Daulet Nurakhmetov - Academia.edu (original) (raw)
Papers by Daulet Nurakhmetov
Уфимский математический журнал, 2011
Известия высших учебных заведений. Математика, 2014
Alexandria Engineering Journal
Journal of Sound and Vibration
BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2021
The inverse problem of determining the weight of three intermediate masses on a uniform beam from... more The inverse problem of determining the weight of three intermediate masses on a uniform beam from the known three natural frequencies has been solved. The performed numerical analysis allows restoring the value of only the second mass in a unique way. The inverse problem of determining the weight of three intermediate masses is solved uniquely except in the case when the first and the third masses are located geometrically symmetric relative to the middle of the beam. The hybrid algorithm for the unique solving inverse problem of determining the weight of three intermediate masses has been developed. The first three natural frequencies of the beam are calculated numerically by using the Maple computer package. Analytical relations between the masses are found.
International Journal of Mathematics and Physics, 2021
In this article is considered the models of uniform Euler-Bernoulli beams with an arbitrary varia... more In this article is considered the models of uniform Euler-Bernoulli beams with an arbitrary variable coefficient of foundation on a finite segment. The variable of foundation corresponds to the Winkler model. The control problem the first eigenvalues of the beam vibration is investigated. Two types of fastenings at the ends are considered: clamped-clamped and hinged-hinged. The control is based on the Kanguzhin algorithm through integral perturbations of one of the boundary conditions of the original problem. Conditions for the boundary parameters for controlling the first eigenvalues are found. First, a result is formulated regarding the control of the first eigenvalue of the oscillation of the Euler-Bernoulli beam with hinge fastening at both ends. The result is then extended to control with several eigenvalues for this beam, which are important from the point of view of the application. Such questions are especially relevant when studying the resonant natural frequencies of a mechanical system. A similar result was obtained for a Euler-Bernoulli beam with clamped fastening at both ends. Such results of eigenvalue control of a mechanical system contribute to the creation of various non-destructive testing devices that are widely used in technical acoustics.
Springer Proceedings in Mathematics & Statistics, 2017
We consider well-posedness issues of problems of the Laplace operator in the unit circle with two... more We consider well-posedness issues of problems of the Laplace operator in the unit circle with two internal points. For boundary value problems, one of the main issues is the well-posedness of the problem. When the problem is considered in a non-simply-connected domain, there usually appear additional conditions depending on the features of the domain under consideration. If for the well-posedness of the problem, in addition to the boundary conditions, one requires to take into account the internal communications of the domain, then such problems are called internal boundary value problems. For such problems there is written out a class of functions in which there exist such kinds of well-posed problems. A constructive method for constructing solutions to such problems is developed. As an illustration, examples are considered.
In this article we try to solve the inverse problem of determining the coefficients of stiffness ... more In this article we try to solve the inverse problem of determining the coefficients of stiffness of the intermediates on the springs on the rod from the two known natural frequencies. We find sufficient conditions for the existence of a unique solution to the inverse problem of determining the stiffness on the intermediates of the springs of non-terminal points of the rod from the two known natural frequencies. It was shown that for the determination of the coefficients of stiffness of the springs played an essential role in the geometric symmetry of the arrangement of the spring relative to the rod center.
In this paper, we consider the second order differential operator of Lσ with nonlocal boundary co... more In this paper, we consider the second order differential operator of Lσ with nonlocal boundary conditions in the functional space L2(0, 1). We construct an explicit system of root functions of Lσ. We study the biorthogonal of properties the systems of root functions of Lσ. We develop a method for constructing biorthogonal systems of root functions of well-posed boundary value problems for the second order differential operator with nonlocal boundary conditions.
Acta Mechanica Sinica, 2021
Nonlinear Dynamics, 2021
Analysis of dynamic pull-in voltage for a micro-electro-mechanical oscillator of platform type is... more Analysis of dynamic pull-in voltage for a micro-electro-mechanical oscillator of platform type is performed. The lumped mass model for the actuated micro-cantilever beam made of power-law material is established and the bifurcation is investigated with respect to the dimensionless voltage parameter using simple phase plane analysis. The necessary and sufficient conditions for the existence of periodic solutions to the lumped mass model equation are derived and proved analytically. The pull-in conditions on the strength coefficient, power-law exponent, and voltage are determined. Moreover, the response time is analyzed and approximate periodic solutions are derived. The established analytical results are illustrated numerically.
Symmetry, 2020
In this paper, the models of Euler–Bernoulli beams on the Winkler foundations are considered. The... more In this paper, the models of Euler–Bernoulli beams on the Winkler foundations are considered. The novelty of the research is in consideration of the models with an arbitrary variable coefficient of foundation. Qualitative results that influence the symmetry of the coefficient of foundation on the spectral properties of the corresponding problems are obtained, for which specific variable coefficients of foundation are tested using numerical calculations. Three types of fixing at the ends are studied: clamped-clamped, hinged-hinged and free-free. The conditions of the stiffness and types of beam fixing have been found for the set of eigenvalues of boundary value problems on a full segment and can be represented as two groups of the eigenvalues of certain problems on a half segment. Such qualitative spectral properties of a mechanical system can contribute to the creation of various algorithms for nondestructive testing, which are widely used in technical acoustics.
Applied and Computational Mechanics, 2018
A novel procedure based on the Sturm's theorem for real-valued polynomials is developed to predic... more A novel procedure based on the Sturm's theorem for real-valued polynomials is developed to predict and identify periodic and non-periodic solutions for a graphene-based MEMS lumped parameter model with general initial conditions. It is demonstrated that under specific conditions on the lumped parameters and the initial conditions, the model has certain periodic solutions and otherwise there are no such solutions. This theoretical procedure is made practical by numerical implementations with Python scripts to verify the predicted behaviour of the solutions. Numerical simulations are performed with sample data to justify by this procedure the analytically predicted existence of periodic solutions.
Matematicheskie Zametki, 2018
Communications in Nonlinear Science and Numerical Simulation, 2020
This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Acta Mechanica Sinica, 2019
We extend the well-known concept and results for lumped parameters used in the spring-like models... more We extend the well-known concept and results for lumped parameters used in the spring-like models for linear materials to Hollomon's power-law materials. We provide the generalized stiffness and effective mass coefficients for the power-law Euler-Bernoulli beams under standard geometric and load conditions. In particular, our mass-spring lumped parameter models reduce to the classical models when Hollomon's law reduces to Hooke's law. Since there are no known solutions to the dynamic power-law beam equations, solutions to our mass lumped models are compared to the low-order Galerkin approximations in the case of cantilever beams with circular and rectangular cross-sections.
Journal of Low Frequency Noise, Vibration and Active Control, 2019
The initial value problem for a lumped parameter model arising from design of magneto–electromech... more The initial value problem for a lumped parameter model arising from design of magneto–electromechanical device with a current-carrying conductor is analyzed. The differential equation is nonlinear because it includes the magnetic force term. The analysis for the dynamic pull-in occurring in the system is presented. The pull-in threshold is given analytically in terms of model parameters. Sufficient conditions for the existence of periodic solutions are proved analytically and verified numerically. The results can be useful for understanding and design of one-degree-of-freedom models of magnetically actuated beams.
PHYSICO-MATHEMATICAL SERIES, 2019
Б а с р е д а к т о р ы ф.-м.ғ.д., проф., ҚР ҰҒА академигі Ғ.М. Мұтанов Р е д а к ц и я а л қ а с... more Б а с р е д а к т о р ы ф.-м.ғ.д., проф., ҚР ҰҒА академигі Ғ.М. Мұтанов Р е д а к ц и я а л қ а с ы: Жұмаділдаев А.С. проф., академик (Қазақстан) Кальменов Т.Ш. проф., академик (Қазақстан) Жантаев Ж.Ш. проф., корр.-мүшесі (Қазақстан) Өмірбаев У.У. проф. корр.-мүшесі (Қазақстан) Жүсіпов М.А. проф. (Қазақстан) Жұмабаев Д.С. проф. (Қазақстан) Асанова А.Т. проф. (Қазақстан) Бошкаев К.А. PhD докторы (Қазақстан) Сұраған Д. корр.-мүшесі (Қазақстан) Quevedo Hernando проф. (Мексика), Джунушалиев В.Д. проф. (Қырғыстан) Вишневский И.Н. проф., академик (Украина) Ковалев А.М. проф., академик (Украина) Михалевич А.А. проф., академик (Белорус) Пашаев А. проф., академик (Əзірбайжан) Такибаев Н.Ж. проф., академик (Қазақстан), бас ред. орынбасары Тигиняну И. проф., академик (Молдова) «ҚР ҰҒА Хабарлары. Физика-математикалық сериясы».
Nonlinear Analysis: Real World Applications, 2019
Bifurcation analysis of dynamic pull-in for a lumped mass model is presented. The restoring force... more Bifurcation analysis of dynamic pull-in for a lumped mass model is presented. The restoring force of the spring is derived based on the nonlinear constitutive stress-strain law and the driving force of the mass attached to the spring is based on the electrostatic Coulomb force, respectively. The analysis is performed on the resulting nonlinear spring-mass equation with initial conditions. The necessary and sufficient conditions for the existence of periodic solutions are derived analytically and illustrated numerically. The conditions for bifurcation points on the parameters associated with the second-order elastic stiffness constant and the voltage are determined.
Уфимский математический журнал, 2011
Известия высших учебных заведений. Математика, 2014
Alexandria Engineering Journal
Journal of Sound and Vibration
BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2021
The inverse problem of determining the weight of three intermediate masses on a uniform beam from... more The inverse problem of determining the weight of three intermediate masses on a uniform beam from the known three natural frequencies has been solved. The performed numerical analysis allows restoring the value of only the second mass in a unique way. The inverse problem of determining the weight of three intermediate masses is solved uniquely except in the case when the first and the third masses are located geometrically symmetric relative to the middle of the beam. The hybrid algorithm for the unique solving inverse problem of determining the weight of three intermediate masses has been developed. The first three natural frequencies of the beam are calculated numerically by using the Maple computer package. Analytical relations between the masses are found.
International Journal of Mathematics and Physics, 2021
In this article is considered the models of uniform Euler-Bernoulli beams with an arbitrary varia... more In this article is considered the models of uniform Euler-Bernoulli beams with an arbitrary variable coefficient of foundation on a finite segment. The variable of foundation corresponds to the Winkler model. The control problem the first eigenvalues of the beam vibration is investigated. Two types of fastenings at the ends are considered: clamped-clamped and hinged-hinged. The control is based on the Kanguzhin algorithm through integral perturbations of one of the boundary conditions of the original problem. Conditions for the boundary parameters for controlling the first eigenvalues are found. First, a result is formulated regarding the control of the first eigenvalue of the oscillation of the Euler-Bernoulli beam with hinge fastening at both ends. The result is then extended to control with several eigenvalues for this beam, which are important from the point of view of the application. Such questions are especially relevant when studying the resonant natural frequencies of a mechanical system. A similar result was obtained for a Euler-Bernoulli beam with clamped fastening at both ends. Such results of eigenvalue control of a mechanical system contribute to the creation of various non-destructive testing devices that are widely used in technical acoustics.
Springer Proceedings in Mathematics & Statistics, 2017
We consider well-posedness issues of problems of the Laplace operator in the unit circle with two... more We consider well-posedness issues of problems of the Laplace operator in the unit circle with two internal points. For boundary value problems, one of the main issues is the well-posedness of the problem. When the problem is considered in a non-simply-connected domain, there usually appear additional conditions depending on the features of the domain under consideration. If for the well-posedness of the problem, in addition to the boundary conditions, one requires to take into account the internal communications of the domain, then such problems are called internal boundary value problems. For such problems there is written out a class of functions in which there exist such kinds of well-posed problems. A constructive method for constructing solutions to such problems is developed. As an illustration, examples are considered.
In this article we try to solve the inverse problem of determining the coefficients of stiffness ... more In this article we try to solve the inverse problem of determining the coefficients of stiffness of the intermediates on the springs on the rod from the two known natural frequencies. We find sufficient conditions for the existence of a unique solution to the inverse problem of determining the stiffness on the intermediates of the springs of non-terminal points of the rod from the two known natural frequencies. It was shown that for the determination of the coefficients of stiffness of the springs played an essential role in the geometric symmetry of the arrangement of the spring relative to the rod center.
In this paper, we consider the second order differential operator of Lσ with nonlocal boundary co... more In this paper, we consider the second order differential operator of Lσ with nonlocal boundary conditions in the functional space L2(0, 1). We construct an explicit system of root functions of Lσ. We study the biorthogonal of properties the systems of root functions of Lσ. We develop a method for constructing biorthogonal systems of root functions of well-posed boundary value problems for the second order differential operator with nonlocal boundary conditions.
Acta Mechanica Sinica, 2021
Nonlinear Dynamics, 2021
Analysis of dynamic pull-in voltage for a micro-electro-mechanical oscillator of platform type is... more Analysis of dynamic pull-in voltage for a micro-electro-mechanical oscillator of platform type is performed. The lumped mass model for the actuated micro-cantilever beam made of power-law material is established and the bifurcation is investigated with respect to the dimensionless voltage parameter using simple phase plane analysis. The necessary and sufficient conditions for the existence of periodic solutions to the lumped mass model equation are derived and proved analytically. The pull-in conditions on the strength coefficient, power-law exponent, and voltage are determined. Moreover, the response time is analyzed and approximate periodic solutions are derived. The established analytical results are illustrated numerically.
Symmetry, 2020
In this paper, the models of Euler–Bernoulli beams on the Winkler foundations are considered. The... more In this paper, the models of Euler–Bernoulli beams on the Winkler foundations are considered. The novelty of the research is in consideration of the models with an arbitrary variable coefficient of foundation. Qualitative results that influence the symmetry of the coefficient of foundation on the spectral properties of the corresponding problems are obtained, for which specific variable coefficients of foundation are tested using numerical calculations. Three types of fixing at the ends are studied: clamped-clamped, hinged-hinged and free-free. The conditions of the stiffness and types of beam fixing have been found for the set of eigenvalues of boundary value problems on a full segment and can be represented as two groups of the eigenvalues of certain problems on a half segment. Such qualitative spectral properties of a mechanical system can contribute to the creation of various algorithms for nondestructive testing, which are widely used in technical acoustics.
Applied and Computational Mechanics, 2018
A novel procedure based on the Sturm's theorem for real-valued polynomials is developed to predic... more A novel procedure based on the Sturm's theorem for real-valued polynomials is developed to predict and identify periodic and non-periodic solutions for a graphene-based MEMS lumped parameter model with general initial conditions. It is demonstrated that under specific conditions on the lumped parameters and the initial conditions, the model has certain periodic solutions and otherwise there are no such solutions. This theoretical procedure is made practical by numerical implementations with Python scripts to verify the predicted behaviour of the solutions. Numerical simulations are performed with sample data to justify by this procedure the analytically predicted existence of periodic solutions.
Matematicheskie Zametki, 2018
Communications in Nonlinear Science and Numerical Simulation, 2020
This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Acta Mechanica Sinica, 2019
We extend the well-known concept and results for lumped parameters used in the spring-like models... more We extend the well-known concept and results for lumped parameters used in the spring-like models for linear materials to Hollomon's power-law materials. We provide the generalized stiffness and effective mass coefficients for the power-law Euler-Bernoulli beams under standard geometric and load conditions. In particular, our mass-spring lumped parameter models reduce to the classical models when Hollomon's law reduces to Hooke's law. Since there are no known solutions to the dynamic power-law beam equations, solutions to our mass lumped models are compared to the low-order Galerkin approximations in the case of cantilever beams with circular and rectangular cross-sections.
Journal of Low Frequency Noise, Vibration and Active Control, 2019
The initial value problem for a lumped parameter model arising from design of magneto–electromech... more The initial value problem for a lumped parameter model arising from design of magneto–electromechanical device with a current-carrying conductor is analyzed. The differential equation is nonlinear because it includes the magnetic force term. The analysis for the dynamic pull-in occurring in the system is presented. The pull-in threshold is given analytically in terms of model parameters. Sufficient conditions for the existence of periodic solutions are proved analytically and verified numerically. The results can be useful for understanding and design of one-degree-of-freedom models of magnetically actuated beams.
PHYSICO-MATHEMATICAL SERIES, 2019
Б а с р е д а к т о р ы ф.-м.ғ.д., проф., ҚР ҰҒА академигі Ғ.М. Мұтанов Р е д а к ц и я а л қ а с... more Б а с р е д а к т о р ы ф.-м.ғ.д., проф., ҚР ҰҒА академигі Ғ.М. Мұтанов Р е д а к ц и я а л қ а с ы: Жұмаділдаев А.С. проф., академик (Қазақстан) Кальменов Т.Ш. проф., академик (Қазақстан) Жантаев Ж.Ш. проф., корр.-мүшесі (Қазақстан) Өмірбаев У.У. проф. корр.-мүшесі (Қазақстан) Жүсіпов М.А. проф. (Қазақстан) Жұмабаев Д.С. проф. (Қазақстан) Асанова А.Т. проф. (Қазақстан) Бошкаев К.А. PhD докторы (Қазақстан) Сұраған Д. корр.-мүшесі (Қазақстан) Quevedo Hernando проф. (Мексика), Джунушалиев В.Д. проф. (Қырғыстан) Вишневский И.Н. проф., академик (Украина) Ковалев А.М. проф., академик (Украина) Михалевич А.А. проф., академик (Белорус) Пашаев А. проф., академик (Əзірбайжан) Такибаев Н.Ж. проф., академик (Қазақстан), бас ред. орынбасары Тигиняну И. проф., академик (Молдова) «ҚР ҰҒА Хабарлары. Физика-математикалық сериясы».
Nonlinear Analysis: Real World Applications, 2019
Bifurcation analysis of dynamic pull-in for a lumped mass model is presented. The restoring force... more Bifurcation analysis of dynamic pull-in for a lumped mass model is presented. The restoring force of the spring is derived based on the nonlinear constitutive stress-strain law and the driving force of the mass attached to the spring is based on the electrostatic Coulomb force, respectively. The analysis is performed on the resulting nonlinear spring-mass equation with initial conditions. The necessary and sufficient conditions for the existence of periodic solutions are derived analytically and illustrated numerically. The conditions for bifurcation points on the parameters associated with the second-order elastic stiffness constant and the voltage are determined.