This work aims to analyze the propagation of fully nonlinear waves, encompassing shear, extension, and bending deformation modes, within homogenized periodic nonlinear hexagonal and triangular networks, successively considering 1D and 2D situations. The wave analysis is conducted from the expression of the effective strain energy density of periodic hexagonal and triangular lattices in the nonlinear regime by a continualization of the discrete lattice equations, considering all forms of energy. We incorporate strain gradient effects into the continuous model to account for the wave‐dispersive nature. The resulting second‐gradient nonlinear continuum exhibits subsonic and supersonic propagation modes. We first examine in a 1D situation the dynamical response of the hexagonal and triangular lattices, considering varying levels of nonlinearity quantified by a single scalar valued parameter. We further evaluate the impact of a fully nonlinear analysis compared to an analysis solely based on the shear energy, regarding both supersonic and subsonic modes. The nonlinear wave propagation analysis is then extended to a 2D situation for the same two lattices. It is shown that the longitudinal mode exhibits a higher frequency at a low degree of nonlinearity; however, as the degree of nonlinearity increases, the shear mode surpasses the longitudinal mode in terms of frequency. As the wavenumber increases, the nonlinearity has a lesser impact on the frequency behavior, and the phase velocity is more influenced by other factors, such as the second gradient contributions of the effective constitutive law. Such a behavior indicates a transition from a highly nonlinear behavior at lower wave numbers to a more linear behavior at higher wave numbers.
{"title":"Nonlinear wave propagation in homogenized strain gradient 1D and 2D lattice materials: Applications to hexagonal and triangular networks","authors":"Abdallah Wazne, Hilal Reda, Jean‐François Ganghoffer, Hassan Lakiss","doi":"10.1002/zamm.202400426","DOIUrl":"https://doi.org/10.1002/zamm.202400426","url":null,"abstract":"This work aims to analyze the propagation of fully nonlinear waves, encompassing shear, extension, and bending deformation modes, within homogenized periodic nonlinear hexagonal and triangular networks, successively considering 1D and 2D situations. The wave analysis is conducted from the expression of the effective strain energy density of periodic hexagonal and triangular lattices in the nonlinear regime by a continualization of the discrete lattice equations, considering all forms of energy. We incorporate strain gradient effects into the continuous model to account for the wave‐dispersive nature. The resulting second‐gradient nonlinear continuum exhibits subsonic and supersonic propagation modes. We first examine in a 1D situation the dynamical response of the hexagonal and triangular lattices, considering varying levels of nonlinearity quantified by a single scalar valued parameter. We further evaluate the impact of a fully nonlinear analysis compared to an analysis solely based on the shear energy, regarding both supersonic and subsonic modes. The nonlinear wave propagation analysis is then extended to a 2D situation for the same two lattices. It is shown that the longitudinal mode exhibits a higher frequency at a low degree of nonlinearity; however, as the degree of nonlinearity increases, the shear mode surpasses the longitudinal mode in terms of frequency. As the wavenumber increases, the nonlinearity has a lesser impact on the frequency behavior, and the phase velocity is more influenced by other factors, such as the second gradient contributions of the effective constitutive law. Such a behavior indicates a transition from a highly nonlinear behavior at lower wave numbers to a more linear behavior at higher wave numbers.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"81 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141576782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
An extended two‐dimensional (2D) elasticity theory based on the weighted residual concept is developed in an attempt to capture thickness effects in vibrating thick plates. Plate theories can only provide approximate solutions due to certain kinematics assumptions. The weighting functions are expressed in terms of Legendre orthogonal polynomials. A formulation in rectangular Cartesian coordinates serves as the basis for an implementation of the finite element method. The applicability of the extended 2D elasticity theory is demonstrated through examples of rectangular, thick plates with different aspect ratios, thickness ratios, and boundary conditions. The accuracy of the extended 2D elasticity theory is assessed through a three‐dimensional finite element analysis. The frequencies and modal stresses show excellent agreement with three‐dimensional finite element calculations.
{"title":"Finite element analysis and evaluation of an extended two‐dimensional elasticity theory: Application to thick plate vibrations","authors":"Abderrahim Houmat","doi":"10.1002/zamm.202400103","DOIUrl":"https://doi.org/10.1002/zamm.202400103","url":null,"abstract":"An extended two‐dimensional (2D) elasticity theory based on the weighted residual concept is developed in an attempt to capture thickness effects in vibrating thick plates. Plate theories can only provide approximate solutions due to certain kinematics assumptions. The weighting functions are expressed in terms of Legendre orthogonal polynomials. A formulation in rectangular Cartesian coordinates serves as the basis for an implementation of the finite element method. The applicability of the extended 2D elasticity theory is demonstrated through examples of rectangular, thick plates with different aspect ratios, thickness ratios, and boundary conditions. The accuracy of the extended 2D elasticity theory is assessed through a three‐dimensional finite element analysis. The frequencies and modal stresses show excellent agreement with three‐dimensional finite element calculations.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"59 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141576859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper is concerned with the region tracking control problem of multiple nonholonomic mobile robot systems with collision avoidance. The peculiar characteristic of the proposed scheme is that a class of potential energy functions is chosen to form the desired target region constraining the robots for aggregation, and some local potential energy functions are selected to maintain collision avoidance among robots. Such that each mobile robot only needs to interact with their neighbors to realize the region tracking control task. Moreover, this paper provides a new analytical framework of region tracking control for a network of wheeled mobile robots, in which the integration of the system decomposition and sliding mode control method enables to convert the nonholonomic constraint problem of the controlled mobile robot system into a holonomic constraint problem. This provides a new approach to solving the mobile robot control problem. Theoretical analysis and numerical simulation results are given to validate the effectiveness of the proposed control scheme.
{"title":"Adaptive region tracking control for multiple nonholonomic mobile robot systems subject to collision avoidance","authors":"Xiaohong Zhang, Jinwei Yu","doi":"10.1002/zamm.202400229","DOIUrl":"https://doi.org/10.1002/zamm.202400229","url":null,"abstract":"The paper is concerned with the region tracking control problem of multiple nonholonomic mobile robot systems with collision avoidance. The peculiar characteristic of the proposed scheme is that a class of potential energy functions is chosen to form the desired target region constraining the robots for aggregation, and some local potential energy functions are selected to maintain collision avoidance among robots. Such that each mobile robot only needs to interact with their neighbors to realize the region tracking control task. Moreover, this paper provides a new analytical framework of region tracking control for a network of wheeled mobile robots, in which the integration of the system decomposition and sliding mode control method enables to convert the nonholonomic constraint problem of the controlled mobile robot system into a holonomic constraint problem. This provides a new approach to solving the mobile robot control problem. Theoretical analysis and numerical simulation results are given to validate the effectiveness of the proposed control scheme.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141576860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abderrahim Oudra, Yassine El Khouddar, Ahmed Adri, Omar Outassafte, Issam El Hantati, Hamza Isksioui, Haj El Moussami
This paper investigates the vibration characteristics, both linear and non‐linear, of beams made from functional gradient materials (FGMs) with layers of Terfenol‐D attached to the top and bottom surfaces. Given the porosities that can occur during the manufacture of FGMs, the study examines the vibrational behaviour of beams with porosities. Euler–Bernoulli beam theory and the von‐Kármán non‐linear deformation field are used to formulate a fundamental equation predicting the free dynamic vibration of Terfenol‐D FGM structures with porosities. To complete this analysis, the paper also presents the application of two advanced methods. The first method involves employing the generalised finite element method (GFEM) associated with the reduced quadrature finite element method (RQFEM). GFEM offers a versatile and powerful approach, while RQFEM provides a specific method for studying dynamic phenomena. The second method utilises a semi‐analytical approach, the variational iteration method (VIM), which examines and complements the first method. Furthermore, we have demonstrated substantial alignment between the proposed solution and the results of finite element analysis, as well as with the existing literature, underscoring the effectiveness and accuracy of our analytical approach. The study also explores the influences of material property distribution, thermal loading, and porosity volume fraction on the linear and non‐linear behaviour of Terfenol‐D FGM beams. This comprehensive exploration furnishes valuable information on the intricate interplay of factors affecting vibration dynamics and control mechanisms in these advanced composite structures, offering insightful perspectives into the potential application of Terfenol‐D FGM beams in various fields.
{"title":"Vibration control and analysis of Terfenol‐D functional gradient material beams with porosities: Linear and nonlinear perspectives in thermal environments","authors":"Abderrahim Oudra, Yassine El Khouddar, Ahmed Adri, Omar Outassafte, Issam El Hantati, Hamza Isksioui, Haj El Moussami","doi":"10.1002/zamm.202400236","DOIUrl":"https://doi.org/10.1002/zamm.202400236","url":null,"abstract":"This paper investigates the vibration characteristics, both linear and non‐linear, of beams made from functional gradient materials (FGMs) with layers of Terfenol‐D attached to the top and bottom surfaces. Given the porosities that can occur during the manufacture of FGMs, the study examines the vibrational behaviour of beams with porosities. Euler–Bernoulli beam theory and the von‐Kármán non‐linear deformation field are used to formulate a fundamental equation predicting the free dynamic vibration of Terfenol‐D FGM structures with porosities. To complete this analysis, the paper also presents the application of two advanced methods. The first method involves employing the generalised finite element method (GFEM) associated with the reduced quadrature finite element method (RQFEM). GFEM offers a versatile and powerful approach, while RQFEM provides a specific method for studying dynamic phenomena. The second method utilises a semi‐analytical approach, the variational iteration method (VIM), which examines and complements the first method. Furthermore, we have demonstrated substantial alignment between the proposed solution and the results of finite element analysis, as well as with the existing literature, underscoring the effectiveness and accuracy of our analytical approach. The study also explores the influences of material property distribution, thermal loading, and porosity volume fraction on the linear and non‐linear behaviour of Terfenol‐D FGM beams. This comprehensive exploration furnishes valuable information on the intricate interplay of factors affecting vibration dynamics and control mechanisms in these advanced composite structures, offering insightful perspectives into the potential application of Terfenol‐D FGM beams in various fields.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141576858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ahmed E. Abouelregal, Marin Marin, Sameh S. Askar, Abdelaziz Foul
This article discusses changes in heat transfer resulting from laser pulses and magnetic fields produced in thermoelastic materials under initial stress. This paper introduces a novel approach to modeling generalized thermoelastic materials by including fractional time derivatives with Eringen's non‐local thermoelastic theory. This model incorporates both the Caputo–Fabrizio and the Atangana–Baleanu derivatives, which are novel forms of fractional derivatives in the domain of fractional calculus. Analytical formulations for system variables, such as temperature and thermal stress, were derived using the Laplace transform method. This was done considering the effects of laser pulses, non‐local actuators, and fractional actuators. The findings of these investigations are showcased through numerical illustrations and visual representations. The research also included comparisons between the acquired results and those derived from earlier theories, which may be regarded as a specific instance. Validating the suggested model and showing its correctness and applicability is seen as a crucial step.
{"title":"A non‐local fractional two‐phase delay thermoelastic model for a solid half‐space whose properties change with temperature and affected by hydrostatic pressure","authors":"Ahmed E. Abouelregal, Marin Marin, Sameh S. Askar, Abdelaziz Foul","doi":"10.1002/zamm.202400102","DOIUrl":"https://doi.org/10.1002/zamm.202400102","url":null,"abstract":"This article discusses changes in heat transfer resulting from laser pulses and magnetic fields produced in thermoelastic materials under initial stress. This paper introduces a novel approach to modeling generalized thermoelastic materials by including fractional time derivatives with Eringen's non‐local thermoelastic theory. This model incorporates both the Caputo–Fabrizio and the Atangana–Baleanu derivatives, which are novel forms of fractional derivatives in the domain of fractional calculus. Analytical formulations for system variables, such as temperature and thermal stress, were derived using the Laplace transform method. This was done considering the effects of laser pulses, non‐local actuators, and fractional actuators. The findings of these investigations are showcased through numerical illustrations and visual representations. The research also included comparisons between the acquired results and those derived from earlier theories, which may be regarded as a specific instance. Validating the suggested model and showing its correctness and applicability is seen as a crucial step.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"55 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141549138","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
RETRACTION: Y. A. Al‐Turki, A. Yarmohammadi, A. Alizadeh, D. Toghraie, “Numerical investigation of nanofluid flow and heat transfer in a pillow plate heat exchanger using a two‐phase model: Effects of the shape of the welding points used in the pillow plate,” Zeitschrift für Angewandte Mathematik und Mechanik (Early View): https://doi.org/10.1002/zamm.202000300.The above article, published online on 14 January 2021 in Wiley Online Library (wileyonlinelibrary.com), has been retracted by agreement between the journal Editor‐in‐Chief, Holm Altenbach; and Wiley‐VCH GmbH. The retraction has been agreed as there is unambiguous evidence that this article was accepted on the basis of a compromised peer review process. Therefore, the review of this article is deemed to be insufficient. The authors disagree with the retraction.
返回：Y. A. Al-Turki、A. Yarmohammadi、A. Alizadeh、D. Toghraie，"使用两相模型对枕板热交换器中的纳米流体流动和传热进行数值研究：Effects of the shape of the welding points used in the pillow plate," Zeitschrift für Angewandte Mathematik und Mechanik (Early View): https://doi.org/10.1002/zamm.202000300.The 上述文章于 2021 年 1 月 14 日在线发表于 Wiley Online Library (wileyonlinelibrary.com)，经期刊主编 Holm Altenbach 和 Wiley-VCH GmbH 协议，已被撤回。之所以同意撤稿，是因为有明确的证据表明，这篇文章是在同行评议程序受到损害的基础上被接受的。因此，对这篇文章的审查被认为是不充分的。作者不同意撤稿。
{"title":"RETRACTION: Numerical investigation of nanofluid flow and heat transfer in a pillow plate heat exchanger using a two‐phase model: Effects of the shape of the welding points used in the pillow plate","authors":"","doi":"10.1002/zamm.202402007","DOIUrl":"https://doi.org/10.1002/zamm.202402007","url":null,"abstract":"RETRACTION: Y. A. Al‐Turki, A. Yarmohammadi, A. Alizadeh, D. Toghraie, “Numerical investigation of nanofluid flow and heat transfer in a pillow plate heat exchanger using a two‐phase model: Effects of the shape of the welding points used in the pillow plate,” <jats:italic>Zeitschrift für Angewandte Mathematik und Mechanik</jats:italic> (Early View): <jats:ext-link xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"https://doi.org/10.1002/zamm.202000300\">https://doi.org/10.1002/zamm.202000300</jats:ext-link>.The above article, published online on 14 January 2021 in Wiley Online Library (wileyonlinelibrary.com), has been retracted by agreement between the journal Editor‐in‐Chief, Holm Altenbach; and Wiley‐VCH GmbH. The retraction has been agreed as there is unambiguous evidence that this article was accepted on the basis of a compromised peer review process. Therefore, the review of this article is deemed to be insufficient. The authors disagree with the retraction.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"134 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141549135","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
RETRACTION: A. Shahsavar, S. Noori, D. Toghraie, P. Barnoon, “Free convection of non‐Newtonian nanofluid flow inside an eccentric annulus from the point of view of first‐law and second‐law of thermodynamics,” Zeitschrift für Angewandte Mathematik und Mechanik (Early View): https://doi.org/10.1002/zamm.202000266.The above article, published online on 28 November 2020 in Wiley Online Library (wileyonlinelibrary.com), has been retracted by agreement between the journal Editor‐in‐Chief, Holm Altenbach, and Wiley‐VCH GmbH. The retraction has been agreed as there is unambiguous evidence that this article was accepted on the basis of a compromised peer review process. Therefore, the review of this article is deemed to be insufficient. The authors disagree with the retraction.
撤回：A. Shahsavar, S. Noori, D. Toghraie, P. Barnoon, "Free convection of non-Newtonian nanofluid flow inside an eccentric annulus from the point of the point of the first law and second law of thermodynamics," Zeitschrift für Angewandte Mathematik und Mechanik (Early View): https://doi.org/10.1002/zamm.202000266.上述文章于 2020 年 11 月 28 日在线发表于 Wiley Online Library (wileyonlinelibrary.com)，经期刊主编 Holm Altenbach 和 Wiley-VCH GmbH 协议，该文章已被撤回。之所以同意撤稿，是因为有明确的证据表明，这篇文章是在同行评议程序受到损害的基础上被接受的。因此，对这篇文章的审查被认为是不充分的。作者不同意撤稿。
{"title":"RETRACTION: Free convection of non‐Newtonian nanofluid flow inside an eccentric annulus from the point of view of first‐law and second‐law of thermodynamics","authors":"","doi":"10.1002/zamm.202402006","DOIUrl":"https://doi.org/10.1002/zamm.202402006","url":null,"abstract":"RETRACTION: A. Shahsavar, S. Noori, D. Toghraie, P. Barnoon, “Free convection of non‐Newtonian nanofluid flow inside an eccentric annulus from the point of view of first‐law and second‐law of thermodynamics,” <jats:italic>Zeitschrift für Angewandte Mathematik und Mechanik</jats:italic> (Early View): <jats:ext-link xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"https://doi.org/10.1002/zamm.202000266\">https://doi.org/10.1002/zamm.202000266</jats:ext-link>.The above article, published online on 28 November 2020 in Wiley Online Library (wileyonlinelibrary.com), has been retracted by agreement between the journal Editor‐in‐Chief, Holm Altenbach, and Wiley‐VCH GmbH. The retraction has been agreed as there is unambiguous evidence that this article was accepted on the basis of a compromised peer review process. Therefore, the review of this article is deemed to be insufficient. The authors disagree with the retraction.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141549139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
RETRACTION: M. R. Faridzadeh, D. Toghraie, M. Khalili, O. A. Akbari, N. Ghajari, A. Alizadeh, “Laminar single‐phase and two‐phase modeling of water/MgO nanofluid flow inside a rectangular microchannel with rhombic vortex generators,” Zeitschrift für Angewandte Mathematik und Mechanik (Early View): https://onlinelibrary.wiley.com/doi/full/10.1002/zamm.202000332The above article, published online on 25 February 2021 in Wiley Online Library (wileyonlinelibrary.com), has been retracted by agreement between the journal Editor‐in‐Chief, Holm Altenbach, and Wiley‐VCH GmbH. The retraction has been agreed as there is unambiguous evidence that this article was accepted on the basis of a compromised peer review process. Therefore, the review of this article is deemed to be insufficient. The authors disagree with the retraction.
撤回：M. R. Faridzadeh、D. Toghraie、M. Khalili、O. A. Akbari、N. Ghajari、A. Alizadeh，"带菱形涡流发生器的矩形微通道内水/氧化镁纳米流体流动的层流单相和两相建模"，Zeitschrift für Angewandte Mathematik und Mechanik（早期视图）：https://onlinelibrary.wiley.com/doi/full/10.1002/zamm.202000332。上述文章于 2021 年 2 月 25 日在线发表于 Wiley Online Library (wileyonlinelibrary.com)，经期刊主编 Holm Altenbach 和 Wiley-VCH GmbH 协议，该文章已被撤回。之所以同意撤稿，是因为有明确的证据表明，这篇文章是在同行评议程序受到损害的基础上被接受的。因此，对这篇文章的审查被认为是不充分的。作者不同意撤稿。
{"title":"RETRACTION: Laminar single‐phase and two‐phase modeling of water/MgO nanofluid flow inside a rectangular microchannel with rhombic vortex generators","authors":"","doi":"10.1002/zamm.202402008","DOIUrl":"https://doi.org/10.1002/zamm.202402008","url":null,"abstract":"RETRACTION: M. R. Faridzadeh, D. Toghraie, M. Khalili, O. A. Akbari, N. Ghajari, A. Alizadeh, “Laminar single‐phase and two‐phase modeling of water/MgO nanofluid flow inside a rectangular microchannel with rhombic vortex generators,” <jats:italic>Zeitschrift für Angewandte Mathematik und Mechanik</jats:italic> (Early View): <jats:ext-link xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"https://onlinelibrary.wiley.com/doi/full/10.1002/zamm.202000332\">https://onlinelibrary.wiley.com/doi/full/10.1002/zamm.202000332</jats:ext-link>The above article, published online on 25 February 2021 in Wiley Online Library (wileyonlinelibrary.com), has been retracted by agreement between the journal Editor‐in‐Chief, Holm Altenbach, and Wiley‐VCH GmbH. The retraction has been agreed as there is unambiguous evidence that this article was accepted on the basis of a compromised peer review process. Therefore, the review of this article is deemed to be insufficient. The authors disagree with the retraction.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141549137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
RETRACTION: S. Enayat, M. Hashemian, D. Toghraie, E. Jaberzadeh, “Bending, buckling and vibration analyses of FG porous nanobeams resting on Pasternak foundation incorporating surface effects,” Zeitschrift für Angewandte Mathematik und Mechanik (Early View): https://doi.org/10.1002/zamm.202000231.The above article, published online on 27 September 2020 in Wiley Online Library (wileyonlinelibrary.com), has been retracted by agreement between the journal Editor‐in‐Chief, Holm Altenbach, and Wiley‐VCH GmbH. The retraction has been agreed as there is unambiguous evidence that this article was accepted on the basis of a compromised peer review process. Therefore, the review of this article is deemed to be insufficient. The authors disagree with the retraction.
撤回：S. Enayat, M. Hashemian, D. Toghraie, E. Jaberzadeh, "Bending, buckling and vibration analyses of FG porous nanobeams resting on Pasternak foundation incorporating surface effects," Zeitschrift für Angewandte Mathematik und Mechanik (Early View): https://doi.org/10.1002/zamm.202000231.The 上述文章于 2020 年 9 月 27 日在线发表于 Wiley Online Library (wileyonlinelibrary.com)，经期刊主编 Holm Altenbach 和 Wiley-VCH GmbH 协议撤回。之所以同意撤稿，是因为有明确的证据表明，这篇文章是在同行评议程序受到损害的基础上被接受的。因此，对这篇文章的审查被认为是不充分的。作者不同意撤稿。
{"title":"RETRACTION: Bending, buckling and vibration analyses of FG porous nanobeams resting on Pasternak foundation incorporating surface effects","authors":"","doi":"10.1002/zamm.202402009","DOIUrl":"https://doi.org/10.1002/zamm.202402009","url":null,"abstract":"RETRACTION: S. Enayat, M. Hashemian, D. Toghraie, E. Jaberzadeh, “Bending, buckling and vibration analyses of FG porous nanobeams resting on Pasternak foundation incorporating surface effects,” <jats:italic>Zeitschrift für Angewandte Mathematik und Mechanik</jats:italic> (Early View): <jats:ext-link xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"https://doi.org/10.1002/zamm.202000231\">https://doi.org/10.1002/zamm.202000231</jats:ext-link>.The above article, published online on 27 September 2020 in Wiley Online Library (wileyonlinelibrary.com), has been retracted by agreement between the journal Editor‐in‐Chief, Holm Altenbach, and Wiley‐VCH GmbH. The retraction has been agreed as there is unambiguous evidence that this article was accepted on the basis of a compromised peer review process. Therefore, the review of this article is deemed to be insufficient. The authors disagree with the retraction.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141549136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：