M. Lazarevic, Darko Radojevic, Stjepko Pisl, G. Maione
This article addresses the problem of finite-time stability for uncertain neutral nonhomogeneous fractional-order systems with time-varying delays where a stability test procedure is suggested. Based on the extended form of the generalized Gr?nwall inequality, a new sufficient condition for robust finite-time stability of such systems is established. Finally, a numerical example is given to show the effectiveness of the obtained result.
{"title":"Robust finite-time stability of uncertain neutral nonhomogeneous fractional-order systems with time-varying delays","authors":"M. Lazarevic, Darko Radojevic, Stjepko Pisl, G. Maione","doi":"10.2298/tam2000016l","DOIUrl":"https://doi.org/10.2298/tam2000016l","url":null,"abstract":"This article addresses the problem of finite-time stability for uncertain neutral nonhomogeneous fractional-order systems with time-varying delays where a stability test procedure is suggested. Based on the extended form of the generalized Gr?nwall inequality, a new sufficient condition for robust finite-time stability of such systems is established. Finally, a numerical example is given to show the effectiveness of the obtained result.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"2 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79116713","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 system of viscoelastic equations with degenerate damping and source terms in a bounded domain. Under appropriate assumptions on the parameters, degenerate damping terms and the relaxation functions 𝜛 𝑖 , ( 𝑖 = 1 , 2), we prove local existence and unique- ness of the solution by using the Faedo–Galerkin method with a new scenario. Then, we prove the blow-up of weak solutions to problem (1.1). This improves earlier results in the literature [ 6 , 23 , 25 ].
{"title":"Local existence and blow-up of solutions for coupled viscoelastic wave equations with degenerate damping terms","authors":"E. Pişkin, F. Ekinci, K. Zennir","doi":"10.2298/tam200428008p","DOIUrl":"https://doi.org/10.2298/tam200428008p","url":null,"abstract":". In this paper, we investigate a nonlinear system of viscoelastic equations with degenerate damping and source terms in a bounded domain. Under appropriate assumptions on the parameters, degenerate damping terms and the relaxation functions 𝜛 𝑖 , ( 𝑖 = 1 , 2), we prove local existence and unique- ness of the solution by using the Faedo–Galerkin method with a new scenario. Then, we prove the blow-up of weak solutions to problem (1.1). This improves earlier results in the literature [ 6 , 23 , 25 ].","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"115 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75711605","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. Borokinni, O. Fadodun, O. Layeni, A. Akinola, B. Olokuntoye
. This paper investigates size effect phenomena associated with the divergence of the transpose of plastic distortion in plastically deformed isotropic materials. The principle of virtual power, balance of energy, second law of thermodynamics, and codirectionality hypothesis are used to formulate the governing microforce balance and thermodynamically consistent constitutive relations for dissipative microscopic stresses associated with the plastic distortion and skew part of the Burgers tensor. It is obtained that the defect energy through the strictly skew Burgers tensor is converted to the defect energy via the divergence of the plastic distortion. The presence of material length scales in the obtained flow rule indicates that it is possible to appre- hend size effects associated with the skew part of the Burgers tensor during the inhomogeneous plastic flow of solid material. Finally and amongst other things, it is shown that the dependency of the microscopic stress vector on the divergence of plastic distortion rate leads to weakening and strengthening effects in the flow rule.
{"title":"Size effects associated with skew symmetric burgers tensor","authors":"A. Borokinni, O. Fadodun, O. Layeni, A. Akinola, B. Olokuntoye","doi":"10.2298/tam191125001b","DOIUrl":"https://doi.org/10.2298/tam191125001b","url":null,"abstract":". This paper investigates size effect phenomena associated with the divergence of the transpose of plastic distortion in plastically deformed isotropic materials. The principle of virtual power, balance of energy, second law of thermodynamics, and codirectionality hypothesis are used to formulate the governing microforce balance and thermodynamically consistent constitutive relations for dissipative microscopic stresses associated with the plastic distortion and skew part of the Burgers tensor. It is obtained that the defect energy through the strictly skew Burgers tensor is converted to the defect energy via the divergence of the plastic distortion. The presence of material length scales in the obtained flow rule indicates that it is possible to appre- hend size effects associated with the skew part of the Burgers tensor during the inhomogeneous plastic flow of solid material. Finally and amongst other things, it is shown that the dependency of the microscopic stress vector on the divergence of plastic distortion rate leads to weakening and strengthening effects in the flow rule.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"33 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81424379","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 survey of the selected published criteria ? expressed by the properties of the system matrices ? for the stability and instability of linear mechanical systems subjected to potential and circulatory forces is presented. In particular, recent generalizations of the well-known Merkin instability theorem are reported. Several simple numerical examples are used to illustrate the usefulness of the presented criteria and also to compare them.
{"title":"On the stability and instability criteria for circulatory systems: A review","authors":"M. Bulatovic","doi":"10.2298/tam201021013b","DOIUrl":"https://doi.org/10.2298/tam201021013b","url":null,"abstract":"A survey of the selected published criteria ? expressed by the properties of the system matrices ? for the stability and instability of linear mechanical systems subjected to potential and circulatory forces is presented. In particular, recent generalizations of the well-known Merkin instability theorem are reported. Several simple numerical examples are used to illustrate the usefulness of the presented criteria and also to compare them.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"187 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88469086","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 complete classification of left invariant metrics of arbitrary signature on solvable Lie groups is given. By identifying the Lie algebra with the algebra of left invariant vector fields on the corresponding Lie group ??, the inner product ??,?? on g = Lie G extends uniquely to a left invariant metric ?? on the Lie group. Therefore, the classification problem is reduced to the problem of classification of pairs (g, ??,??) known as the metric Lie algebras. Although two metric algebras may be isometric even if the corresponding Lie algebras are non-isomorphic, this paper will show that in the 4-dimensional solvable case isometric means isomorphic. Finally, the curvature properties of the obtained metric algebras are considered and, as a corollary, the classification of flat, locally symmetric, Ricciflat, Ricci-parallel and Einstein metrics is also given.
本文给出了可解李群上任意签名左不变度量的完全分类。用相应李群上的左不变向量场的代数来识别李代数?，内积?? ??on g = Lie g唯一地扩展到一个左不变度规??在李群里。因此，分类问题被简化为被称为度量李代数的对(g， ??，??)的分类问题。尽管两个度量代数可以是等距的，即使对应的李代数是非同构的，但本文将证明在四维可解的情况下，等距意味着同构。最后，考虑了所得到的度量代数的曲率性质，并作为推论，给出了平面、局部对称、Ricciflat、Ricci-parallel和Einstein度量的分类。
{"title":"Classification of left invariant metrics on 4-dimensional solvable Lie groups","authors":"T. Šukilović","doi":"10.2298/tam200826014s","DOIUrl":"https://doi.org/10.2298/tam200826014s","url":null,"abstract":"In this paper the complete classification of left invariant metrics of arbitrary signature on solvable Lie groups is given. By identifying the Lie algebra with the algebra of left invariant vector fields on the corresponding Lie group ??, the inner product ??,?? on g = Lie G extends uniquely to a left invariant metric ?? on the Lie group. Therefore, the classification problem is reduced to the problem of classification of pairs (g, ??,??) known as the metric Lie algebras. Although two metric algebras may be isometric even if the corresponding Lie algebras are non-isomorphic, this paper will show that in the 4-dimensional solvable case isometric means isomorphic. Finally, the curvature properties of the obtained metric algebras are considered and, as a corollary, the classification of flat, locally symmetric, Ricciflat, Ricci-parallel and Einstein metrics is also given.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"9 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75465532","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 give a brief introduction and a partial survey of some of the results about spectral numbers in symplectic topology that we are aware of. Without attempting to be comprehensive, we will select just some of the constructions and ideas that, according to our personal taste and our point of view, give a flavor of this fast developing theory.
{"title":"A brief survey of the spectral numbers in floer homology","authors":"J. Katić, D. Milinkovi'c, Jovan Nikolic","doi":"10.2298/tam200831012k","DOIUrl":"https://doi.org/10.2298/tam200831012k","url":null,"abstract":"We give a brief introduction and a partial survey of some of the results about spectral numbers in symplectic topology that we are aware of. Without attempting to be comprehensive, we will select just some of the constructions and ideas that, according to our personal taste and our point of view, give a flavor of this fast developing theory.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"4 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73281743","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 translational-rotational motion of a triaxial body with constant dynamic shape and variable size and mass in a non-stationary Newtonian central gravitational field is investigated. Differential equations of motion of the triaxial body in the relative coordinate system with the origin at the center of a non-stationary spherical body are obtained. The axes of the Cartesian coordinate system fixed to the non-stationary triaxial body are coincident with its principal axes and their relative orientation is assumed to remain unchanged in the course of evolution. An analytical expression for the force function of the Newtonian interaction of the triaxial body of variable mass and size with a spherical body of variable size and mass is obtained. Differential equations of translational-rotational motion of the non-stationary triaxial body are derived in Jacobi osculating variables and are studied with the perturba- tion theory methods. The perturbing function is expanded in power series in terms of the Delaunay–Andoyer elements up to the second harmonic element inclusive. The evolution equations of the translational-rotational motion of the non-stationary triaxial body are obtained in the osculating elements of Delaunay–Andoyer.
{"title":"Evolution equations of translational-rotational motion of a non-stationary triaxial body in a central gravitational field","authors":"M. Minglibayev, A. Prokopenya, O. Baisbayeva","doi":"10.2298/tam191130007m","DOIUrl":"https://doi.org/10.2298/tam191130007m","url":null,"abstract":". The translational-rotational motion of a triaxial body with constant dynamic shape and variable size and mass in a non-stationary Newtonian central gravitational field is investigated. Differential equations of motion of the triaxial body in the relative coordinate system with the origin at the center of a non-stationary spherical body are obtained. The axes of the Cartesian coordinate system fixed to the non-stationary triaxial body are coincident with its principal axes and their relative orientation is assumed to remain unchanged in the course of evolution. An analytical expression for the force function of the Newtonian interaction of the triaxial body of variable mass and size with a spherical body of variable size and mass is obtained. Differential equations of translational-rotational motion of the non-stationary triaxial body are derived in Jacobi osculating variables and are studied with the perturba- tion theory methods. The perturbing function is expanded in power series in terms of the Delaunay–Andoyer elements up to the second harmonic element inclusive. The evolution equations of the translational-rotational motion of the non-stationary triaxial body are obtained in the osculating elements of Delaunay–Andoyer.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"24 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82766336","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 paper considers the problem of modal analysis and finding the closed-form solution to free vibrations of planar serial frame structures composed of Euler?Bernoulli beams of variable cross-sectional geometric characteristics in the case of axially functionally graded materials. Each of these beams is performing coupled axial and bending vibrations, where coupling occurs due to the boundary conditions at their joints. The numerical procedure for solving the system of partial differential equations, after the separation of variables, is reduced to solving the two-point boundary value problem of ordinary linear differential equations with nonlinear coefficients and linear boundary conditions. In this case, it is possible to transfer the boundary conditions and reduce the problem to the Cauchy initial value problem. Also, it is possible to analyze the influence of different parameters on the structure dynamic behavior. The method is applicable in the case of different boundary conditions at the right and left ends of such structures, as illustrated by an appropriate numerical example.
{"title":"Free vibrations of planar serial frame structures in the case of axially functionally graded materials","authors":"A. Obradović, S. Šalinić, A. Tomović","doi":"10.2298/tam2000017o","DOIUrl":"https://doi.org/10.2298/tam2000017o","url":null,"abstract":"This paper considers the problem of modal analysis and finding the closed-form solution to free vibrations of planar serial frame structures composed of Euler?Bernoulli beams of variable cross-sectional geometric characteristics in the case of axially functionally graded materials. Each of these beams is performing coupled axial and bending vibrations, where coupling occurs due to the boundary conditions at their joints. The numerical procedure for solving the system of partial differential equations, after the separation of variables, is reduced to solving the two-point boundary value problem of ordinary linear differential equations with nonlinear coefficients and linear boundary conditions. In this case, it is possible to transfer the boundary conditions and reduce the problem to the Cauchy initial value problem. Also, it is possible to analyze the influence of different parameters on the structure dynamic behavior. The method is applicable in the case of different boundary conditions at the right and left ends of such structures, as illustrated by an appropriate numerical example.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"6 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81651263","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 simple procedure is presented for the study of the conservation of energy equation with dissipation in continuum mechanics in 1D. This procedure is used to transform this nonlinear evolution-diffusion equation into a hyperbolic PDE; specifically, a second-order quasi-linear wave equation. An immediate implication of this procedure is the formation of a least action principle for the balance of energy with dissipation. The corresponding action functional enables us to establish a complete analytic mechanics for thermomechanical systems: a Lagrangian?Hamiltonian theory, integrals of motion, bracket formalism, and Noether?s theorem. Furthermore, we apply our procedure iteratively and produce an infinite sequence of interlocked variational principles, a variational hierarchy, where at each level or iteration the full implication of the least action principle can be shown again.
{"title":"An analytical mechanics approach to the first law of thermodynamics and construction of a variational hierarchy","authors":"H. Said","doi":"10.2298/tam200315011s","DOIUrl":"https://doi.org/10.2298/tam200315011s","url":null,"abstract":"A simple procedure is presented for the study of the conservation of energy equation with dissipation in continuum mechanics in 1D. This procedure is used to transform this nonlinear evolution-diffusion equation into a hyperbolic PDE; specifically, a second-order quasi-linear wave equation. An immediate implication of this procedure is the formation of a least action principle for the balance of energy with dissipation. The corresponding action functional enables us to establish a complete analytic mechanics for thermomechanical systems: a Lagrangian?Hamiltonian theory, integrals of motion, bracket formalism, and Noether?s theorem. Furthermore, we apply our procedure iteratively and produce an infinite sequence of interlocked variational principles, a variational hierarchy, where at each level or iteration the full implication of the least action principle can be shown again.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"10 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88126620","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 consider the multi-dimensional generalisation of the problem of a sphere, with axi-symmetric mass distribution, that rolls without slipping or spinning over a plane. Using recent results from Garc?a-Naranjo [21] and Garc?a-Naranjo and Marrero [22], we show that the reduced equations of motion possess an invariant measure and may be represented in Hamiltonian form by Chaplygin?s reducing multiplier method. We also prove a general result on the existence of first integrals for certain Hamiltonisable Chaplygin systems with internal symmetries that is used to determine conserved quantities of the problem.
{"title":"Hamiltonisation, measure preservation and first integrals of the multi-dimensional rubber Routh sphere","authors":"Luis C. Garc'ia-Naranjo","doi":"10.2298/TAM190130004G","DOIUrl":"https://doi.org/10.2298/TAM190130004G","url":null,"abstract":"We consider the multi-dimensional generalisation of the problem of a sphere, with axi-symmetric mass distribution, that rolls without slipping or spinning over a plane. Using recent results from Garc?a-Naranjo [21] and Garc?a-Naranjo and Marrero [22], we show that the reduced equations of motion possess an invariant measure and may be represented in Hamiltonian form by Chaplygin?s reducing multiplier method. We also prove a general result on the existence of first integrals for certain Hamiltonisable Chaplygin systems with internal symmetries that is used to determine conserved quantities of the problem.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"41 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79075216","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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