Constrained oscillations and contact interaction of the structure, consisting of two parallel plates with internal set of local ribs, used in the theory of gyroscopes
The relevance of the study is caused by the need to develop algorithmic methods for improving the reliability and accuracy of gyroscopic devices, which are used in oil and gas industry. Strength, accuracy and resistance to high temperature of the sensors are extremely important while drilling, to co...
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| Format: | Article |
| Language: | Russian |
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Tomsk Polytechnic University
2016-10-01
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| Series: | Известия Томского политехнического университета: Инжиниринг георесурсов |
| Subjects: | |
| Online Access: | http://izvestiya-tpu.ru/archive/article/view/1809 |
| _version_ | 1797812372550713344 |
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| author | Tatyana Vladimirovna Yakovleva Anton Vadimovich Krysko Vadim Sergeevich Kruzhilin |
| author_facet | Tatyana Vladimirovna Yakovleva Anton Vadimovich Krysko Vadim Sergeevich Kruzhilin |
| author_sort | Tatyana Vladimirovna Yakovleva |
| collection | DOAJ |
| description | The relevance of the study is caused by the need to develop algorithmic methods for improving the reliability and accuracy of gyroscopic devices, which are used in oil and gas industry. Strength, accuracy and resistance to high temperature of the sensors are extremely important while drilling, to control spatial orientation of wells and downhole objects. The aim of work is to construct a mathematical model of the constrained oscillations and contact interaction of the structure consisting of two plates with the internal set of ribs and gaps between the elements, which will be used in the gyroscopes theory. To study such structural and nonlinear problems the authors have applied the methods of qualitative theory of differential equations, wavelet analysis, three methods (Wolf, Rosenstein, Kantz) for analyzing the sign of the highest Lyapunov exponent, numerical simulation using MATLAB software package. The solution was obtained by the Bubnov-Galerkin method in higher approximations in space coordinate and by the Runge-Kutta method of the 4th order of accuracy in time. Results. The authors studied the effect of the number of ribs between the plates on character of their oscillations and contact interaction with longitudinal loading on the top plate, and identified the scenarios of transition of the system from harmonic into a chaotic state. The paper deals with two tasks: 1) the inner set of ribs consists of two beams, 2) the inner set of ribs consists of three beams. It was revealed that in chaotic regime in both tasks the frequency intermittency phenomenon is observed, that is changing time intervals with different frequencies and different oscillation modes. The reliability of the solution is provided by application of different methods for determining the highest Lyapunov exponent, by comparing the results obtained by the Bubnov-Galerkin method and finite difference method. |
| first_indexed | 2024-03-13T07:36:30Z |
| format | Article |
| id | doaj.art-395f41a234a94e20a8be35fae836e019 |
| institution | Directory Open Access Journal |
| issn | 2500-1019 2413-1830 |
| language | Russian |
| last_indexed | 2024-03-13T07:36:30Z |
| publishDate | 2016-10-01 |
| publisher | Tomsk Polytechnic University |
| record_format | Article |
| series | Известия Томского политехнического университета: Инжиниринг георесурсов |
| spelling | doaj.art-395f41a234a94e20a8be35fae836e0192023-06-03T21:12:43ZrusTomsk Polytechnic UniversityИзвестия Томского политехнического университета: Инжиниринг георесурсов2500-10192413-18302016-10-0132710Constrained oscillations and contact interaction of the structure, consisting of two parallel plates with internal set of local ribs, used in the theory of gyroscopesTatyana Vladimirovna YakovlevaAnton Vadimovich KryskoVadim Sergeevich KruzhilinThe relevance of the study is caused by the need to develop algorithmic methods for improving the reliability and accuracy of gyroscopic devices, which are used in oil and gas industry. Strength, accuracy and resistance to high temperature of the sensors are extremely important while drilling, to control spatial orientation of wells and downhole objects. The aim of work is to construct a mathematical model of the constrained oscillations and contact interaction of the structure consisting of two plates with the internal set of ribs and gaps between the elements, which will be used in the gyroscopes theory. To study such structural and nonlinear problems the authors have applied the methods of qualitative theory of differential equations, wavelet analysis, three methods (Wolf, Rosenstein, Kantz) for analyzing the sign of the highest Lyapunov exponent, numerical simulation using MATLAB software package. The solution was obtained by the Bubnov-Galerkin method in higher approximations in space coordinate and by the Runge-Kutta method of the 4th order of accuracy in time. Results. The authors studied the effect of the number of ribs between the plates on character of their oscillations and contact interaction with longitudinal loading on the top plate, and identified the scenarios of transition of the system from harmonic into a chaotic state. The paper deals with two tasks: 1) the inner set of ribs consists of two beams, 2) the inner set of ribs consists of three beams. It was revealed that in chaotic regime in both tasks the frequency intermittency phenomenon is observed, that is changing time intervals with different frequencies and different oscillation modes. The reliability of the solution is provided by application of different methods for determining the highest Lyapunov exponent, by comparing the results obtained by the Bubnov-Galerkin method and finite difference method.http://izvestiya-tpu.ru/archive/article/view/1809distributed mechanical structurescontact interactionsmall gapswavelet analysisparametric oscillationLyapunov exponents |
| spellingShingle | Tatyana Vladimirovna Yakovleva Anton Vadimovich Krysko Vadim Sergeevich Kruzhilin Constrained oscillations and contact interaction of the structure, consisting of two parallel plates with internal set of local ribs, used in the theory of gyroscopes Известия Томского политехнического университета: Инжиниринг георесурсов distributed mechanical structures contact interaction small gaps wavelet analysis parametric oscillation Lyapunov exponents |
| title | Constrained oscillations and contact interaction of the structure, consisting of two parallel plates with internal set of local ribs, used in the theory of gyroscopes |
| title_full | Constrained oscillations and contact interaction of the structure, consisting of two parallel plates with internal set of local ribs, used in the theory of gyroscopes |
| title_fullStr | Constrained oscillations and contact interaction of the structure, consisting of two parallel plates with internal set of local ribs, used in the theory of gyroscopes |
| title_full_unstemmed | Constrained oscillations and contact interaction of the structure, consisting of two parallel plates with internal set of local ribs, used in the theory of gyroscopes |
| title_short | Constrained oscillations and contact interaction of the structure, consisting of two parallel plates with internal set of local ribs, used in the theory of gyroscopes |
| title_sort | constrained oscillations and contact interaction of the structure consisting of two parallel plates with internal set of local ribs used in the theory of gyroscopes |
| topic | distributed mechanical structures contact interaction small gaps wavelet analysis parametric oscillation Lyapunov exponents |
| url | http://izvestiya-tpu.ru/archive/article/view/1809 |
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