M. Gorgone, F. Oliveri, A. Ricciardello, P. Rogolino
In this paper, after reviewing the form of the constitutive equations for a third grade Korteweg fluid, recently derived by means of an extended Liu procedure, an equilibrium problem is investigated. By considering a two-dimensional setting, a single nonlinear elliptic equation is derived such that the equilibrium conditions are identically satisfied. Such an equation is discussed both analytically and numerically. Moreover, by considering a particular boundary value problem of Dirichlet type, some preliminary numerical solutions are presented.
{"title":"Two-dimensional equilibrium configurations in Korteweg fluids","authors":"M. Gorgone, F. Oliveri, A. Ricciardello, P. Rogolino","doi":"10.2298/tam220930008g","DOIUrl":"https://doi.org/10.2298/tam220930008g","url":null,"abstract":"In this paper, after reviewing the form of the constitutive equations for a third grade Korteweg fluid, recently derived by means of an extended Liu procedure, an equilibrium problem is investigated. By considering a two-dimensional setting, a single nonlinear elliptic equation is derived such that the equilibrium conditions are identically satisfied. Such an equation is discussed both analytically and numerically. Moreover, by considering a particular boundary value problem of Dirichlet type, some preliminary numerical solutions are presented.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"2 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89478633","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}
Given a Lie group G, we elaborate the dynamics on T+T+G and T+TG, which is given by a Hamiltonian, as well as the dynamics on the Tulczyjew symplectic space TT+G, which may be defined by a Lagrangian or a Hamiltonian function. As the trivializations we adapted respect the group structures of the iterated bundles, we exploit all possible subgroup reductions (Poisson, symplectic or both) of higher order dynamics.
{"title":"Tulczyjew’s triplet for lie groups III: Higher order dynamics and reductions for iterated bundles","authors":"Ougul Esen, H. Gumral, S. Sutlu","doi":"10.2298/TAM210312009E","DOIUrl":"https://doi.org/10.2298/TAM210312009E","url":null,"abstract":"Given a Lie group G, we elaborate the dynamics on T+T+G and T+TG,\u0000 which is given by a Hamiltonian, as well as the dynamics on the Tulczyjew\u0000 symplectic space TT+G, which may be defined by a Lagrangian or a\u0000 Hamiltonian function. As the trivializations we adapted respect the group\u0000 structures of the iterated bundles, we exploit all possible subgroup\u0000 reductions (Poisson, symplectic or both) of higher order dynamics.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83208972","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 study a class of initial value problems subject to nonlinear partial differential equations of hyperbolic type. A new topological approach is applied to prove the existence of nontrivial nonnegative solutions. More precisely, we propose a new integral representation of the solutions for the considered initial value problems and using this integral representation we establish existence of classical solutions for the considered classes of nonlinear wave equations.
{"title":"Classical solutions for a class of nonlinear wave equations","authors":"S. Georgiev, K. Mebarki, K. Zennir","doi":"10.2298/tam201123013g","DOIUrl":"https://doi.org/10.2298/tam201123013g","url":null,"abstract":"We study a class of initial value problems subject to nonlinear partial differential equations of hyperbolic type. A new topological approach is applied to prove the existence of nontrivial nonnegative solutions. More precisely, we propose a new integral representation of the solutions for the considered initial value problems and using this integral representation we establish existence of classical solutions for the considered classes of nonlinear wave equations.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"475 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87230599","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 metric graph model is suggested for description of elastic vibration in a network of rods under the assumption that the rod lengths vary in time. A single rod and star-like graph are considered. Influence of the length variation law on the vibration distribution is investigated. For high-frequency length variation one observes a fast transition to high-frequency amplitude distribution
{"title":"A time-dependent metric graph with a fourth-order operator on the edges","authors":"I. Blinova, A.S. Gnedash, I. Popov","doi":"10.2298/tam200928007b","DOIUrl":"https://doi.org/10.2298/tam200928007b","url":null,"abstract":"The metric graph model is suggested for description of elastic vibration in a network of rods under the assumption that the rod lengths vary in time. A single rod and star-like graph are considered. Influence of the length variation law on the vibration distribution is investigated. For high-frequency length variation one observes a fast transition to high-frequency amplitude distribution","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73683774","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 article aims to find the buckling loads for pinned?rotationally restrained shallow circular arches in terms of the rotational end stiffness, geometry and material distribution. The loading is a concentrated vertical force placed at the crown. A geometrically nonlinear model is presented which relates not only the axial force but also the bending moment to the membrane strain. The nonlinear load-strain relationship is established between the strain and load parameters. This equation is then solved and evaluated analytically. It turns out that the stiffness of the end-restraint has, in general, a significant effect on the lowest buckling load. At the same time, some geometries are not affected by this. As the stiffness becomes zero, the arch is pinned-pinned and as the stiffness tends to infinity, the arch behaves as if it were pinned-fixed and has the best load-bearing abilities.
{"title":"Stability of pinned-rotationally restrained arches","authors":"L. Peter","doi":"10.2298/tam200402010k","DOIUrl":"https://doi.org/10.2298/tam200402010k","url":null,"abstract":"The article aims to find the buckling loads for pinned?rotationally restrained shallow circular arches in terms of the rotational end stiffness, geometry and material distribution. The loading is a concentrated vertical force placed at the crown. A geometrically nonlinear model is presented which relates not only the axial force but also the bending moment to the membrane strain. The nonlinear load-strain relationship is established between the strain and load parameters. This equation is then solved and evaluated analytically. It turns out that the stiffness of the end-restraint has, in general, a significant effect on the lowest buckling load. At the same time, some geometries are not affected by this. As the stiffness becomes zero, the arch is pinned-pinned and as the stiffness tends to infinity, the arch behaves as if it were pinned-fixed and has the best load-bearing abilities.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"29 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90762517","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, we consider a nonlinear Timoshenko equation. First, we prove the local existence solution by the Faedo?Galerkin method, and, under suitable assumptions with positive initial energy, we prove that the local existence is global in time. Finally, the stability result is established based on Komornik?s integral inequality.
{"title":"Existence and stability results of a nonlinear Timoshenko equation with damping and source terms","authors":"Amar Ouaoua, A. Khaldi, M. Maouni","doi":"10.2298/TAM200703002O","DOIUrl":"https://doi.org/10.2298/TAM200703002O","url":null,"abstract":"In this paper, we consider a nonlinear Timoshenko equation. First, we prove the local existence solution by the Faedo?Galerkin method, and, under suitable assumptions with positive initial energy, we prove that the local existence is global in time. Finally, the stability result is established based on Komornik?s integral inequality.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"129 12","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72568575","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}
This is a review article which elaborates the results presented in [1], where the variational principle of Herglotz type with a Lagrangian that depends on fractional derivatives of both real and complex orders is formulated and the invariance of this principle under the action of a local group of symmetries is determined. The conservation law for the corresponding fractional Euler Lagrange equation is obtained and a sequence of approximations of a fractional Euler-Lagrange equation by systems of integer order equations established and analyzed.
{"title":"Noether’s theorem for Herglotz type variational problems utilizing complex fractional derivatives","authors":"M. Janev, T. Atanacković, S. Pilipovic","doi":"10.2298/tam210913011j","DOIUrl":"https://doi.org/10.2298/tam210913011j","url":null,"abstract":"This is a review article which elaborates the results presented in [1], where the variational principle of Herglotz type with a Lagrangian that depends on fractional derivatives of both real and complex orders is formulated and the invariance of this principle under the action of a local group of symmetries is determined. The conservation law for the corresponding fractional Euler Lagrange equation is obtained and a sequence of approximations of a fractional Euler-Lagrange equation by systems of integer order equations established and analyzed.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"480 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78120629","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}
J. Svorcan, Aleksandar Kovačević, Dragoljub Tanović, M. Hasan
The paper focuses on the possibilities of adequately simulating complex flow fields that appear around small-scale propellers of multicopter aircraft. Such unmanned air vehicles (UAVs) are steadily gaining popularity for their diverse applications (surveillance, communication, deliveries, etc.) and the need for a viable (i.e. usable, satisfactory, practical) computational tool is also surging. From an engineering standpoint, it is important to obtain sufficiently accurate predictions of flow field variables in a reasonable amount of time so that the design process can be fast and efficient, in particular the subsequent structural and flight mechanics analyses. That is why more or less standard fluid flow models, e.g. Reynolds-averaged Navier-Stokes (RANS) equations solved by the finite volume method (FVM), are constantly being employed and validated. On the other hand, special attention must be given to various flow peculiarities occurring around the blade segments shaped like airfoils since these flows are characterized by small chords (length-scales), low speeds and, therefore, low Reynolds numbers (Re) and pronounced viscous effects. The investigated low-Re flows include both transitional and turbulent zones, laminar separation bubbles (LSBs), flow separation, as well as rotating wakes, which require somewhat specific approaches to flow modeling (advanced turbulence models, fine spatial and temporal scales, etc). Here, the conducted computations (around stationary blade segments as well as rotating rotors), closed by different turbulence models, are presented and explained. Various qualitative and quantitative results are provided, compared and discussed. The main possibilities and obstacles of each computational approach are mentioned. Where possible, numerical results are validated against experimental data. The correspondence between the two sets of results can be considered satisfactory (relative differences for the thrust coefficient amount to 15%, while they are even lower for the torque coefficient). It can be concluded that the choice of turbulence modeling (and/or resolving) greatly affects the final output, even in design operating conditions (at medium angles-of-attack where laminar, attached flow dominates). Distinctive flow phenomena still exist, and in order to be adequately simulated, a comprehensive modeling approach should be adopted.
{"title":"Towards viable flow simulations of small-scale rotors and blade segments","authors":"J. Svorcan, Aleksandar Kovačević, Dragoljub Tanović, M. Hasan","doi":"10.2298/tam211011008s","DOIUrl":"https://doi.org/10.2298/tam211011008s","url":null,"abstract":"The paper focuses on the possibilities of adequately simulating complex flow fields that appear around small-scale propellers of multicopter aircraft. Such unmanned air vehicles (UAVs) are steadily gaining popularity for their diverse applications (surveillance, communication, deliveries, etc.) and the need for a viable (i.e. usable, satisfactory, practical) computational tool is also surging. From an engineering standpoint, it is important to obtain sufficiently accurate predictions of flow field variables in a reasonable amount of time so that the design process can be fast and efficient, in particular the subsequent structural and flight mechanics analyses. That is why more or less standard fluid flow models, e.g. Reynolds-averaged Navier-Stokes (RANS) equations solved by the finite volume method (FVM), are constantly being employed and validated. On the other hand, special attention must be given to various flow peculiarities occurring around the blade segments shaped like airfoils since these flows are characterized by small chords (length-scales), low speeds and, therefore, low Reynolds numbers (Re) and pronounced viscous effects. The investigated low-Re flows include both transitional and turbulent zones, laminar separation bubbles (LSBs), flow separation, as well as rotating wakes, which require somewhat specific approaches to flow modeling (advanced turbulence models, fine spatial and temporal scales, etc). Here, the conducted computations (around stationary blade segments as well as rotating rotors), closed by different turbulence models, are presented and explained. Various qualitative and quantitative results are provided, compared and discussed. The main possibilities and obstacles of each computational approach are mentioned. Where possible, numerical results are validated against experimental data. The correspondence between the two sets of results can be considered satisfactory (relative differences for the thrust coefficient amount to 15%, while they are even lower for the torque coefficient). It can be concluded that the choice of turbulence modeling (and/or resolving) greatly affects the final output, even in design operating conditions (at medium angles-of-attack where laminar, attached flow dominates). Distinctive flow phenomena still exist, and in order to be adequately simulated, a comprehensive modeling approach should be adopted.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"108 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79388133","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 study the problem of propagating longitudinal waves in an elastic rod connected to a locally damaged foundation through a thin elastic layer. The motion of the rigid foundation blocks is considered predetermined. We formulated the initial-boundary problem for the Klein?Gordon equation with a discontinuous right-hand side. The nonstationary fields of displacements, velocities, and deformations were investigated by the Laplace integral transformation method. Examples of sudden divergence of fragments of the foundation by a given value and their mutual separation at a constant speed are considered.
{"title":"Longitudinal waves in an elastic rod caused by sudden damage to the foundation","authors":"I. Shatskyi, V. Perepichka, M. Vaskovskyi","doi":"10.2298/TAM200615001S","DOIUrl":"https://doi.org/10.2298/TAM200615001S","url":null,"abstract":"We study the problem of propagating longitudinal waves in an elastic rod connected to a locally damaged foundation through a thin elastic layer. The motion of the rigid foundation blocks is considered predetermined. We formulated the initial-boundary problem for the Klein?Gordon equation with a discontinuous right-hand side. The nonstationary fields of displacements, velocities, and deformations were investigated by the Laplace integral transformation method. Examples of sudden divergence of fragments of the foundation by a given value and their mutual separation at a constant speed are considered.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"61 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75824888","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, we investigate a nonlinear viscoelastic equation. By assuming time-varying delay feedback acting on the boundary, under certain assumptions on the given data, the general decay estimates for the energy are established by introducing suitable Lyapunov functionals. This model improves earlier ones in the literature in which only the dissipative term in the feedback condition is considered.
{"title":"Asymptotic stability of a viscoelastic problem with time-varying delay in boundary feedback","authors":"Abita Rahmoune","doi":"10.2298/TAM200629003R","DOIUrl":"https://doi.org/10.2298/TAM200629003R","url":null,"abstract":"In this paper, we investigate a nonlinear viscoelastic equation. By assuming time-varying delay feedback acting on the boundary, under certain assumptions on the given data, the general decay estimates for the energy are established by introducing suitable Lyapunov functionals. This model improves earlier ones in the literature in which only the dissipative term in the feedback condition is considered.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"96 1","pages":"3-3"},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75918134","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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