016/j.apm.2026.116742
Jiadong Wang, Xianqing Liu, Shiyu Zhao, Gang Liu
Liquid sloshing in partially filled cylindrical tanks can generate large hydrodynamic loads that threaten the safety of marine vessels, spacecraft, and storage tanks. This work introduces a complex-mode framework for liquid sloshing in cylindrical tanks equipped with annular porous baffles, based on linear potential-flow theory with a porous-jump condition. The governing equations are cast as a non-self-adjoint quadratic eigenvalue problem and solved via state-space linearization. Natural frequencies and damping ratios then follow directly from the complex eigenvalues, providing a physically based description of energy dissipation. An orthogonality relation for the complex sloshing modes is established, enabling modal decoupling of the dynamic response equations. Parametric analyses show that the sloshing characteristics are strongly influenced by the porous baffle elevation, inner radius, and porous-effect parameter. Raising the elevation or decreasing the inner radius lowers the fundamental sloshing frequency while increasing the damping ratio. For each elevation and inner radius, an optimal porous-effect parameter exists that maximizes the damping ratio of the fundamental mode. Frequency response analyses confirm that a properly tuned porous-effect parameter suppresses near-resonant sloshing responses effectively. These results provide a robust basis for sloshing mitigation in practical engineering applications.
{"title":"Complex-mode framework for sloshing damping in cylindrical tanks with porous baffles","authors":"Jiadong Wang, Xianqing Liu, Shiyu Zhao, Gang Liu","doi":"10.1016/j.apm.2026.116742","DOIUrl":"10.1016/j.apm.2026.116742","url":null,"abstract":"<div><div>Liquid sloshing in partially filled cylindrical tanks can generate large hydrodynamic loads that threaten the safety of marine vessels, spacecraft, and storage tanks. This work introduces a complex-mode framework for liquid sloshing in cylindrical tanks equipped with annular porous baffles, based on linear potential-flow theory with a porous-jump condition. The governing equations are cast as a non-self-adjoint quadratic eigenvalue problem and solved via state-space linearization. Natural frequencies and damping ratios then follow directly from the complex eigenvalues, providing a physically based description of energy dissipation. An orthogonality relation for the complex sloshing modes is established, enabling modal decoupling of the dynamic response equations. Parametric analyses show that the sloshing characteristics are strongly influenced by the porous baffle elevation, inner radius, and porous-effect parameter. Raising the elevation or decreasing the inner radius lowers the fundamental sloshing frequency while increasing the damping ratio. For each elevation and inner radius, an optimal porous-effect parameter exists that maximizes the damping ratio of the fundamental mode. Frequency response analyses confirm that a properly tuned porous-effect parameter suppresses near-resonant sloshing responses effectively. These results provide a robust basis for sloshing mitigation in practical engineering applications.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"155 ","pages":"Article 116742"},"PeriodicalIF":4.4,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145956849","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-01-07DOI: 10.1016/j.apm.2026.116739
Chang Li , Rongjun Chen , Limin Guo , Hai Qing
Viscoelastic nanobeams on viscoelastic foundations enable enhanced vibration suppression and novel functionalities in M/NEMS devices. However, accurately predicting their size-dependent, time-damped vibrations demands robust nonclassical theories. This study presents a precise theoretical framework for the free damping vibration characteristics of a curved viscoelastic Timoshenko nanobeam resting on a size-dependent viscoelastic foundation. We develop a mathematically well-posed viscoelastic integral nonlocal strain gradient theory (VINSGT) by integrating integral nonlocal strain gradient theory (INSGT with the Kelvin-Voigt model, while accounting for the size effect in the foundations’ reaction force. The integral constitutive equations are transformed into an equivalent differential form, incorporating essential constitutive boundary conditions (CBCs). The governing equations are discretized via the generalized differential quadrature method (GDQM), yielding a complex eigenvalue problem. A two-step numerical scheme resolves the vibration frequencies and establishes the relationship between damping and viscous coefficients. Numerical examples validate the VINSGT framework and systematically investigate size effects in the damped vibration behavior of viscoelastic curved Timoshenko nanobeams on size-dependent foundations. This work provides a reliable theoretical basis for designing and optimizing vibration control in advanced M/NEMS with viscoelastic nanobeam-foundation systems.
{"title":"Size-dependent damped free vibration of viscoelastic curved Timoshenko nanobeams resting on viscoelastic foundation through viscoelastic integral nonlocal strain gradient model","authors":"Chang Li , Rongjun Chen , Limin Guo , Hai Qing","doi":"10.1016/j.apm.2026.116739","DOIUrl":"10.1016/j.apm.2026.116739","url":null,"abstract":"<div><div>Viscoelastic nanobeams on viscoelastic foundations enable enhanced vibration suppression and novel functionalities in M/NEMS devices. However, accurately predicting their size-dependent, time-damped vibrations demands robust nonclassical theories. This study presents a precise theoretical framework for the free damping vibration characteristics of a curved viscoelastic Timoshenko nanobeam resting on a size-dependent viscoelastic foundation. We develop a mathematically well-posed viscoelastic integral nonlocal strain gradient theory (VINSGT) by integrating integral nonlocal strain gradient theory (INSGT with the Kelvin-Voigt model, while accounting for the size effect in the foundations’ reaction force. The integral constitutive equations are transformed into an equivalent differential form, incorporating essential constitutive boundary conditions (CBCs). The governing equations are discretized via the generalized differential quadrature method (GDQM), yielding a complex eigenvalue problem. A two-step numerical scheme resolves the vibration frequencies and establishes the relationship between damping and viscous coefficients. Numerical examples validate the VINSGT framework and systematically investigate size effects in the damped vibration behavior of viscoelastic curved Timoshenko nanobeams on size-dependent foundations. This work provides a reliable theoretical basis for designing and optimizing vibration control in advanced M/NEMS with viscoelastic nanobeam-foundation systems.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"155 ","pages":"Article 116739"},"PeriodicalIF":4.4,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145956904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-01-05DOI: 10.1016/j.apm.2025.116737
Yiming Lu , Haicheng Zhang , Xubin Sun , Daolin Xu
Marine animals achieve remarkable swimming performance through precisely coordinated interactions among different body segments. Current bio-inspired swimmers generally fail to account for the distinct mechanical functions of various anatomical structures and often overlook the critical nonlinear fluid-structure interaction mechanisms. To bridge this gap, an elastic-joint rigid fin model is developed that conceptualizes propulsion as three synergistic phases: active muscular actuation, elastic peduncle energy transmission, and vortex-generating caudal fin motion. This model uniquely enables the quantitative dissection of individual component contributions to overall performance. To address the fluid-structure interaction problem in swimming, a Nonlinear Vortex Sheet Method (NVSM) is proposed. The method seamlessly integrates a vortex sheet model based flow reconstruction, a coupled system modeling for structural motion and vortex tracking, and the Broyden method based synchronized solving, achieving robust and efficient performance. Rigorously validated against computational fluid dynamics, the NVSM accurately captures the key physics of dynamic response and vortex shedding with significantly reduced computational cost.
Comparative analyses demonstrate a threefold enhancement in peak propulsion efficiency at optimal frequencies over rigid counterparts. A detailed examination of the fluid-structure interaction reveals the propulsion mechanisms. These are identified as hydrodynamic phase synchronization, suppression of energy-dissipating vortex structures, and superior fluid energy utilization efficiency. Furthermore, this study establishes a quantitative mapping between structural stiffness and key performance metrics, providing actionable design guidelines for next-generation biomimetic propulsion systems.
{"title":"Dynamic modelling and vortex dynamics in elastic-joint caudal fin propulsor for efficient swimming","authors":"Yiming Lu , Haicheng Zhang , Xubin Sun , Daolin Xu","doi":"10.1016/j.apm.2025.116737","DOIUrl":"10.1016/j.apm.2025.116737","url":null,"abstract":"<div><div>Marine animals achieve remarkable swimming performance through precisely coordinated interactions among different body segments. Current bio-inspired swimmers generally fail to account for the distinct mechanical functions of various anatomical structures and often overlook the critical nonlinear fluid-structure interaction mechanisms. To bridge this gap, an elastic-joint rigid fin model is developed that conceptualizes propulsion as three synergistic phases: active muscular actuation, elastic peduncle energy transmission, and vortex-generating caudal fin motion. This model uniquely enables the quantitative dissection of individual component contributions to overall performance. To address the fluid-structure interaction problem in swimming, a Nonlinear Vortex Sheet Method (NVSM) is proposed. The method seamlessly integrates a vortex sheet model based flow reconstruction, a coupled system modeling for structural motion and vortex tracking, and the Broyden method based synchronized solving, achieving robust and efficient performance. Rigorously validated against computational fluid dynamics, the NVSM accurately captures the key physics of dynamic response and vortex shedding with significantly reduced computational cost.</div><div>Comparative analyses demonstrate a threefold enhancement in peak propulsion efficiency at optimal frequencies over rigid counterparts. A detailed examination of the fluid-structure interaction reveals the propulsion mechanisms. These are identified as hydrodynamic phase synchronization, suppression of energy-dissipating vortex structures, and superior fluid energy utilization efficiency. Furthermore, this study establishes a quantitative mapping between structural stiffness and key performance metrics, providing actionable design guidelines for next-generation biomimetic propulsion systems.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"155 ","pages":"Article 116737"},"PeriodicalIF":4.4,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145902634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-01-03DOI: 10.1016/j.apm.2025.116732
Tao Zhang , Xiaofeng Zhou , Jian Li
We propose a meshless essentially non-oscillatory (MENO) scheme based on flux vector splitting (FVS) methods that can be integrated with various meshless methods to solve compressible flows problems involving upwind bias and discontinuities. The central idea is to generate multiple generalized finite difference method (GFDM) approximations at each node by employing asymmetric or eccentric stars. The smoothness indicator is then applied to each candidate approximation to select the optimal one for suppressing oscillations at discontinuities, in a manner similar to the Essentially Non-Oscillatory (ENO) scheme. First, based on the meshless methods, the Steger-Warming flux splitting method for the Euler equations is developed; Second, a one-side upwind stencil is constructed; Third, two additional stencils are constructed along the upwind or downwind direction to identify discontinuities; Finally, the stencil with the smallest smoothness indicator is selected as the optimal one. It seems that this is the first attempt to develop a shock-capturing scheme in the meshless FVS methods. Compared to the meshless FDS methods, the proposed meshless FVS methods combined with MENO scheme is simpler and somewhat more efficient, as it identifies the upwind direction with less effort and does not require mid-point reconstruction. Several benchmark tests demonstrate that the proposed MENO scheme under meshless FVS methods effectively achieves second- or third-order accuracy in smooth regions while maintaining robust and non-oscillatory shock-capturing, representing a significant improvement over the upwind GFDM scheme.
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