Krysko, Anton V.
Overview
Works:  13 works in 41 publications in 2 languages and 742 library holdings 

Roles:  Author, htt 
Classifications:  TA660.P6, 624.17765 
Publication Timeline
.
Most widely held works by
Anton V Krysko
Thermodynamics of plates and shells by
J Awrejcewicz(
)
20 editions published between 2006 and 2007 in English and held by 505 WorldCat member libraries worldwide
"This monograph is devoted to the investigation of nonlinear dynamics of plates and shells embedded in a temperature field. Numerical approaches and rigorous mathematical proofs of solution existence in certain classes of differential equations with various dimensions are applied. Both closed shelltype constructions and sectorial shells are studied. The considered problems are approximated by 2D and 3D constructions taking into account various types of nonlinearities (geometrical and/or physical with coupled deformation and temperature fields), and are subjected to an action of stationary and nonstationary thermal loads. Variational and finite difference numerical approaches are used to study numerous problems important for civil and mechanical engineering. Furthermore, a novel and exact computational method to solve large systems of linear algebraic equations especially suitable for computational speed and memory storage of a computer is proposed." "This book is expected to be useful for researchers, engineers and students dealing with thermal and dynamical problems of stability and strength of shelltype constructions."Jacket
20 editions published between 2006 and 2007 in English and held by 505 WorldCat member libraries worldwide
"This monograph is devoted to the investigation of nonlinear dynamics of plates and shells embedded in a temperature field. Numerical approaches and rigorous mathematical proofs of solution existence in certain classes of differential equations with various dimensions are applied. Both closed shelltype constructions and sectorial shells are studied. The considered problems are approximated by 2D and 3D constructions taking into account various types of nonlinearities (geometrical and/or physical with coupled deformation and temperature fields), and are subjected to an action of stationary and nonstationary thermal loads. Variational and finite difference numerical approaches are used to study numerous problems important for civil and mechanical engineering. Furthermore, a novel and exact computational method to solve large systems of linear algebraic equations especially suitable for computational speed and memory storage of a computer is proposed." "This book is expected to be useful for researchers, engineers and students dealing with thermal and dynamical problems of stability and strength of shelltype constructions."Jacket
Mathematical Models of Higher Orders : Shells in Temperature Fields by
V. A Krysʹko(
)
7 editions published in 2019 in English and held by 189 WorldCat member libraries worldwide
This book offers a valuable methodological approach to the stateoftheart of the classical plate/shell mathematical models, exemplifying the vast range of mathematical models of nonlinear dynamics and statics of continuous mechanical structural members. The main objective highlights the need for further study of the classical problem of shell dynamics consisting of mathematical modeling, derivation of nonlinear PDEs, and of finding their solutions based on the development of new and effective numerical techniques. The book is designed for a broad readership of graduate students in mechanical and civil engineering, applied mathematics, and physics, as well as to researchers and professionals interested in a rigorous and comprehensive study of modeling nonlinear phenomena governed by PDEs
7 editions published in 2019 in English and held by 189 WorldCat member libraries worldwide
This book offers a valuable methodological approach to the stateoftheart of the classical plate/shell mathematical models, exemplifying the vast range of mathematical models of nonlinear dynamics and statics of continuous mechanical structural members. The main objective highlights the need for further study of the classical problem of shell dynamics consisting of mathematical modeling, derivation of nonlinear PDEs, and of finding their solutions based on the development of new and effective numerical techniques. The book is designed for a broad readership of graduate students in mechanical and civil engineering, applied mathematics, and physics, as well as to researchers and professionals interested in a rigorous and comprehensive study of modeling nonlinear phenomena governed by PDEs
Deterministic chaos in one dimensional continuous systems by
J Awrejcewicz(
)
3 editions published in 2016 in English and held by 39 WorldCat member libraries worldwide
"This book focuses on the computational analysis of nonlinear vibrations of structural members (beams, plates, panels, shells), where the studied dynamical problems can be reduced to the consideration of one spatial variable and time. The reduction is carried out based on a formal mathematical approach aimed at reducing the problems with infinite dimension to finite ones. The process also includes a transition from governing nonlinear partial differential equations to a set of finite number of ordinary differential equations. Beginning with an overview of the recent results devoted to the analysis and control of nonlinear dynamics of structural members, placing emphasis on stability, buckling, bifurcation and deterministic chaos, simple chaotic systems are briefly discussed. Next, bifurcation and chaotic dynamics of the EulerBernoulli and Timoshenko beams including the geometric and physical nonlinearity as well as the elasticplastic deformations are illustrated. Despite the employed classical numerical analysis of nonlinear phenomena, the various wavelet transforms and the four Lyapunov exponents are used to detect, monitor and possibly control chaos, hyperchaos, hyperhyperchaos and deep chaos exhibited by rectangular platestrips and cylindrical panels. The book is intended for postgraduate and doctoral students, applied mathematicians, physicists, teachers and lecturers of universities and companies dealing with a nonlinear dynamical system, as well as theoretically inclined engineers of mechanical and civil engineering."Provided by publisher
3 editions published in 2016 in English and held by 39 WorldCat member libraries worldwide
"This book focuses on the computational analysis of nonlinear vibrations of structural members (beams, plates, panels, shells), where the studied dynamical problems can be reduced to the consideration of one spatial variable and time. The reduction is carried out based on a formal mathematical approach aimed at reducing the problems with infinite dimension to finite ones. The process also includes a transition from governing nonlinear partial differential equations to a set of finite number of ordinary differential equations. Beginning with an overview of the recent results devoted to the analysis and control of nonlinear dynamics of structural members, placing emphasis on stability, buckling, bifurcation and deterministic chaos, simple chaotic systems are briefly discussed. Next, bifurcation and chaotic dynamics of the EulerBernoulli and Timoshenko beams including the geometric and physical nonlinearity as well as the elasticplastic deformations are illustrated. Despite the employed classical numerical analysis of nonlinear phenomena, the various wavelet transforms and the four Lyapunov exponents are used to detect, monitor and possibly control chaos, hyperchaos, hyperhyperchaos and deep chaos exhibited by rectangular platestrips and cylindrical panels. The book is intended for postgraduate and doctoral students, applied mathematicians, physicists, teachers and lecturers of universities and companies dealing with a nonlinear dynamical system, as well as theoretically inclined engineers of mechanical and civil engineering."Provided by publisher
Istoricheskaja Grammatika Drevnerusskogo Jazyka : Vol. I, II, III, IV(
Book
)
1 edition published in 2000 in Russian and held by 2 WorldCat member libraries worldwide
1 edition published in 2000 in Russian and held by 2 WorldCat member libraries worldwide
Mathematical Models of Higher Orders: Shells in Temperature Fields by
Anton V Krysko(
Book
)
1 edition published in 2019 in Undetermined and held by 2 WorldCat member libraries worldwide
1 edition published in 2019 in Undetermined and held by 2 WorldCat member libraries worldwide
Chaotic dynamics of flexible beams driven by external white noise(
)
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
Abstract: Mathematical models of continuous structural members (beams, plates and shells) subjected to an external additive white noise are studied. The structural members are considered as systems with infinite number of degrees of freedom. We show that in mechanical structural systems external noise can not only lead to quantitative changes in the system dynamics (that is obvious), but also cause the qualitative, and sometimes surprising changes in the vibration regimes. Furthermore, we show that scenarios of the transition from regular to chaotic regimes quantified by Fast Fourier Transform (FFT) can lead to erroneous conclusions, and a support of the wavelet analysis is needed. We have detected and illustrated the modifications of classical three scenarios of transition from regular vibrations to deterministic chaos. The carried out numerical experiment shows that the white noise lowers the threshold for transition into spatiotemporal chaotic dynamics. A transition into chaos via the proposed modified scenarios developed in this work is sensitive to small noise and significantly reduces occurrence of periodic vibrations. Increase of noise intensity yields decrease of the duration of the laminar signal range, i.e., time between two successive turbulent bursts decreases. Scenario of transition into chaos of the studied mechanical structures essentially depends on the control parameters, and it can be different in different zones of the constructed charts (control parameter planes). Furthermore, we found an interesting phenomenon, when increase of the noise intensity yields surprisingly the vibrational characteristics with a lack of noisy effect (chaos is destroyed by noise and windows of periodicity appear). Highlights: Novel scenarios of transition from regular to chaotic dynamics are detected. Combination of the classical scenarios are illustrated. White noise may either destroy or amplify deterministic chaos
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
Abstract: Mathematical models of continuous structural members (beams, plates and shells) subjected to an external additive white noise are studied. The structural members are considered as systems with infinite number of degrees of freedom. We show that in mechanical structural systems external noise can not only lead to quantitative changes in the system dynamics (that is obvious), but also cause the qualitative, and sometimes surprising changes in the vibration regimes. Furthermore, we show that scenarios of the transition from regular to chaotic regimes quantified by Fast Fourier Transform (FFT) can lead to erroneous conclusions, and a support of the wavelet analysis is needed. We have detected and illustrated the modifications of classical three scenarios of transition from regular vibrations to deterministic chaos. The carried out numerical experiment shows that the white noise lowers the threshold for transition into spatiotemporal chaotic dynamics. A transition into chaos via the proposed modified scenarios developed in this work is sensitive to small noise and significantly reduces occurrence of periodic vibrations. Increase of noise intensity yields decrease of the duration of the laminar signal range, i.e., time between two successive turbulent bursts decreases. Scenario of transition into chaos of the studied mechanical structures essentially depends on the control parameters, and it can be different in different zones of the constructed charts (control parameter planes). Furthermore, we found an interesting phenomenon, when increase of the noise intensity yields surprisingly the vibrational characteristics with a lack of noisy effect (chaos is destroyed by noise and windows of periodicity appear). Highlights: Novel scenarios of transition from regular to chaotic dynamics are detected. Combination of the classical scenarios are illustrated. White noise may either destroy or amplify deterministic chaos
ThermoDynamics of Plates and Shells. Foundations of Engineering Mechanics(
)
1 edition published in 2007 in English and held by 1 WorldCat member library worldwide
The present monograph is devoted to nonlinear dynamics of thin plates and shells with thermosensitive excitation. Since the investigated mathematical models are of different sizes (two and threedimensional differential equation) and different types (differential equations of hyperbolic and parabolic types with respect to spatial coordinates), there is no hope to solve them analytically. On the other hand, the proposed mathematical models and the proposed methods of their solutions allow to achieve more accurate approximation to the real processes exhibited by dynamics of shell (plate)  type structures with thermosensitive excitation. Furthermore, in this monograph an emphasis is put into a rigorous mathematical treatment of the obtained differential equations, since it helps efficiently in further developing of various suitable numerical algorithms to solve the stated problems
1 edition published in 2007 in English and held by 1 WorldCat member library worldwide
The present monograph is devoted to nonlinear dynamics of thin plates and shells with thermosensitive excitation. Since the investigated mathematical models are of different sizes (two and threedimensional differential equation) and different types (differential equations of hyperbolic and parabolic types with respect to spatial coordinates), there is no hope to solve them analytically. On the other hand, the proposed mathematical models and the proposed methods of their solutions allow to achieve more accurate approximation to the real processes exhibited by dynamics of shell (plate)  type structures with thermosensitive excitation. Furthermore, in this monograph an emphasis is put into a rigorous mathematical treatment of the obtained differential equations, since it helps efficiently in further developing of various suitable numerical algorithms to solve the stated problems
Kontaktnye zadači teorii mnogoslojnych nespajannych plastin na prjamougolʹnom plane by
V. A Krysʹko(
Book
)
1 edition published in 1998 in Russian and held by 1 WorldCat member library worldwide
1 edition published in 1998 in Russian and held by 1 WorldCat member library worldwide
Chaotic dynamics of size dependent Timoshenko beams with functionally graded properties along their thickness(
)
1 edition published in 2017 in English and held by 1 WorldCat member library worldwide
Highlights: Dynamics of the sizedependent FG Timoshenko beams with the von Kármán nonlinearity are studied. The reference line simplifying the governing equations is introduced. The results are validated through Lyapunov and wavelet spectra. Influence of size and material grading coefficients on vibration characteristics is given. Transition from regular to chaotic beam vibrations coincides with the RuelleTakensNewhouse scenario. Abstract: Chaotic dynamics of microbeams made of functionally graded materials (FGMs) is investigated in this paper based on the modified couple stress theory and von Kármán geometric nonlinearity. We assume that the beam properties are graded along the thickness direction. The influence of sizedependent and functionally graded coefficients on the vibration characteristics, scenarios of transition from regular to chaotic vibrations as well as a series of static problems with an emphasis put on the loaddeflection behavior are studied. Our theoretical/numerical analysis is supported by methods of nonlinear dynamics and the qualitative theory of differential equations supplemented by Fourier and wavelet spectra, phase portraits, and Lyapunov exponents spectra estimated by different algorithms, including Wolf's, Rosenstein's, Kantz's, and neural networks. We have also detected and numerically validated a general scenario governing transition into chaotic vibrations, which follows the classical RuelleTakensNewhouse scenario for the considered values of the sizedependent and grading parameters
1 edition published in 2017 in English and held by 1 WorldCat member library worldwide
Highlights: Dynamics of the sizedependent FG Timoshenko beams with the von Kármán nonlinearity are studied. The reference line simplifying the governing equations is introduced. The results are validated through Lyapunov and wavelet spectra. Influence of size and material grading coefficients on vibration characteristics is given. Transition from regular to chaotic beam vibrations coincides with the RuelleTakensNewhouse scenario. Abstract: Chaotic dynamics of microbeams made of functionally graded materials (FGMs) is investigated in this paper based on the modified couple stress theory and von Kármán geometric nonlinearity. We assume that the beam properties are graded along the thickness direction. The influence of sizedependent and functionally graded coefficients on the vibration characteristics, scenarios of transition from regular to chaotic vibrations as well as a series of static problems with an emphasis put on the loaddeflection behavior are studied. Our theoretical/numerical analysis is supported by methods of nonlinear dynamics and the qualitative theory of differential equations supplemented by Fourier and wavelet spectra, phase portraits, and Lyapunov exponents spectra estimated by different algorithms, including Wolf's, Rosenstein's, Kantz's, and neural networks. We have also detected and numerically validated a general scenario governing transition into chaotic vibrations, which follows the classical RuelleTakensNewhouse scenario for the considered values of the sizedependent and grading parameters
Mathematical modelling of physically/geometrically nonlinear microshells with account of coupling of temperature and deformation
fields(
)
1 edition published in 2017 in English and held by 1 WorldCat member library worldwide
Abstract: A mathematical model of flexible physically nonlinear microshells is presented in this paper, taking into account the coupling of temperature and deformation fields. The geometric nonlinearity is introduced by means of the von Kármán shell theory and the shells are assumed to be shallow. The KirchhoffLove hypothesis is employed, whereas the physical nonlinearity is yielded by the theory of plastic deformations. The coupling of fields is governed by the variational Biot principle. The derived partial differential equations are reduced to ordinary differential equations by means of both the finite difference method of the second order and the FaedoGalerkin method. The Cauchy problem is solved with methods of the RungeKutta type, i.e. the RungeKutta methods of the 4th (RK4) and the 2nd (RK2) order, the RungeKuttaFehlberg method of the 4th order (rkf45), the CashKarp method of the 4th order (RKCK), the RungeKuttaDormandPrince (RKDP) method of the 8th order (rk8pd), the implicit 2ndorder (rk2imp) and 4thorder (rk4imp) methods. Each of the employed approaches is investigated with respect to time and spatial coordinates. Analysis of stability and nature (type) of vibrations is carried out with the help of the Largest Lyapunov Exponent (LLE) using the Wolf, Rosenstein and Kantz methods as well as the modified method of neural networks. The existence of a solution of the FaedoGalerkin method for geometrically nonlinear problems of thermoelasticity is formulated and proved. A priori estimates of the convergence of the FaedoGalerkin method are reported. Examples of calculation of vibrations and loss of stability of square shells are illustrated and discussed
1 edition published in 2017 in English and held by 1 WorldCat member library worldwide
Abstract: A mathematical model of flexible physically nonlinear microshells is presented in this paper, taking into account the coupling of temperature and deformation fields. The geometric nonlinearity is introduced by means of the von Kármán shell theory and the shells are assumed to be shallow. The KirchhoffLove hypothesis is employed, whereas the physical nonlinearity is yielded by the theory of plastic deformations. The coupling of fields is governed by the variational Biot principle. The derived partial differential equations are reduced to ordinary differential equations by means of both the finite difference method of the second order and the FaedoGalerkin method. The Cauchy problem is solved with methods of the RungeKutta type, i.e. the RungeKutta methods of the 4th (RK4) and the 2nd (RK2) order, the RungeKuttaFehlberg method of the 4th order (rkf45), the CashKarp method of the 4th order (RKCK), the RungeKuttaDormandPrince (RKDP) method of the 8th order (rk8pd), the implicit 2ndorder (rk2imp) and 4thorder (rk4imp) methods. Each of the employed approaches is investigated with respect to time and spatial coordinates. Analysis of stability and nature (type) of vibrations is carried out with the help of the Largest Lyapunov Exponent (LLE) using the Wolf, Rosenstein and Kantz methods as well as the modified method of neural networks. The existence of a solution of the FaedoGalerkin method for geometrically nonlinear problems of thermoelasticity is formulated and proved. A priori estimates of the convergence of the FaedoGalerkin method are reported. Examples of calculation of vibrations and loss of stability of square shells are illustrated and discussed
Mathematical model of a threelayer micro and nanobeams based on the hypotheses of the GrigolyukChulkov and the modified
couple stress theory(
)
1 edition published in 2017 in English and held by 1 WorldCat member library worldwide
Highlights: Mathematical models of the functionally graded micro/nanobeams are given. The proposed model allows taking into account large differences of layers thickness. Computation example validating our theory is included. Both static and dynamic problems are solved. Abstract: The mathematical model of threelayered beams developed based on the hypothesis of the GrigolyukChulkov and the modified couple stress theory and the size depended equations governing the layers motions on the micro and nanoscales is constructed. The Hamilton's principle yields the novel equations of motion as well as the boundary/initial conditions regarding beams displacement. The latter ones clearly exhibit the size dependent dynamics of the studied micro and nanobeams, and the introduced theory overlaps with the classical beam equations for large enough layer thickness. In particular, a threelayer beam with the microlayer thickness has been investigated with respect to the classical theory of GrigolyukChulkov. The derived boundary problem is of sixth order and can be solved analytically in the case of statics. The carried out numerical experiments allowed to detect and explain size dependent effects exhibited by the microbeams. The beam deflections and stress yielded by the employed couple stress model are less than those predicted by the classical GrigolyukChulkov theory, while the estimated eigen frequencies are higher, respectively. It has been shown that the proposed model can be reduced to the classical threelayer GrigolyukChulkov beam through increase of the layers thickness, which validates our approach
1 edition published in 2017 in English and held by 1 WorldCat member library worldwide
Highlights: Mathematical models of the functionally graded micro/nanobeams are given. The proposed model allows taking into account large differences of layers thickness. Computation example validating our theory is included. Both static and dynamic problems are solved. Abstract: The mathematical model of threelayered beams developed based on the hypothesis of the GrigolyukChulkov and the modified couple stress theory and the size depended equations governing the layers motions on the micro and nanoscales is constructed. The Hamilton's principle yields the novel equations of motion as well as the boundary/initial conditions regarding beams displacement. The latter ones clearly exhibit the size dependent dynamics of the studied micro and nanobeams, and the introduced theory overlaps with the classical beam equations for large enough layer thickness. In particular, a threelayer beam with the microlayer thickness has been investigated with respect to the classical theory of GrigolyukChulkov. The derived boundary problem is of sixth order and can be solved analytically in the case of statics. The carried out numerical experiments allowed to detect and explain size dependent effects exhibited by the microbeams. The beam deflections and stress yielded by the employed couple stress model are less than those predicted by the classical GrigolyukChulkov theory, while the estimated eigen frequencies are higher, respectively. It has been shown that the proposed model can be reduced to the classical threelayer GrigolyukChulkov beam through increase of the layers thickness, which validates our approach
Nonsymmetric forms of nonlinear vibrations of flexible cylindrical panels and plates under longitudinal load and additive
white noise(
)
1 edition published in 2018 in English and held by 1 WorldCat member library worldwide
Abstract: Parametric nonlinear vibrations of flexible cylindrical panels subjected to additive white noise are studied. The governing Marguerre equations are investigated using the finite difference method (FDM) of the secondorder accuracy and the RungeKutta method. The considered mechanical structural member is treated as a system of many/infinite number of degrees of freedom (DoF). The dependence of chaotic vibrations on the number of DoFs is investigated. Reliability of results is guaranteed by comparing the results obtained using two qualitatively different methods to reduce the problem of PDEs (partial differential equations) to ODEs (ordinary differential equations), i.e. the FaedoGalerkin method in higher approximations and the 4th and 6th order FDM. The Cauchy problem obtained by the FDM is eventually solved using the 4thorder RungeKutta methods. The numerical experiment yielded, for a certain set of parameters, the nonsymmetric vibration modes/forms with and without white noise. In particular, it has been illustrated and discussed that action of white noise on chaotic vibrations implies quasiperiodicity, whereas the previously nonsymmetric vibration modes are closer to symmetric ones. Highlights: PDEs are modelled by infinite number of ODEs. Results reliability are discussed and validated. Fourier wavelet spectra and Lyapunov exponents are computed. Novel results of noisy transition from regular to chaotic dynamics are reported. Occurrence of symmetric/nonsymmetric modes under noise are illustrated
1 edition published in 2018 in English and held by 1 WorldCat member library worldwide
Abstract: Parametric nonlinear vibrations of flexible cylindrical panels subjected to additive white noise are studied. The governing Marguerre equations are investigated using the finite difference method (FDM) of the secondorder accuracy and the RungeKutta method. The considered mechanical structural member is treated as a system of many/infinite number of degrees of freedom (DoF). The dependence of chaotic vibrations on the number of DoFs is investigated. Reliability of results is guaranteed by comparing the results obtained using two qualitatively different methods to reduce the problem of PDEs (partial differential equations) to ODEs (ordinary differential equations), i.e. the FaedoGalerkin method in higher approximations and the 4th and 6th order FDM. The Cauchy problem obtained by the FDM is eventually solved using the 4thorder RungeKutta methods. The numerical experiment yielded, for a certain set of parameters, the nonsymmetric vibration modes/forms with and without white noise. In particular, it has been illustrated and discussed that action of white noise on chaotic vibrations implies quasiperiodicity, whereas the previously nonsymmetric vibration modes are closer to symmetric ones. Highlights: PDEs are modelled by infinite number of ODEs. Results reliability are discussed and validated. Fourier wavelet spectra and Lyapunov exponents are computed. Novel results of noisy transition from regular to chaotic dynamics are reported. Occurrence of symmetric/nonsymmetric modes under noise are illustrated
ThermoDynamics of Plates and Shells(
)
1 edition published in 2007 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 2007 in English and held by 0 WorldCat member libraries worldwide
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Building materials BuildingsVibration Differential equations, Partial Engineering Engineering mathematics Materials Mechanics, Applied Physics Plates (Engineering) Shells (Engineering) Shells (Engineering)Mathematical models Strength of materialsMathematics Thermodynamics ThermodynamicsMathematical models Vibration