Pub Date : 2025-01-21DOI: 10.1016/j.apm.2025.115959
Shuya Onodera , Takayuki Yamada
In this study, a topology optimization method for coupled thermomechanical problems is proposed by incorporating approximated thermal radiation boundary conditions that depend on design variables. The challenge of designing mechanical structures influenced by thermal radiation is briefly discussed. Partial Differential Equations are introduced to represent the geometric features influenced by thermal radiation. The boundary under thermal radiation conditions is expressed using the solution. In addition, a mathematical model is developed to approximate the view factor, which is related to the contribution of thermal radiation. To address this, the historical temperature data calculated during the optimization iterations are employed to create a linear approximation of the sensitivity analysis. The objective functional for temperature and displacement are evaluated using the weighted sum method. Furthermore, a specific optimization algorithm using the finite element method is proposed. The proposed method is applied to two- and three-dimensional problems to confirm the effectiveness and applicability of the proposed method.
{"title":"Topology optimization for coupled thermomechanical problems with approximated thermal radiation boundary conditions depending on design variables","authors":"Shuya Onodera , Takayuki Yamada","doi":"10.1016/j.apm.2025.115959","DOIUrl":"10.1016/j.apm.2025.115959","url":null,"abstract":"<div><div>In this study, a topology optimization method for coupled thermomechanical problems is proposed by incorporating approximated thermal radiation boundary conditions that depend on design variables. The challenge of designing mechanical structures influenced by thermal radiation is briefly discussed. Partial Differential Equations are introduced to represent the geometric features influenced by thermal radiation. The boundary under thermal radiation conditions is expressed using the solution. In addition, a mathematical model is developed to approximate the view factor, which is related to the contribution of thermal radiation. To address this, the historical temperature data calculated during the optimization iterations are employed to create a linear approximation of the sensitivity analysis. The objective functional for temperature and displacement are evaluated using the weighted sum method. Furthermore, a specific optimization algorithm using the finite element method is proposed. The proposed method is applied to two- and three-dimensional problems to confirm the effectiveness and applicability of the proposed method.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"142 ","pages":"Article 115959"},"PeriodicalIF":4.4,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143035293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-01-21DOI: 10.1016/j.apm.2025.115955
Yutao Guo, Manjur Alam
Beams resting on elastic foundation are widely employed as smart nanostructures, which commonly consists of intelligent materials to offer multifunctional capabilities. Molecular interactions, in these cases, are incorporated into the mechanics of nanostructures through the Nonlocal (NL) and Strain Gradient (SG) continuum model. Surface elasticity theory integrates the influence of surface molecules resulting from high surface-to-bulk ratio of nanostructures. This study explores the nonlinear bending and thermal postbuckling of magneto-electro-elastic (MEE), NLSG beam including the impact of surface molecules. The governing equations for laminated MEE beam supported on Pasternak foundation are derived using variational principles, involving higher-order shear deformation theory and von-Kármán nonlinearity. The electric and magnetic potential are given by a thickness-wise cosine distribution. A closed-form analytical solution is obtained by solving the resulting nonlinear partial differential equations using asymptotic expansions of the field variables. The numerical illustration of the solution highlights the importance of molecular interaction in bending compared to the postbuckling scenario. The prevailing impact of foundation stiffness is demonstrated. Surface molecules are observed to show a comparable effect as the electric or magnetic fields. The solution can be used to develop basic design concepts for MEE nanobeams at different temperatures and to validate numerical solutions.
{"title":"Nonlinear bending and thermal postbuckling of magneto-electro-elastic nonlocal strain-gradient beam including surface effects","authors":"Yutao Guo, Manjur Alam","doi":"10.1016/j.apm.2025.115955","DOIUrl":"10.1016/j.apm.2025.115955","url":null,"abstract":"<div><div>Beams resting on elastic foundation are widely employed as smart nanostructures, which commonly consists of intelligent materials to offer multifunctional capabilities. Molecular interactions, in these cases, are incorporated into the mechanics of nanostructures through the Nonlocal (NL) and Strain Gradient (SG) continuum model. Surface elasticity theory integrates the influence of surface molecules resulting from high surface-to-bulk ratio of nanostructures. This study explores the nonlinear bending and thermal postbuckling of magneto-electro-elastic (MEE), NLSG beam including the impact of surface molecules. The governing equations for laminated MEE beam supported on Pasternak foundation are derived using variational principles, involving higher-order shear deformation theory and von-Kármán nonlinearity. The electric and magnetic potential are given by a thickness-wise cosine distribution. A closed-form analytical solution is obtained by solving the resulting nonlinear partial differential equations using asymptotic expansions of the field variables. The numerical illustration of the solution highlights the importance of molecular interaction in bending compared to the postbuckling scenario. The prevailing impact of foundation stiffness is demonstrated. Surface molecules are observed to show a comparable effect as the electric or magnetic fields. The solution can be used to develop basic design concepts for MEE nanobeams at different temperatures and to validate numerical solutions.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"142 ","pages":"Article 115955"},"PeriodicalIF":4.4,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143174927","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 : 2025-01-21DOI: 10.1016/j.apm.2025.115960
Alia Al-Ghosoun , Mohammed Seaid , Ashraf S. Osman
Sediment transport in shallow waters occurs when the water flows over the bed for which the amount of generated sediments can be determined from the transport mechanism caused by the consequent flow. Recently, investigating the bedload and sediment transport using numerical models has been rapidly increased and various techniques have been developed to quantify both the hydrodynamics and morphodynamics in these systems but not the stress distributions in the deformed beds. In the present study, we propose a novel class of coupled finite element/finite volume methods to resolve the effect of sedimentary shallow water flows on the internal stresses in bed topographies. The coupled model employs the linear elasticity for the bed and the nonlinear shallow water equations for the water flow. Suspended sediments are also taken into consideration in this study, and impacts of the erosion and deposition are modelled using well-established empirical equations. The linear equations of elasticity are solved numerically using a finite element approach on unstructured meshes, while the nonlinear shallow water equations are numerically solved using a well-balanced finite volume method. We also introduce an accurate algorithm to sample forces on the interface between the water flow and bed topography to be implemented as coupling conditions between finite volume cells and finite element nodes. Distributions of stress fields in the bed topography due to erosion and sediment transport by shallow water flows are presented for several test examples. The novel coupled model is stable, efficient, accurate, well-balanced and it can be used for solving complex geometries. In addition, the proposed approach offers significant advancements in understanding sedimentary processes in shallow water environments and the induced underground stresses as a result of these processes.
{"title":"A novel approach for modelling stress fields induced by shallow water flows on movable beds","authors":"Alia Al-Ghosoun , Mohammed Seaid , Ashraf S. Osman","doi":"10.1016/j.apm.2025.115960","DOIUrl":"10.1016/j.apm.2025.115960","url":null,"abstract":"<div><div>Sediment transport in shallow waters occurs when the water flows over the bed for which the amount of generated sediments can be determined from the transport mechanism caused by the consequent flow. Recently, investigating the bedload and sediment transport using numerical models has been rapidly increased and various techniques have been developed to quantify both the hydrodynamics and morphodynamics in these systems but not the stress distributions in the deformed beds. In the present study, we propose a novel class of coupled finite element/finite volume methods to resolve the effect of sedimentary shallow water flows on the internal stresses in bed topographies. The coupled model employs the linear elasticity for the bed and the nonlinear shallow water equations for the water flow. Suspended sediments are also taken into consideration in this study, and impacts of the erosion and deposition are modelled using well-established empirical equations. The linear equations of elasticity are solved numerically using a finite element approach on unstructured meshes, while the nonlinear shallow water equations are numerically solved using a well-balanced finite volume method. We also introduce an accurate algorithm to sample forces on the interface between the water flow and bed topography to be implemented as coupling conditions between finite volume cells and finite element nodes. Distributions of stress fields in the bed topography due to erosion and sediment transport by shallow water flows are presented for several test examples. The novel coupled model is stable, efficient, accurate, well-balanced and it can be used for solving complex geometries. In addition, the proposed approach offers significant advancements in understanding sedimentary processes in shallow water environments and the induced underground stresses as a result of these processes.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"142 ","pages":"Article 115960"},"PeriodicalIF":4.4,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143035292","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 : 2025-01-20DOI: 10.1016/j.apm.2025.115957
Yuhang Tian , Qingya Li , Yuan Feng , Wei Gao
This study presents a semi-analytical method to investigate the nonlinear dynamic responses of a geometrically imperfect multi-direction functionally graded graphene platelets reinforced composite plate with magneto-electro-elastic coupling (MDFG GPLRC-MEE) under blast loads. The mechanical properties of the plate structure are tailored by adjusting the spatial distribution of graphene platelets (GPL) content in the core layer. The localised geometrical imperfections of the structure are introduced and modelled as an initial deflection of the plate in the form of products of hyperbolic and trigonometric functions. Three boundary conditions are considered for the plate with different combinations of the simply supported and clamped edges. Based on the third-order shear deformation theory (TSDT) and von Kármán nonlinearity, the equations of motion are derived according to Hamilton's principle. The Galerkin method is then used to reduce the system to a set of ordinary differential equations. The fourth-order Runge-Kutta approach is subsequently employed to address the dynamic behaviours of the structure subjected to blast load. After verification, parametric experiments are conducted to explore the influences of some key factors, including boundary conditions, damping ratios, the Winkler-Pasternak foundation moduli, geometrical imperfection configurations, GPL content and distribution, blast load parameters, and external electromagnetic potentials. The numerical results indicate that for MDFG GPLRC-MEE plates, incorporating more GPL in the middle portion of the plate provides superior blast impact resistance compared to structures with more GPL at the margins.
{"title":"Nonlinear dynamic analysis of geometrically imperfect multi-direction functionally graded graphene platelet reinforced composite plates with magneto-electro-elastic sheets subjected to blast load","authors":"Yuhang Tian , Qingya Li , Yuan Feng , Wei Gao","doi":"10.1016/j.apm.2025.115957","DOIUrl":"10.1016/j.apm.2025.115957","url":null,"abstract":"<div><div>This study presents a semi-analytical method to investigate the nonlinear dynamic responses of a geometrically imperfect multi-direction functionally graded graphene platelets reinforced composite plate with magneto-electro-elastic coupling (MDFG GPLRC-MEE) under blast loads. The mechanical properties of the plate structure are tailored by adjusting the spatial distribution of graphene platelets (GPL) content in the core layer. The localised geometrical imperfections of the structure are introduced and modelled as an initial deflection of the plate in the form of products of hyperbolic and trigonometric functions. Three boundary conditions are considered for the plate with different combinations of the simply supported and clamped edges. Based on the third-order shear deformation theory (TSDT) and von Kármán nonlinearity, the equations of motion are derived according to Hamilton's principle. The Galerkin method is then used to reduce the system to a set of ordinary differential equations. The fourth-order Runge-Kutta approach is subsequently employed to address the dynamic behaviours of the structure subjected to blast load. After verification, parametric experiments are conducted to explore the influences of some key factors, including boundary conditions, damping ratios, the Winkler-Pasternak foundation moduli, geometrical imperfection configurations, GPL content and distribution, blast load parameters, and external electromagnetic potentials. The numerical results indicate that for MDFG GPLRC-MEE plates, incorporating more GPL in the middle portion of the plate provides superior blast impact resistance compared to structures with more GPL at the margins.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"142 ","pages":"Article 115957"},"PeriodicalIF":4.4,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143174368","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-01-20DOI: 10.1016/j.apm.2025.115952
Tianshu Liu , Xiao-Jin Wan , Zhengjie Zhou
This paper presents a novel design procedure of the finger of a compliant gripper, which is used for grasping objects of different shapes under uncertain loads. The compliant finger is divided into two stages for design: finger root and fingertip. The finger root is designed using compliant mechanisms of topology optimization. The stochastic perturbation approach is introduced for the first time into a compliant mechanism topology optimization model under load uncertainty to quantify the uncertainty of load and node displacement of the finger root. The objective function of finger root optimization is maximizing the expectation of the output displacement while minimizing its standard deviation. The fingertip is designed using continuum structure topology optimization based on stiffness optimization. The optimization problems are solved using the method of moving asymptotes. Then, three numerical cases show that, compared with deterministic optimization, the compliant finger designed considering load uncertainty exhibits reduced sensitivity to load direction uncertainty and possesses greater stiffness. The finger prototype is manufactured using 3D printing, and the maximum gripping weight of the compliant gripper is tested. The grasping experiments indicate that the designed gripper can grasp various objects' shapes and avoid damage to fragile and high-precision surface objects.
{"title":"Novel two-stage uncertainty optimization design of a compliant finger based on stochastic perturbation approach","authors":"Tianshu Liu , Xiao-Jin Wan , Zhengjie Zhou","doi":"10.1016/j.apm.2025.115952","DOIUrl":"10.1016/j.apm.2025.115952","url":null,"abstract":"<div><div>This paper presents a novel design procedure of the finger of a compliant gripper, which is used for grasping objects of different shapes under uncertain loads. The compliant finger is divided into two stages for design: finger root and fingertip. The finger root is designed using compliant mechanisms of topology optimization. The stochastic perturbation approach is introduced for the first time into a compliant mechanism topology optimization model under load uncertainty to quantify the uncertainty of load and node displacement of the finger root. The objective function of finger root optimization is maximizing the expectation of the output displacement while minimizing its standard deviation. The fingertip is designed using continuum structure topology optimization based on stiffness optimization. The optimization problems are solved using the method of moving asymptotes. Then, three numerical cases show that, compared with deterministic optimization, the compliant finger designed considering load uncertainty exhibits reduced sensitivity to load direction uncertainty and possesses greater stiffness. The finger prototype is manufactured using 3D printing, and the maximum gripping weight of the compliant gripper is tested. The grasping experiments indicate that the designed gripper can grasp various objects' shapes and avoid damage to fragile and high-precision surface objects.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"142 ","pages":"Article 115952"},"PeriodicalIF":4.4,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143035295","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 : 2025-01-19DOI: 10.1016/j.apm.2025.115958
Yuchen Zang , F.G. Mitri
The time-averaged elastic radiation force and spin torque exerted on a solid viscoelastic sphere embedded in an unbounded elastic medium are considered, with the incident field composed of elastic compressional Bessel non-vortex or vortex progressive waves. Based on the multipole expansion method using spherical wave functions, partial-wave series expressions are derived for the elastic radiation force and torque through the integration of the elastodynamic Poynting vector as well as the cross product of the position vector and the time-averaged elastic radiation stress tensor. The dimensionless absorption, scattering and extinction efficiencies are also calculated. Numerical computations are performed for a brass sphere in a soft elastic gel matrix to illustrate the analysis with particular emphasis on varying the dimensionless size parameter of the sphere, the half-cone angle and order of the incident Bessel waves. The component related to mode preservation contributes dominantly to the total radiation force, while the component related to mode conversion alternates between positive, negative and neutral values. The elastic radiation torque components related to mode preservation and conversion are opposite in sign and approximately equal in magnitude. The results may find potential applications in the activation of implantable spherical devices, characterization of biological tissue, elastic wave scattering, non-destructive evaluation, and geophysical prospecting to name some examples.
{"title":"Radiation force and torque of elastic compressional Bessel waves on a solid sphere embedded in an unbounded elastic medium","authors":"Yuchen Zang , F.G. Mitri","doi":"10.1016/j.apm.2025.115958","DOIUrl":"10.1016/j.apm.2025.115958","url":null,"abstract":"<div><div>The time-averaged elastic radiation force and spin torque exerted on a solid viscoelastic sphere embedded in an unbounded elastic medium are considered, with the incident field composed of elastic compressional Bessel non-vortex or vortex progressive waves. Based on the multipole expansion method using spherical wave functions, partial-wave series expressions are derived for the elastic radiation force and torque through the integration of the elastodynamic Poynting vector as well as the cross product of the position vector and the time-averaged elastic radiation stress tensor. The dimensionless absorption, scattering and extinction efficiencies are also calculated. Numerical computations are performed for a brass sphere in a soft elastic gel matrix to illustrate the analysis with particular emphasis on varying the dimensionless size parameter of the sphere, the half-cone angle and order of the incident Bessel waves. The component related to mode preservation contributes dominantly to the total radiation force, while the component related to mode conversion alternates between positive, negative and neutral values. The elastic radiation torque components related to mode preservation and conversion are opposite in sign and approximately equal in magnitude. The results may find potential applications in the activation of implantable spherical devices, characterization of biological tissue, elastic wave scattering, non-destructive evaluation, and geophysical prospecting to name some examples.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"142 ","pages":"Article 115958"},"PeriodicalIF":4.4,"publicationDate":"2025-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143174351","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 : 2025-01-18DOI: 10.1016/j.apm.2025.115961
Tengfei Tang , Hanliang Fang , Fufu Yang , Jun Zhang
This paper presents a quantitative analysis comparing the elastodynamic performance of a redundantly actuated parallel manipulator to its non-redundantly actuated counterpart. A unified elastodynamic model is established to encompasses both actuation types, facilitating a comprehensive analysis of their performance characteristics. To assess the impact of redundant actuation, frequency variation indices are defined to measure the influence of the redundantly actuated limbs on the overall system dynamics. Two global sensitivity indices are introduced to quantify how variations in design variables affect elastodynamic performance. An adaptive Kriging-based algorithm is developed to predict elastodynamic behavior, and it is numerically validated for both accuracy and efficiency. Through a detailed elastodynamic comparison and sensitivity analysis, we identify the key effects of redundant actuation and pinpoint the most significant design variables. Our findings reveal that the enhancements in low-order natural frequencies due to redundant actuation are configuration- and order-dependent. The redundantly actuated parallel manipulator demonstrates heightened sensitivity to geometric variables in terms of elastodynamic performance, surpassing that of its non-redundantly actuated variant. The sensitivity analysis provides valuable insights, guiding future improvements in elastodynamic performance. Notably, the thickness of the moving platform emerges as a critical parameter that warrants optimization during the design phase. Therefore, this analysis is particularly pivotal in the initial evaluation stages of parallel manipulators, ensuring that designs are refined for enhanced dynamic responses. With necessary modifications, this work can be applied to other redundantly actuated parallel manipulators to contribute a deeper understanding of how redundancy influences their dynamic characteristics.
{"title":"Adaptive Kriging elastodynamic modelling and analysis for a redundantly actuated parallel manipulator","authors":"Tengfei Tang , Hanliang Fang , Fufu Yang , Jun Zhang","doi":"10.1016/j.apm.2025.115961","DOIUrl":"10.1016/j.apm.2025.115961","url":null,"abstract":"<div><div>This paper presents a quantitative analysis comparing the elastodynamic performance of a redundantly actuated parallel manipulator to its non-redundantly actuated counterpart. A unified elastodynamic model is established to encompasses both actuation types, facilitating a comprehensive analysis of their performance characteristics. To assess the impact of redundant actuation, frequency variation indices are defined to measure the influence of the redundantly actuated limbs on the overall system dynamics. Two global sensitivity indices are introduced to quantify how variations in design variables affect elastodynamic performance. An adaptive Kriging-based algorithm is developed to predict elastodynamic behavior, and it is numerically validated for both accuracy and efficiency. Through a detailed elastodynamic comparison and sensitivity analysis, we identify the key effects of redundant actuation and pinpoint the most significant design variables. Our findings reveal that the enhancements in low-order natural frequencies due to redundant actuation are configuration- and order-dependent. The redundantly actuated parallel manipulator demonstrates heightened sensitivity to geometric variables in terms of elastodynamic performance, surpassing that of its non-redundantly actuated variant. The sensitivity analysis provides valuable insights, guiding future improvements in elastodynamic performance. Notably, the thickness of the moving platform emerges as a critical parameter that warrants optimization during the design phase. Therefore, this analysis is particularly pivotal in the initial evaluation stages of parallel manipulators, ensuring that designs are refined for enhanced dynamic responses. With necessary modifications, this work can be applied to other redundantly actuated parallel manipulators to contribute a deeper understanding of how redundancy influences their dynamic characteristics.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"142 ","pages":"Article 115961"},"PeriodicalIF":4.4,"publicationDate":"2025-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143035294","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 : 2025-01-18DOI: 10.1016/j.apm.2025.115951
Zhi Yong Ai, Lei Yang, Zi Kun Ye, Da Shan Wang
An analytical method is proposed to obtain the stress and displacement around shallow arbitrarily shaped tunnels excavated in viscoelastic transversely isotropic strata. Firstly, combined with the fractional calculus theory, the fractional viscoelastic half-plane solution is obtained by displacement modification. Then, based on the solution of the half-plane, the Schwartz alternating method and the conformal mapping technique are introduced to obtain the solution of the fractional viscoelastic arbitrarily shaped shallow tunnels. According to the proposed theory, a MATLAB program is developed, and the accuracy of the theory is proved by degraded comparison with results of the existing literature and finite element software ABAQUS. Finally, numerical examples are designed to discuss the influence of tunnel shapes, transverse isotropy and viscoelastic parameters on the boundary stress and displacement around shallow arbitrarily shaped tunnels.
{"title":"Analytical solution of shallow arbitrarily shaped tunnels in fractional viscoelastic transversely isotropic strata","authors":"Zhi Yong Ai, Lei Yang, Zi Kun Ye, Da Shan Wang","doi":"10.1016/j.apm.2025.115951","DOIUrl":"10.1016/j.apm.2025.115951","url":null,"abstract":"<div><div>An analytical method is proposed to obtain the stress and displacement around shallow arbitrarily shaped tunnels excavated in viscoelastic transversely isotropic strata. Firstly, combined with the fractional calculus theory, the fractional viscoelastic half-plane solution is obtained by displacement modification. Then, based on the solution of the half-plane, the Schwartz alternating method and the conformal mapping technique are introduced to obtain the solution of the fractional viscoelastic arbitrarily shaped shallow tunnels. According to the proposed theory, a MATLAB program is developed, and the accuracy of the theory is proved by degraded comparison with results of the existing literature and finite element software ABAQUS. Finally, numerical examples are designed to discuss the influence of tunnel shapes, transverse isotropy and viscoelastic parameters on the boundary stress and displacement around shallow arbitrarily shaped tunnels.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"141 ","pages":"Article 115951"},"PeriodicalIF":4.4,"publicationDate":"2025-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143035297","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}
This paper proposes a new design philosophy of integrating a nonlinear energy sink (NES) with a negative stiffness spring (NSS) to construct a two-stage hybrid vibration isolator for low-frequency vibration attenuation. A theoretical model of the proposed two-stage hybrid vibration isolator is established to investigate the vibration isolation performance. The effect of a linear vibration absorber (LVA), the NES, and the NSS on the force transmissibility of the structure is compared, in which the parametric study including negative stiffness coefficient, mass ratio, frequency ratio, and barrier height is conducted. The nonlinear dynamic characteristics and energy transfer efficiency of the vibration isolation system are analyzed based on motion phase trajectories, Poincaré mapping and chaotic bifurcation analysis. The results demonstrate that the two-stage isolator with the NES and NSS architecture exhibits superior broadband vibration isolation compared to its counterpart with the LVA and NSS. The structure with the LVA and NSS shows a wider forbidden band range than the device without the LVA. Besides, the negative stiffness configuration between the vibration source and the protected base is a critical factor to influence vibration isolation. A larger negative stiffness coefficient results in lower force transmissibility and the onset frequency of the forbidden zone but the broader bandwidth of the forbidden zone. This work paves a new theoretical venue for low-frequency hybrid vibration isolators in precision instrument fields.
{"title":"A theoretical model for a low-frequency two-stage hybrid vibration isolator with a nonlinear energy sink and a negative stiffness spring","authors":"Xingbao Huang , Biao Wang , Zhiwen Huang , Xugang Hua , Zhengqing Chen","doi":"10.1016/j.apm.2025.115948","DOIUrl":"10.1016/j.apm.2025.115948","url":null,"abstract":"<div><div>This paper proposes a new design philosophy of integrating a nonlinear energy sink (NES) with a negative stiffness spring (NSS) to construct a two-stage hybrid vibration isolator for low-frequency vibration attenuation. A theoretical model of the proposed two-stage hybrid vibration isolator is established to investigate the vibration isolation performance. The effect of a linear vibration absorber (LVA), the NES, and the NSS on the force transmissibility of the structure is compared, in which the parametric study including negative stiffness coefficient, mass ratio, frequency ratio, and barrier height is conducted. The nonlinear dynamic characteristics and energy transfer efficiency of the vibration isolation system are analyzed based on motion phase trajectories, Poincaré mapping and chaotic bifurcation analysis. The results demonstrate that the two-stage isolator with the NES and NSS architecture exhibits superior broadband vibration isolation compared to its counterpart with the LVA and NSS. The structure with the LVA and NSS shows a wider forbidden band range than the device without the LVA. Besides, the negative stiffness configuration between the vibration source and the protected base is a critical factor to influence vibration isolation. A larger negative stiffness coefficient results in lower force transmissibility and the onset frequency of the forbidden zone but the broader bandwidth of the forbidden zone. This work paves a new theoretical venue for low-frequency hybrid vibration isolators in precision instrument fields.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"142 ","pages":"Article 115948"},"PeriodicalIF":4.4,"publicationDate":"2025-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143035296","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 : 2025-01-17DOI: 10.1016/j.apm.2025.115945
Le Chang, Li Cheng
The acoustics black hole (ABH) effect shows promising potential for wave manipulation and vibration control. An ABH structure features a gradual reduction of the phase velocity of flexural waves alongside wave compression and energy accumulation when entering the tapered ABH portion where the thickness is tailored according to a power-law (with power index m no less than 2). The corresponding non-uniform wavelength distribution over the ABH structure poses great challenges to conventional modelling methods. To alleviate the problem, this paper proposes an exact dynamic stiffness method for modelling ABH beams with arbitrary exponent equal to or greater than 2 under the framework of Euler-Bernoulli beam theory. For ABH with m > 2, a change of variable and the Mellin integral transformation are conducted to derive the integral representations of the exact solution using Meijer G-functions. The solution for the case with m = 2 is also derived for completeness. Then the dynamic stiffness matrix is formulated through symbolic operation. The Wittrick-Williams (WW) algorithm is revamped to cope with the ABH-specific requirement. Numerical examples are given to validate the solution in integral form, the dynamic stiffness matrix, and the efficacy of the improved WW algorithm. The clear advantage of the accurate integral representations over series representations is justified in the higher frequency range. Covering all ABH-relevant scenarios (with m ≥ 2), the exact modelling framework established in this work offers a powerful tool for the modelling and investigation of more complex structures which are built upon ABH beam elements.
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