We examine a saturated bidispersive porous medium undergoing an exothermic chemical reaction at its lower boundary. The fluid flow within this medium is modelled using the Darcy approach. While the Dufour effect is disregarded, the influence of the Soret effect is thoroughly explored. This problem represents a complex multiphysical phenomenon that integrates fluid dynamics, heat and mass transfer, chemical kinetics and thermoelectric effects. This problem finds relevance in various scientific and engineering applications, including enhanced oil recovery, chemical engineering, environmental engineering and energy systems. We introduce a complementary energy theory alongside a linear theoretical framework for the model. The Chebyshev collocation method is employed to derive both linear and nonlinear results. Our findings reveal that the effect of enhancing the Soret coefficient on the system's stability is contingent upon the boundary conditions and the Lewis number. Specifically, an increase in the Soret coefficient generally stabilises the system during stationary convection. Conversely, in scenarios where oscillatory convection prevails, a higher Soret coefficient tends to destabilise the system.
{"title":"Soret effect on stability of Darcy problem in a bidispersive porous medium with an exothermic chemical surface reaction","authors":"Zaid Abbas Afluk, A. Harfash","doi":"10.1002/zamm.202300786","DOIUrl":"https://doi.org/10.1002/zamm.202300786","url":null,"abstract":"We examine a saturated bidispersive porous medium undergoing an exothermic chemical reaction at its lower boundary. The fluid flow within this medium is modelled using the Darcy approach. While the Dufour effect is disregarded, the influence of the Soret effect is thoroughly explored. This problem represents a complex multiphysical phenomenon that integrates fluid dynamics, heat and mass transfer, chemical kinetics and thermoelectric effects. This problem finds relevance in various scientific and engineering applications, including enhanced oil recovery, chemical engineering, environmental engineering and energy systems. We introduce a complementary energy theory alongside a linear theoretical framework for the model. The Chebyshev collocation method is employed to derive both linear and nonlinear results. Our findings reveal that the effect of enhancing the Soret coefficient on the system's stability is contingent upon the boundary conditions and the Lewis number. Specifically, an increase in the Soret coefficient generally stabilises the system during stationary convection. Conversely, in scenarios where oscillatory convection prevails, a higher Soret coefficient tends to destabilise the system.","PeriodicalId":509544,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140366971","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}
Ali Rehman, M. Khun, Shahram Rezapour, Mostafa Inc, Hakim A. L. Garalleh, Taseer Muhammad
This research work investigates the semi‐numerical analysis and heat transfer of MHD 2D, Copper Oxide, and Magnesium oxide engine oil base nanofluid with the consider effect of dynamic viscosity and convective boundary conditions (BCs). The convective BCs and the effect of dynamic viscosity on an extensible surface are considered by the flow system. We converted a set of PDEs into NODEs by applying the appropriate transformations. Using the HAM, we solve this dimensionless coupled equation one for temperature and other for velocity. The impact of various parameters for both temperature and velocity are demonstrated, such as the slip parameter, magnetic parameter (MP), Eckert number (EN), PN, and dynamic viscosity. In response to changes in developing factors, the flow features, such as temperature profiles (TPs) and velocity profiles (VPs), are analyzed and simulated using a physical description. The results of this study add to our knowledge of how engine oil‐based nanofluids promote heat transmission and offer practical advice for thermal management and engineering applications.
{"title":"Analytical analysis and heat transfer of CuO and MgO engine oil base nanofluid with the influence of dynamic viscosity, magnetic field, and convective boundary conditions","authors":"Ali Rehman, M. Khun, Shahram Rezapour, Mostafa Inc, Hakim A. L. Garalleh, Taseer Muhammad","doi":"10.1002/zamm.202300510","DOIUrl":"https://doi.org/10.1002/zamm.202300510","url":null,"abstract":"This research work investigates the semi‐numerical analysis and heat transfer of MHD 2D, Copper Oxide, and Magnesium oxide engine oil base nanofluid with the consider effect of dynamic viscosity and convective boundary conditions (BCs). The convective BCs and the effect of dynamic viscosity on an extensible surface are considered by the flow system. We converted a set of PDEs into NODEs by applying the appropriate transformations. Using the HAM, we solve this dimensionless coupled equation one for temperature and other for velocity. The impact of various parameters for both temperature and velocity are demonstrated, such as the slip parameter, magnetic parameter (MP), Eckert number (EN), PN, and dynamic viscosity. In response to changes in developing factors, the flow features, such as temperature profiles (TPs) and velocity profiles (VPs), are analyzed and simulated using a physical description. The results of this study add to our knowledge of how engine oil‐based nanofluids promote heat transmission and offer practical advice for thermal management and engineering applications.","PeriodicalId":509544,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140368441","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 nanofluids became much of interest due to their superior heat mechanism over the conventional fluids. The addition of nanoparticles in the host solvent enhances the internal ability of the liquid to store and transmit heat. Therefore, these fluids are widely used in biomedical engineering, detergents, medication, applied thermal engineering, mechanical, and chemical engineering and so forth. Keeping in mind the significance of nanofluids, this study is conducted to investigate the comparative heat transmission in and under the Effective Prandtl Number Model (EPNM) effects over a vertical permeable cylinder. Formulation of the model is carried out over a vertical cylinder about the stagnation point and the heat transport model is achieved after the successful implementation of the cylindrical stream function, nanofluids effective characteristics, and cylindrical similarity equations. The mathematical treatment was done via RK technique and furnished the results. The nanofluids have the capacity to control the fluid motion more effectively than ordinary fluid and combined convection is better where rapid fluid movement is desired. In the existence of EPNM, higher heat transmission is achieved and is prominent for based on their thermophysical values. Further, the skin friction and Nusselt number are optimum for against .
{"title":"Numerical analysis of thermal improvement in hydrogen‐based host fluids under buoyancy force and EPNM effects: Study for vertical cylinder","authors":"Adnan, W. Abbas, Aboulbaba Eladeb, L. Kolsi","doi":"10.1002/zamm.202200449","DOIUrl":"https://doi.org/10.1002/zamm.202200449","url":null,"abstract":"The nanofluids became much of interest due to their superior heat mechanism over the conventional fluids. The addition of nanoparticles in the host solvent enhances the internal ability of the liquid to store and transmit heat. Therefore, these fluids are widely used in biomedical engineering, detergents, medication, applied thermal engineering, mechanical, and chemical engineering and so forth. Keeping in mind the significance of nanofluids, this study is conducted to investigate the comparative heat transmission in and under the Effective Prandtl Number Model (EPNM) effects over a vertical permeable cylinder. Formulation of the model is carried out over a vertical cylinder about the stagnation point and the heat transport model is achieved after the successful implementation of the cylindrical stream function, nanofluids effective characteristics, and cylindrical similarity equations. The mathematical treatment was done via RK technique and furnished the results. The nanofluids have the capacity to control the fluid motion more effectively than ordinary fluid and combined convection is better where rapid fluid movement is desired. In the existence of EPNM, higher heat transmission is achieved and is prominent for based on their thermophysical values. Further, the skin friction and Nusselt number are optimum for against .","PeriodicalId":509544,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140210453","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 general expression for the time‐independent electrophoretic velocity of a spherical colloidal particle with a slippage surface in a microstructure electrolyte solution is derived. The two extreme cases of nonconducting and perfect conducting particles are investigated. The derived expression is valid for arbitrary Debye length and low particle zeta potentials. The concept of velocity spin slip is incorporated with the usual velocity slip at the particle's surface. The effect of the microstructure of fluid particles on the electrophoresis phenomena is discussed based on a micropolar fluid model. The influences of velocity slip and velocity spin slip are shown through various plots of electrophoretic velocity. The limiting case of electrolyte viscous solution is recovered. The principal findings of this research can be summarized as follows: As the micropolarity parameter increases, the normalized electrophoretic velocity decreases and reaches its peak in the case of Newtonian fluids. Additionally, the velocity slip acts as a counteracting factor that promotes an increase in the electrophoretic velocity. In the context of nonconducting particles, the normalized electrophoretic velocity rises as the spin slip parameter and Debye length decrease. Conversely, for perfectly conducting particles, it increases as the spin slip parameter and Debye length increase.
{"title":"Electrophoresis analysis of a hydrophobic spherical particle in a micropolar electrolyte solution","authors":"M. S. Faltas, H. Sherief, Mohamed Mahmoud Ismail","doi":"10.1002/zamm.202300226","DOIUrl":"https://doi.org/10.1002/zamm.202300226","url":null,"abstract":"The general expression for the time‐independent electrophoretic velocity of a spherical colloidal particle with a slippage surface in a microstructure electrolyte solution is derived. The two extreme cases of nonconducting and perfect conducting particles are investigated. The derived expression is valid for arbitrary Debye length and low particle zeta potentials. The concept of velocity spin slip is incorporated with the usual velocity slip at the particle's surface. The effect of the microstructure of fluid particles on the electrophoresis phenomena is discussed based on a micropolar fluid model. The influences of velocity slip and velocity spin slip are shown through various plots of electrophoretic velocity. The limiting case of electrolyte viscous solution is recovered. The principal findings of this research can be summarized as follows: As the micropolarity parameter increases, the normalized electrophoretic velocity decreases and reaches its peak in the case of Newtonian fluids. Additionally, the velocity slip acts as a counteracting factor that promotes an increase in the electrophoretic velocity. In the context of nonconducting particles, the normalized electrophoretic velocity rises as the spin slip parameter and Debye length decrease. Conversely, for perfectly conducting particles, it increases as the spin slip parameter and Debye length increase.","PeriodicalId":509544,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139782540","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 general expression for the time‐independent electrophoretic velocity of a spherical colloidal particle with a slippage surface in a microstructure electrolyte solution is derived. The two extreme cases of nonconducting and perfect conducting particles are investigated. The derived expression is valid for arbitrary Debye length and low particle zeta potentials. The concept of velocity spin slip is incorporated with the usual velocity slip at the particle's surface. The effect of the microstructure of fluid particles on the electrophoresis phenomena is discussed based on a micropolar fluid model. The influences of velocity slip and velocity spin slip are shown through various plots of electrophoretic velocity. The limiting case of electrolyte viscous solution is recovered. The principal findings of this research can be summarized as follows: As the micropolarity parameter increases, the normalized electrophoretic velocity decreases and reaches its peak in the case of Newtonian fluids. Additionally, the velocity slip acts as a counteracting factor that promotes an increase in the electrophoretic velocity. In the context of nonconducting particles, the normalized electrophoretic velocity rises as the spin slip parameter and Debye length decrease. Conversely, for perfectly conducting particles, it increases as the spin slip parameter and Debye length increase.
{"title":"Electrophoresis analysis of a hydrophobic spherical particle in a micropolar electrolyte solution","authors":"M. S. Faltas, H. Sherief, Mohamed Mahmoud Ismail","doi":"10.1002/zamm.202300226","DOIUrl":"https://doi.org/10.1002/zamm.202300226","url":null,"abstract":"The general expression for the time‐independent electrophoretic velocity of a spherical colloidal particle with a slippage surface in a microstructure electrolyte solution is derived. The two extreme cases of nonconducting and perfect conducting particles are investigated. The derived expression is valid for arbitrary Debye length and low particle zeta potentials. The concept of velocity spin slip is incorporated with the usual velocity slip at the particle's surface. The effect of the microstructure of fluid particles on the electrophoresis phenomena is discussed based on a micropolar fluid model. The influences of velocity slip and velocity spin slip are shown through various plots of electrophoretic velocity. The limiting case of electrolyte viscous solution is recovered. The principal findings of this research can be summarized as follows: As the micropolarity parameter increases, the normalized electrophoretic velocity decreases and reaches its peak in the case of Newtonian fluids. Additionally, the velocity slip acts as a counteracting factor that promotes an increase in the electrophoretic velocity. In the context of nonconducting particles, the normalized electrophoretic velocity rises as the spin slip parameter and Debye length decrease. Conversely, for perfectly conducting particles, it increases as the spin slip parameter and Debye length increase.","PeriodicalId":509544,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139842537","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}
Zeeshan Ikram Butt, Iftikhar Ahmad, Muhammad Shoaib, Hira Ilyas, A. Kiani, Muhammad Asif Zahoor Raja
In this communication, a new stochastic numerical paradigm is introduced for thorough scrutinization of the magnetohydrodynamic (MHD) boundary layer flow of Prandtl–Eyring fluidic model along a stretched sheet impact on thermal radiation as well as convective heating scenarios by exploiting the accurate approximation knacks of ANNs (artificial‐neural‐networks) modeling by using the inverse multiquadric (IMQ) function optimized/trained with well‐reputed global search with genetic algorithms (GAs) and local search efficacy of sequential quadratic programming (SQP), that is, ANNs‐IMQ‐GA‐SQP. The mathematical model of the Prandtl–Eyring fluid flow is portrayed in the form of PDEs and then converted in the form of a nonlinear system of ODEs by utilizing suitable similarity transformation to calculate/analyze the solution dynamics. The kinematic and thermodynamic properties of MHD Prandtl–Eyring fluid flow are examined/observed by varying the sundry physical parameters. The obtained intelligent computing designed solver‐based numerical results are consistently found in good agreement with reference results obtained through the Adams numerical technique. First and second‐order cumulant‐based statistical assessments are extensively exploited to endorse trustily the efficacy of ANNs‐IMQ‐GA‐SQP solver based on exhaustive simulations for the Prandtl–Eyring fluidic system.
{"title":"Integrated intelligence of inverse multiquadric radial base neuro‐evolution for radiative MHD Prandtl–Eyring fluid flow model with convective heating","authors":"Zeeshan Ikram Butt, Iftikhar Ahmad, Muhammad Shoaib, Hira Ilyas, A. Kiani, Muhammad Asif Zahoor Raja","doi":"10.1002/zamm.202300302","DOIUrl":"https://doi.org/10.1002/zamm.202300302","url":null,"abstract":"In this communication, a new stochastic numerical paradigm is introduced for thorough scrutinization of the magnetohydrodynamic (MHD) boundary layer flow of Prandtl–Eyring fluidic model along a stretched sheet impact on thermal radiation as well as convective heating scenarios by exploiting the accurate approximation knacks of ANNs (artificial‐neural‐networks) modeling by using the inverse multiquadric (IMQ) function optimized/trained with well‐reputed global search with genetic algorithms (GAs) and local search efficacy of sequential quadratic programming (SQP), that is, ANNs‐IMQ‐GA‐SQP. The mathematical model of the Prandtl–Eyring fluid flow is portrayed in the form of PDEs and then converted in the form of a nonlinear system of ODEs by utilizing suitable similarity transformation to calculate/analyze the solution dynamics. The kinematic and thermodynamic properties of MHD Prandtl–Eyring fluid flow are examined/observed by varying the sundry physical parameters. The obtained intelligent computing designed solver‐based numerical results are consistently found in good agreement with reference results obtained through the Adams numerical technique. First and second‐order cumulant‐based statistical assessments are extensively exploited to endorse trustily the efficacy of ANNs‐IMQ‐GA‐SQP solver based on exhaustive simulations for the Prandtl–Eyring fluidic system.","PeriodicalId":509544,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139793282","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}
Zeeshan Ikram Butt, Iftikhar Ahmad, Muhammad Shoaib, Hira Ilyas, A. Kiani, Muhammad Asif Zahoor Raja
In this communication, a new stochastic numerical paradigm is introduced for thorough scrutinization of the magnetohydrodynamic (MHD) boundary layer flow of Prandtl–Eyring fluidic model along a stretched sheet impact on thermal radiation as well as convective heating scenarios by exploiting the accurate approximation knacks of ANNs (artificial‐neural‐networks) modeling by using the inverse multiquadric (IMQ) function optimized/trained with well‐reputed global search with genetic algorithms (GAs) and local search efficacy of sequential quadratic programming (SQP), that is, ANNs‐IMQ‐GA‐SQP. The mathematical model of the Prandtl–Eyring fluid flow is portrayed in the form of PDEs and then converted in the form of a nonlinear system of ODEs by utilizing suitable similarity transformation to calculate/analyze the solution dynamics. The kinematic and thermodynamic properties of MHD Prandtl–Eyring fluid flow are examined/observed by varying the sundry physical parameters. The obtained intelligent computing designed solver‐based numerical results are consistently found in good agreement with reference results obtained through the Adams numerical technique. First and second‐order cumulant‐based statistical assessments are extensively exploited to endorse trustily the efficacy of ANNs‐IMQ‐GA‐SQP solver based on exhaustive simulations for the Prandtl–Eyring fluidic system.
{"title":"Integrated intelligence of inverse multiquadric radial base neuro‐evolution for radiative MHD Prandtl–Eyring fluid flow model with convective heating","authors":"Zeeshan Ikram Butt, Iftikhar Ahmad, Muhammad Shoaib, Hira Ilyas, A. Kiani, Muhammad Asif Zahoor Raja","doi":"10.1002/zamm.202300302","DOIUrl":"https://doi.org/10.1002/zamm.202300302","url":null,"abstract":"In this communication, a new stochastic numerical paradigm is introduced for thorough scrutinization of the magnetohydrodynamic (MHD) boundary layer flow of Prandtl–Eyring fluidic model along a stretched sheet impact on thermal radiation as well as convective heating scenarios by exploiting the accurate approximation knacks of ANNs (artificial‐neural‐networks) modeling by using the inverse multiquadric (IMQ) function optimized/trained with well‐reputed global search with genetic algorithms (GAs) and local search efficacy of sequential quadratic programming (SQP), that is, ANNs‐IMQ‐GA‐SQP. The mathematical model of the Prandtl–Eyring fluid flow is portrayed in the form of PDEs and then converted in the form of a nonlinear system of ODEs by utilizing suitable similarity transformation to calculate/analyze the solution dynamics. The kinematic and thermodynamic properties of MHD Prandtl–Eyring fluid flow are examined/observed by varying the sundry physical parameters. The obtained intelligent computing designed solver‐based numerical results are consistently found in good agreement with reference results obtained through the Adams numerical technique. First and second‐order cumulant‐based statistical assessments are extensively exploited to endorse trustily the efficacy of ANNs‐IMQ‐GA‐SQP solver based on exhaustive simulations for the Prandtl–Eyring fluidic system.","PeriodicalId":509544,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139853466","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}
We apply Muskhelishvili's complex variable method to solve the plane strain problem associated with two circular incompressible liquid inclusions embedded in an infinite isotropic elastic matrix subjected to uniform remote in‐plane normal stresses. An analytical solution to the problem is derived primarily with the aid of conformal mapping and analytic continuation. To demonstrate our analytical solution, we present detailed numerical results characterizing the internal uniform hydrostatic stresses within the two liquid inclusions, the nonuniform hoop stresses along the two circular liquid‐solid interfaces on the matrix side and the nonuniform rigid body rotations within the two circular liquid inclusions.
{"title":"Two circular incompressible liquid inclusions","authors":"Xu Wang, P. Schiavone","doi":"10.1002/zamm.202300679","DOIUrl":"https://doi.org/10.1002/zamm.202300679","url":null,"abstract":"We apply Muskhelishvili's complex variable method to solve the plane strain problem associated with two circular incompressible liquid inclusions embedded in an infinite isotropic elastic matrix subjected to uniform remote in‐plane normal stresses. An analytical solution to the problem is derived primarily with the aid of conformal mapping and analytic continuation. To demonstrate our analytical solution, we present detailed numerical results characterizing the internal uniform hydrostatic stresses within the two liquid inclusions, the nonuniform hoop stresses along the two circular liquid‐solid interfaces on the matrix side and the nonuniform rigid body rotations within the two circular liquid inclusions.","PeriodicalId":509544,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139525407","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}
In this study, the vibrational behavior of Rayleigh and shear beams placed over the Hetényi and Pasternak foundations is investigated, with special attention paid to the effects of axial stresses (both tensile and compressive). The uniqueness of the work comes from the thorough consideration of how axial forces, shear deformation, rotational inertia, and foundation factors affect the eigenfrequencies and eigenmodes that control beam vibrations. Eigenfrequencies and eigenmodes are determined through computational analyses with the Galerkin finite element method (GFEM) employing quadratic and cubic polynomials. Comparisons between finite element results and analytical outcomes, both in generalized and specialized contexts, serve to demonstrate the correctness and effectiveness of the approximate solution. The study shows that the Hetényi foundation's influence on eigenfrequency depends on foundation stiffness and relative beam magnitudes, and that shear deformation affects eigenfrequencies more than rotary inertia does. Higher frequencies are largely unaffected by compressive and tensile stresses, but the fundamental frequency is rigorously influenced. Further demonstrating its accuracy, the finite element approach shows great agreement in forecasting eigenmodes and eigenfrequencies. A variety of real‐world situations involving elastically confined beams resting on elastic foundations and being subjected to axial forces are the focus of the study. Axial forces commonly result from external loads, thermal expansion, or structural interactions in real‐world settings. Therefore, it is crucial to understand how they affect beam vibration when designing structures that can endure expected stresses and vibrations while maintaining safety and performance criteria.
{"title":"Analytical and computational analysis of vibrational behavior of axially loaded beams placed on elastic foundations","authors":"H. Alahmadi, Rab Nawaz, G. Kanwal, A. Alruwaili","doi":"10.1002/zamm.202300856","DOIUrl":"https://doi.org/10.1002/zamm.202300856","url":null,"abstract":"In this study, the vibrational behavior of Rayleigh and shear beams placed over the Hetényi and Pasternak foundations is investigated, with special attention paid to the effects of axial stresses (both tensile and compressive). The uniqueness of the work comes from the thorough consideration of how axial forces, shear deformation, rotational inertia, and foundation factors affect the eigenfrequencies and eigenmodes that control beam vibrations. Eigenfrequencies and eigenmodes are determined through computational analyses with the Galerkin finite element method (GFEM) employing quadratic and cubic polynomials. Comparisons between finite element results and analytical outcomes, both in generalized and specialized contexts, serve to demonstrate the correctness and effectiveness of the approximate solution. The study shows that the Hetényi foundation's influence on eigenfrequency depends on foundation stiffness and relative beam magnitudes, and that shear deformation affects eigenfrequencies more than rotary inertia does. Higher frequencies are largely unaffected by compressive and tensile stresses, but the fundamental frequency is rigorously influenced. Further demonstrating its accuracy, the finite element approach shows great agreement in forecasting eigenmodes and eigenfrequencies. A variety of real‐world situations involving elastically confined beams resting on elastic foundations and being subjected to axial forces are the focus of the study. Axial forces commonly result from external loads, thermal expansion, or structural interactions in real‐world settings. Therefore, it is crucial to understand how they affect beam vibration when designing structures that can endure expected stresses and vibrations while maintaining safety and performance criteria.","PeriodicalId":509544,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139525672","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}
In this paper, a nonlinearly damped system of wave equations is considered. Uniform energy decay was discussed in the previous work (Discrete Contin. Dyn. Syst. Ser. S, 2 (2009) 583–608) for if the space dimension is 3. New energy decay is proposed for by choosing appropriate multiplier related to a non‐increasing differential function. As an example, a logarithmic energy decay is also presented.
{"title":"New energy decay for a nonlinearly damped system of wave equations","authors":"Xiangyu Zhu, Menglan Liao","doi":"10.1002/zamm.202200442","DOIUrl":"https://doi.org/10.1002/zamm.202200442","url":null,"abstract":"In this paper, a nonlinearly damped system of wave equations is considered. Uniform energy decay was discussed in the previous work (Discrete Contin. Dyn. Syst. Ser. S, 2 (2009) 583–608) for if the space dimension is 3. New energy decay is proposed for by choosing appropriate multiplier related to a non‐increasing differential function. As an example, a logarithmic energy decay is also presented.","PeriodicalId":509544,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139439055","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}
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