In this study, a steady magnetohydrodynamic (MHD) flow due to stretchable rotating disk in the presence of gyrotactic microorganisms is investigated. The governing equations modeling the flow are solved numerically using the newly introduced simple iteration method (SIM) that seeks to linearize a system using relaxation technique that effectively decouples the system. To verify the convergence and accuracy of the method, solution error and residual error analysis are carried out, respectively. The obtained results suggest that the SIM is a highly efficient method that produces convergent and highly accurate solutions. The effects of various parameters as well as combined parameter effects on the solution profiles are also investigated. An increase in the Hall and permeability parameters leads to a corresponding rise in the microorganism?s density and nanoparticle volume fraction.
{"title":"Numerical simulation of nanofluid flow due to a stretchable rotating disk","authors":"M. Ayano, O. Otegbeye, J. Mathunjwa","doi":"10.2298/tam220810005a","DOIUrl":"https://doi.org/10.2298/tam220810005a","url":null,"abstract":"In this study, a steady magnetohydrodynamic (MHD) flow due to stretchable rotating disk in the presence of gyrotactic microorganisms is investigated. The governing equations modeling the flow are solved numerically using the newly introduced simple iteration method (SIM) that seeks to linearize a system using relaxation technique that effectively decouples the system. To verify the convergence and accuracy of the method, solution error and residual error analysis are carried out, respectively. The obtained results suggest that the SIM is a highly efficient method that produces convergent and highly accurate solutions. The effects of various parameters as well as combined parameter effects on the solution profiles are also investigated. An increase in the Hall and permeability parameters leads to a corresponding rise in the microorganism?s density and nanoparticle volume fraction.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"23 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76526994","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, the free transverse vibration of a nonlinear Euler-Bernoulli beam under a neutral type delay is considered. In order to suppress the beam transverse vibrations, a boundary control based on the Lyapunov method is designed. The novelty of this paper is the ability to get a wide variety of energy decay rates under free vibration conditions.
{"title":"Arbitrary decay for a nonlinear Euler-Bernoulli beam with neutral delay","authors":"Ibrahim Lakehal, D. Benterki, K. Zennir","doi":"10.2298/tam220811002l","DOIUrl":"https://doi.org/10.2298/tam220811002l","url":null,"abstract":"In this paper, the free transverse vibration of a nonlinear Euler-Bernoulli beam under a neutral type delay is considered. In order to suppress the beam transverse vibrations, a boundary control based on the Lyapunov method is designed. The novelty of this paper is the ability to get a wide variety of energy decay rates under free vibration conditions.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"34 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78942328","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 transmutation of central forces, or dual law, is a transformation linking potentials in power law relative to the distance, that is, those having a positive exponent to those having a negative exponent. A well known example is that of the Newtonian and Hookean potentials, which are also strongly linked by Bertrand?s famous theorem. This article shows how the use of dual law provides a better understanding of this theorem, and a new way to complete its demonstration.
{"title":"Transmutation of central forces and Bertrand’s theorem","authors":"C. Carimalo","doi":"10.2298/tam220602001c","DOIUrl":"https://doi.org/10.2298/tam220602001c","url":null,"abstract":"The transmutation of central forces, or dual law, is a transformation linking potentials in power law relative to the distance, that is, those having a positive exponent to those having a negative exponent. A well known example is that of the Newtonian and Hookean potentials, which are also strongly linked by Bertrand?s famous theorem. This article shows how the use of dual law provides a better understanding of this theorem, and a new way to complete its demonstration.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"14 9 Pt 1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78463023","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 constitutive relations between stresses and strains in the mechanics of a deformable solid, including their operator connection, are considered. Some important and frequently occurring properties of tangent modulus and tangent pliability as rank four tensors are described. Depending on this, a possible classification of continuous media is proposed. Scleronomous and rheonomic media, homogeneous and inhomogeneous media (in particular, composites), media with memory, spatially nonlocal media, materials with hard or soft characteristics are distinguished. For non-linearly elastic isotropic media, the apparatus of tensor nonlinear isotropic functions of one argument is developed. Particular attention is paid to the three-term representation of power tensor series in three-dimensional space, reversibility of tensor functions, Taylor tensor series, tensor linearity (quasilinearity) and nonlinearity.
{"title":"Properties of operator constitutive relations in mechanics of deformable solid","authors":"Dimitri Georgievskii","doi":"10.2298/tam230719008g","DOIUrl":"https://doi.org/10.2298/tam230719008g","url":null,"abstract":"The constitutive relations between stresses and strains in the mechanics of a deformable solid, including their operator connection, are considered. Some important and frequently occurring properties of tangent modulus and tangent pliability as rank four tensors are described. Depending on this, a possible classification of continuous media is proposed. Scleronomous and rheonomic media, homogeneous and inhomogeneous media (in particular, composites), media with memory, spatially nonlocal media, materials with hard or soft characteristics are distinguished. For non-linearly elastic isotropic media, the apparatus of tensor nonlinear isotropic functions of one argument is developed. Particular attention is paid to the three-term representation of power tensor series in three-dimensional space, reversibility of tensor functions, Taylor tensor series, tensor linearity (quasilinearity) and nonlinearity.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135052868","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}
Structures in the form of cylindrical ribbed shells and panels are widely used in engineering and construction. The problem of the action of moving loads on an infinitely long cylindrical shell, reinforced along the outer surface with longitudinal stiffeners and containing a viscoelastic inertial filler, is considered. The moving load is transferred to the shell only through the ribs, and there is no load outside the ribs. The discreteness of the location of the ribs is taken into account by writing the equations of motion of the beams, followed by the satisfaction of the conjugation conditions. The influence of the number and stiffness of ribs on the nature of the distribution of shell displacements and contact pressure at the boundary of a viscoelastic filler is shown. The movement of the shell is described by classic equations based on the Kirchhoff-Love hypothesis; for the filler, dynamic equations of the theory of visco-elasticity are used. It has been established that the reinforcement of shells with longitudinal ribs (oscillations of a cantilevered cylindrical shell) leads to a decrease in natural frequencies and damping coefficients in some shells, an increase in the density of the spectrum of natural frequencies, and the appearance of intermediate forms and forms with the same wave numbers, but with different frequencies. External forces increase natural frequencies and damping coefficients. It is found that the frequencies for the inner edges are lower than for the outer edges. In the high-frequency zone, any efforts reduce the natural frequencies and the damping coefficient. This means that additional mass plays a more significant role than additional rigidity. Consequently, the longitudinal strengthening of the shell worsens its dynamic properties.
{"title":"Control of resonant oscillations of viscoelastic systems","authors":"Ismoil Safarov, Muhsin Teshaev","doi":"10.2298/tam220510007s","DOIUrl":"https://doi.org/10.2298/tam220510007s","url":null,"abstract":"Structures in the form of cylindrical ribbed shells and panels are widely used in engineering and construction. The problem of the action of moving loads on an infinitely long cylindrical shell, reinforced along the outer surface with longitudinal stiffeners and containing a viscoelastic inertial filler, is considered. The moving load is transferred to the shell only through the ribs, and there is no load outside the ribs. The discreteness of the location of the ribs is taken into account by writing the equations of motion of the beams, followed by the satisfaction of the conjugation conditions. The influence of the number and stiffness of ribs on the nature of the distribution of shell displacements and contact pressure at the boundary of a viscoelastic filler is shown. The movement of the shell is described by classic equations based on the Kirchhoff-Love hypothesis; for the filler, dynamic equations of the theory of visco-elasticity are used. It has been established that the reinforcement of shells with longitudinal ribs (oscillations of a cantilevered cylindrical shell) leads to a decrease in natural frequencies and damping coefficients in some shells, an increase in the density of the spectrum of natural frequencies, and the appearance of intermediate forms and forms with the same wave numbers, but with different frequencies. External forces increase natural frequencies and damping coefficients. It is found that the frequencies for the inner edges are lower than for the outer edges. In the high-frequency zone, any efforts reduce the natural frequencies and the damping coefficient. This means that additional mass plays a more significant role than additional rigidity. Consequently, the longitudinal strengthening of the shell worsens its dynamic properties.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135551380","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}
Honeycomb plates are commonly used in aerospace structures for their lightweight and rigidity characteristics. However, for modeling honeycomb structure many equivalent methods are established to represent the behavior of detailed model. In the present paper, we focus on the equivalent methods precision compared to the miso-scale model. Therefore, we compare two equivalent assumptions regarding the detailed design of a honeycomb plate (miso-scale). Then, we perform modal analysis and microvibration assessments to verify the effectiveness of methods accuracy regarding modes values and microvibration transmissibility. It can be noticed that each method has the advantage to be a candidate to represent the honeycomb plate behavior due to the lower error percentage. The sandwich plate theory gives minimal difference error for both modal analysis and the measurement of disturbance transmissibility from the reaction wheel to the structures. Hence, the sandwich theory is more or less accurate for representing a detailed model for structural analysis of honeycomb plates.
{"title":"Assessment of equivalent methods effectiveness used for honeycomb plate structure","authors":"A Mankour, A. Smahat","doi":"10.2298/tam221115004m","DOIUrl":"https://doi.org/10.2298/tam221115004m","url":null,"abstract":"Honeycomb plates are commonly used in aerospace structures for their lightweight and rigidity characteristics. However, for modeling honeycomb structure many equivalent methods are established to represent the behavior of detailed model. In the present paper, we focus on the equivalent methods precision compared to the miso-scale model. Therefore, we compare two equivalent assumptions regarding the detailed design of a honeycomb plate (miso-scale). Then, we perform modal analysis and microvibration assessments to verify the effectiveness of methods accuracy regarding modes values and microvibration transmissibility. It can be noticed that each method has the advantage to be a candidate to represent the honeycomb plate behavior due to the lower error percentage. The sandwich plate theory gives minimal difference error for both modal analysis and the measurement of disturbance transmissibility from the reaction wheel to the structures. Hence, the sandwich theory is more or less accurate for representing a detailed model for structural analysis of honeycomb plates.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"44 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91231063","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, the behavior of a satellite trajectory near the equilibrium points of the Sun-Earth system is studied. The equations describing the motion of the satellite in the circular restricted three body problem for the Sun-Earth system, are discussed for their ordinary differential equations form, and Lagrange points are determined. Then, the stability is studied at each Lagrange point. The trajectories of a satellite starting its motion near Lagrange points are illustrated, showing the stability and instability behavior. Finally, the unstable trajectory is controlled by using ??2-method at ??1 as an example.
{"title":"The behavior of a satellite trajectory near the equilibrium points of sun-earth system and its control","authors":"L. Shalby, Noha Ali","doi":"10.2298/tam220816003s","DOIUrl":"https://doi.org/10.2298/tam220816003s","url":null,"abstract":"In this paper, the behavior of a satellite trajectory near the equilibrium points of the Sun-Earth system is studied. The equations describing the motion of the satellite in the circular restricted three body problem for the Sun-Earth system, are discussed for their ordinary differential equations form, and Lagrange points are determined. Then, the stability is studied at each Lagrange point. The trajectories of a satellite starting its motion near Lagrange points are illustrated, showing the stability and instability behavior. Finally, the unstable trajectory is controlled by using ??2-method at ??1 as an example.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"91 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76992185","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 mechanism is formulated and a principle is proposed that makes it possible to explain and, in some cases, to predict the shape of secondary flows of Prandtl?s second kind that arise in turbulent flows in straight pipes of non-circular cross-section. The effectiveness of the proposed principle is demonstrated by a number of known examples from the literature. The results of this work provide a rational basis for understanding the reasons for the formation and prediction of the shape of secondary flows of Prandtl?s second kind in straight pipes of non-circular cross-section.
{"title":"Secondary flows of Prandtl’s second kind. Mechanism of formation and methods of prediction","authors":"Nikolay Nikitin","doi":"10.2298/tam231005008n","DOIUrl":"https://doi.org/10.2298/tam231005008n","url":null,"abstract":"In this paper a mechanism is formulated and a principle is proposed that makes it possible to explain and, in some cases, to predict the shape of secondary flows of Prandtl?s second kind that arise in turbulent flows in straight pipes of non-circular cross-section. The effectiveness of the proposed principle is demonstrated by a number of known examples from the literature. The results of this work provide a rational basis for understanding the reasons for the formation and prediction of the shape of secondary flows of Prandtl?s second kind in straight pipes of non-circular cross-section.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"179 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135666940","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}
A novel quasi-brittle damage model implemented under quasistatic loading condition using bond-based peridynamics theory for progressive failure is proposed to better predict damage initiation and propagation in solid materials. Since peridynamics equation of motion was invented in dynamic configuration, this paper applies the adaptive dynamic relaxation equation to achieve steady-state in peridynamics formulation. To accurately characterise the progressive failure process in cohesive materials, we incorporate the dynamic equation with the novel damage model for quasi-brittle materials. Computational examples of 2D compressive and tensile problems using the proposed model are presented. This paper presents advancement by incorporating the adaptive dynamic equation approach into a new damage model for quasi-brittle materials. This amalgamation allows for a more accurate representation of the behavior of damaged materials, particularly in static or quasi-static loading situations, bringing the framework closer to reality. This research paves the way for the peridynamics formulation to be employed for a far broader class of loading condition behaviour than it is now able to.
{"title":"A new quasi-brittle damage model implemented under quasi-static condition using bond-based peridynamics theory for progressive failure","authors":"H. Yakin, M. Rejab, Nur Hashim, N. Nikabdullah","doi":"10.2298/tam230404006y","DOIUrl":"https://doi.org/10.2298/tam230404006y","url":null,"abstract":"A novel quasi-brittle damage model implemented under quasistatic loading condition using bond-based peridynamics theory for progressive failure is proposed to better predict damage initiation and propagation in solid materials. Since peridynamics equation of motion was invented in dynamic configuration, this paper applies the adaptive dynamic relaxation equation to achieve steady-state in peridynamics formulation. To accurately characterise the progressive failure process in cohesive materials, we incorporate the dynamic equation with the novel damage model for quasi-brittle materials. Computational examples of 2D compressive and tensile problems using the proposed model are presented. This paper presents advancement by incorporating the adaptive dynamic equation approach into a new damage model for quasi-brittle materials. This amalgamation allows for a more accurate representation of the behavior of damaged materials, particularly in static or quasi-static loading situations, bringing the framework closer to reality. This research paves the way for the peridynamics formulation to be employed for a far broader class of loading condition behaviour than it is now able to.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"8 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89519413","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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