Nonlinear characteristics and analysis of an exponential variable cross-section beam-based micro-gyroscope with electrostatic driven
Abstract In this paper, a novel vibrating beam gyroscope with exponential variable cross-section is designed. Relationship between the width and length of the variable cross-section exponential beam is in the form of an exponential function change. The exponential shape factor (ESF) of beam is less...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Zhang, Kunpeng [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2023 |
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| Anmerkung: |
© The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2023 |
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| Übergeordnetes Werk: |
Enthalten in: Acta mechanica Sinica - Berlin : Springer, 1985, 39(2023), 3 vom: 16. Jan. |
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| Übergeordnetes Werk: |
volume:39 ; year:2023 ; number:3 ; day:16 ; month:01 |
| Links: |
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| DOI / URN: |
10.1007/s10409-022-22371-x |
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| Katalog-ID: |
SPR051453487 |
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| 100 | 1 | |a Zhang, Kunpeng |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Nonlinear characteristics and analysis of an exponential variable cross-section beam-based micro-gyroscope with electrostatic driven |
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| 520 | |a Abstract In this paper, a novel vibrating beam gyroscope with exponential variable cross-section is designed. Relationship between the width and length of the variable cross-section exponential beam is in the form of an exponential function change. The exponential shape factor (ESF) of beam is less than or equal to zero, and the thickness of the beam remains constant with the beam length. The effects of curvature nonlinearity and inertia nonlinearity on the system are considered. The vibration control equations, boundary conditions, and nonlinear discretization model of the exponential beam micro-gyroscope (EBMG) are developed by using the extended Hamiltonian principle, the single-mode approximation method, and the Lagrange differential equations. The effects of direct current (DC) and alternating current (AC) voltages on the system response in both the drive and sense directions of the gyroscope are analyzed. The static response of the gyroscope system under the different ESF is solved by the Adomian decomposition method (ADM). The nonlinear discretization model is solved by the multi-scale method to analyze the influence of each parameter on the dynamic response of the gyroscope. The results show that with the increase of the ESF, the pull-in voltage and the first-order natural frequency of the EBMG increase gradually, and have a linear change pattern approximately. By adjusting the ESF, the difference between the peak frequency of Coriolis force response and the sense peak frequency can be controlled. Utilizing the nonlinear harden characteristics of the EBMG system, when the AC voltage is applied in the thickness direction of exponential beam, the EBMG system can obtain better bandwidth performance and linear measurable range by choosing the appropriate ESF, damping ratio, and AC voltage; when the AC voltage is applied in the width direction of the exponential beam, the EBMG can not only obtain the higher sensitivity performance, but also increase the linear detectable range by choosing an appropriate ESF. | ||
| 700 | 1 | |a Chang, Zhaomin |4 aut | |
| 700 | 1 | |a Hao, Shuying |4 aut | |
| 700 | 1 | |a Zhang, Qichang |4 aut | |
| 700 | 1 | |a Feng, Jingjing |4 aut | |
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10.1007/s10409-022-22371-x doi (DE-627)SPR051453487 (SPR)s10409-022-22371-x-e DE-627 ger DE-627 rakwb eng Zhang, Kunpeng verfasserin aut Nonlinear characteristics and analysis of an exponential variable cross-section beam-based micro-gyroscope with electrostatic driven 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2023 Abstract In this paper, a novel vibrating beam gyroscope with exponential variable cross-section is designed. Relationship between the width and length of the variable cross-section exponential beam is in the form of an exponential function change. The exponential shape factor (ESF) of beam is less than or equal to zero, and the thickness of the beam remains constant with the beam length. The effects of curvature nonlinearity and inertia nonlinearity on the system are considered. The vibration control equations, boundary conditions, and nonlinear discretization model of the exponential beam micro-gyroscope (EBMG) are developed by using the extended Hamiltonian principle, the single-mode approximation method, and the Lagrange differential equations. The effects of direct current (DC) and alternating current (AC) voltages on the system response in both the drive and sense directions of the gyroscope are analyzed. The static response of the gyroscope system under the different ESF is solved by the Adomian decomposition method (ADM). The nonlinear discretization model is solved by the multi-scale method to analyze the influence of each parameter on the dynamic response of the gyroscope. The results show that with the increase of the ESF, the pull-in voltage and the first-order natural frequency of the EBMG increase gradually, and have a linear change pattern approximately. By adjusting the ESF, the difference between the peak frequency of Coriolis force response and the sense peak frequency can be controlled. Utilizing the nonlinear harden characteristics of the EBMG system, when the AC voltage is applied in the thickness direction of exponential beam, the EBMG system can obtain better bandwidth performance and linear measurable range by choosing the appropriate ESF, damping ratio, and AC voltage; when the AC voltage is applied in the width direction of the exponential beam, the EBMG can not only obtain the higher sensitivity performance, but also increase the linear detectable range by choosing an appropriate ESF. Chang, Zhaomin aut Hao, Shuying aut Zhang, Qichang aut Feng, Jingjing aut Enthalten in Acta mechanica Sinica Berlin : Springer, 1985 39(2023), 3 vom: 16. Jan. (DE-627)481908277 (DE-600)2181030-8 1614-3116 nnns volume:39 year:2023 number:3 day:16 month:01 https://dx.doi.org/10.1007/s10409-022-22371-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2023 3 16 01 |
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10.1007/s10409-022-22371-x doi (DE-627)SPR051453487 (SPR)s10409-022-22371-x-e DE-627 ger DE-627 rakwb eng Zhang, Kunpeng verfasserin aut Nonlinear characteristics and analysis of an exponential variable cross-section beam-based micro-gyroscope with electrostatic driven 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2023 Abstract In this paper, a novel vibrating beam gyroscope with exponential variable cross-section is designed. Relationship between the width and length of the variable cross-section exponential beam is in the form of an exponential function change. The exponential shape factor (ESF) of beam is less than or equal to zero, and the thickness of the beam remains constant with the beam length. The effects of curvature nonlinearity and inertia nonlinearity on the system are considered. The vibration control equations, boundary conditions, and nonlinear discretization model of the exponential beam micro-gyroscope (EBMG) are developed by using the extended Hamiltonian principle, the single-mode approximation method, and the Lagrange differential equations. The effects of direct current (DC) and alternating current (AC) voltages on the system response in both the drive and sense directions of the gyroscope are analyzed. The static response of the gyroscope system under the different ESF is solved by the Adomian decomposition method (ADM). The nonlinear discretization model is solved by the multi-scale method to analyze the influence of each parameter on the dynamic response of the gyroscope. The results show that with the increase of the ESF, the pull-in voltage and the first-order natural frequency of the EBMG increase gradually, and have a linear change pattern approximately. By adjusting the ESF, the difference between the peak frequency of Coriolis force response and the sense peak frequency can be controlled. Utilizing the nonlinear harden characteristics of the EBMG system, when the AC voltage is applied in the thickness direction of exponential beam, the EBMG system can obtain better bandwidth performance and linear measurable range by choosing the appropriate ESF, damping ratio, and AC voltage; when the AC voltage is applied in the width direction of the exponential beam, the EBMG can not only obtain the higher sensitivity performance, but also increase the linear detectable range by choosing an appropriate ESF. Chang, Zhaomin aut Hao, Shuying aut Zhang, Qichang aut Feng, Jingjing aut Enthalten in Acta mechanica Sinica Berlin : Springer, 1985 39(2023), 3 vom: 16. Jan. (DE-627)481908277 (DE-600)2181030-8 1614-3116 nnns volume:39 year:2023 number:3 day:16 month:01 https://dx.doi.org/10.1007/s10409-022-22371-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2023 3 16 01 |
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10.1007/s10409-022-22371-x doi (DE-627)SPR051453487 (SPR)s10409-022-22371-x-e DE-627 ger DE-627 rakwb eng Zhang, Kunpeng verfasserin aut Nonlinear characteristics and analysis of an exponential variable cross-section beam-based micro-gyroscope with electrostatic driven 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2023 Abstract In this paper, a novel vibrating beam gyroscope with exponential variable cross-section is designed. Relationship between the width and length of the variable cross-section exponential beam is in the form of an exponential function change. The exponential shape factor (ESF) of beam is less than or equal to zero, and the thickness of the beam remains constant with the beam length. The effects of curvature nonlinearity and inertia nonlinearity on the system are considered. The vibration control equations, boundary conditions, and nonlinear discretization model of the exponential beam micro-gyroscope (EBMG) are developed by using the extended Hamiltonian principle, the single-mode approximation method, and the Lagrange differential equations. The effects of direct current (DC) and alternating current (AC) voltages on the system response in both the drive and sense directions of the gyroscope are analyzed. The static response of the gyroscope system under the different ESF is solved by the Adomian decomposition method (ADM). The nonlinear discretization model is solved by the multi-scale method to analyze the influence of each parameter on the dynamic response of the gyroscope. The results show that with the increase of the ESF, the pull-in voltage and the first-order natural frequency of the EBMG increase gradually, and have a linear change pattern approximately. By adjusting the ESF, the difference between the peak frequency of Coriolis force response and the sense peak frequency can be controlled. Utilizing the nonlinear harden characteristics of the EBMG system, when the AC voltage is applied in the thickness direction of exponential beam, the EBMG system can obtain better bandwidth performance and linear measurable range by choosing the appropriate ESF, damping ratio, and AC voltage; when the AC voltage is applied in the width direction of the exponential beam, the EBMG can not only obtain the higher sensitivity performance, but also increase the linear detectable range by choosing an appropriate ESF. Chang, Zhaomin aut Hao, Shuying aut Zhang, Qichang aut Feng, Jingjing aut Enthalten in Acta mechanica Sinica Berlin : Springer, 1985 39(2023), 3 vom: 16. Jan. (DE-627)481908277 (DE-600)2181030-8 1614-3116 nnns volume:39 year:2023 number:3 day:16 month:01 https://dx.doi.org/10.1007/s10409-022-22371-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2023 3 16 01 |
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10.1007/s10409-022-22371-x doi (DE-627)SPR051453487 (SPR)s10409-022-22371-x-e DE-627 ger DE-627 rakwb eng Zhang, Kunpeng verfasserin aut Nonlinear characteristics and analysis of an exponential variable cross-section beam-based micro-gyroscope with electrostatic driven 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2023 Abstract In this paper, a novel vibrating beam gyroscope with exponential variable cross-section is designed. Relationship between the width and length of the variable cross-section exponential beam is in the form of an exponential function change. The exponential shape factor (ESF) of beam is less than or equal to zero, and the thickness of the beam remains constant with the beam length. The effects of curvature nonlinearity and inertia nonlinearity on the system are considered. The vibration control equations, boundary conditions, and nonlinear discretization model of the exponential beam micro-gyroscope (EBMG) are developed by using the extended Hamiltonian principle, the single-mode approximation method, and the Lagrange differential equations. The effects of direct current (DC) and alternating current (AC) voltages on the system response in both the drive and sense directions of the gyroscope are analyzed. The static response of the gyroscope system under the different ESF is solved by the Adomian decomposition method (ADM). The nonlinear discretization model is solved by the multi-scale method to analyze the influence of each parameter on the dynamic response of the gyroscope. The results show that with the increase of the ESF, the pull-in voltage and the first-order natural frequency of the EBMG increase gradually, and have a linear change pattern approximately. By adjusting the ESF, the difference between the peak frequency of Coriolis force response and the sense peak frequency can be controlled. Utilizing the nonlinear harden characteristics of the EBMG system, when the AC voltage is applied in the thickness direction of exponential beam, the EBMG system can obtain better bandwidth performance and linear measurable range by choosing the appropriate ESF, damping ratio, and AC voltage; when the AC voltage is applied in the width direction of the exponential beam, the EBMG can not only obtain the higher sensitivity performance, but also increase the linear detectable range by choosing an appropriate ESF. Chang, Zhaomin aut Hao, Shuying aut Zhang, Qichang aut Feng, Jingjing aut Enthalten in Acta mechanica Sinica Berlin : Springer, 1985 39(2023), 3 vom: 16. Jan. (DE-627)481908277 (DE-600)2181030-8 1614-3116 nnns volume:39 year:2023 number:3 day:16 month:01 https://dx.doi.org/10.1007/s10409-022-22371-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2023 3 16 01 |
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10.1007/s10409-022-22371-x doi (DE-627)SPR051453487 (SPR)s10409-022-22371-x-e DE-627 ger DE-627 rakwb eng Zhang, Kunpeng verfasserin aut Nonlinear characteristics and analysis of an exponential variable cross-section beam-based micro-gyroscope with electrostatic driven 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2023 Abstract In this paper, a novel vibrating beam gyroscope with exponential variable cross-section is designed. Relationship between the width and length of the variable cross-section exponential beam is in the form of an exponential function change. The exponential shape factor (ESF) of beam is less than or equal to zero, and the thickness of the beam remains constant with the beam length. The effects of curvature nonlinearity and inertia nonlinearity on the system are considered. The vibration control equations, boundary conditions, and nonlinear discretization model of the exponential beam micro-gyroscope (EBMG) are developed by using the extended Hamiltonian principle, the single-mode approximation method, and the Lagrange differential equations. The effects of direct current (DC) and alternating current (AC) voltages on the system response in both the drive and sense directions of the gyroscope are analyzed. The static response of the gyroscope system under the different ESF is solved by the Adomian decomposition method (ADM). The nonlinear discretization model is solved by the multi-scale method to analyze the influence of each parameter on the dynamic response of the gyroscope. The results show that with the increase of the ESF, the pull-in voltage and the first-order natural frequency of the EBMG increase gradually, and have a linear change pattern approximately. By adjusting the ESF, the difference between the peak frequency of Coriolis force response and the sense peak frequency can be controlled. Utilizing the nonlinear harden characteristics of the EBMG system, when the AC voltage is applied in the thickness direction of exponential beam, the EBMG system can obtain better bandwidth performance and linear measurable range by choosing the appropriate ESF, damping ratio, and AC voltage; when the AC voltage is applied in the width direction of the exponential beam, the EBMG can not only obtain the higher sensitivity performance, but also increase the linear detectable range by choosing an appropriate ESF. Chang, Zhaomin aut Hao, Shuying aut Zhang, Qichang aut Feng, Jingjing aut Enthalten in Acta mechanica Sinica Berlin : Springer, 1985 39(2023), 3 vom: 16. Jan. (DE-627)481908277 (DE-600)2181030-8 1614-3116 nnns volume:39 year:2023 number:3 day:16 month:01 https://dx.doi.org/10.1007/s10409-022-22371-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2023 3 16 01 |
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Zhang, Kunpeng @@aut@@ Chang, Zhaomin @@aut@@ Hao, Shuying @@aut@@ Zhang, Qichang @@aut@@ Feng, Jingjing @@aut@@ |
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Relationship between the width and length of the variable cross-section exponential beam is in the form of an exponential function change. The exponential shape factor (ESF) of beam is less than or equal to zero, and the thickness of the beam remains constant with the beam length. The effects of curvature nonlinearity and inertia nonlinearity on the system are considered. The vibration control equations, boundary conditions, and nonlinear discretization model of the exponential beam micro-gyroscope (EBMG) are developed by using the extended Hamiltonian principle, the single-mode approximation method, and the Lagrange differential equations. The effects of direct current (DC) and alternating current (AC) voltages on the system response in both the drive and sense directions of the gyroscope are analyzed. The static response of the gyroscope system under the different ESF is solved by the Adomian decomposition method (ADM). The nonlinear discretization model is solved by the multi-scale method to analyze the influence of each parameter on the dynamic response of the gyroscope. The results show that with the increase of the ESF, the pull-in voltage and the first-order natural frequency of the EBMG increase gradually, and have a linear change pattern approximately. By adjusting the ESF, the difference between the peak frequency of Coriolis force response and the sense peak frequency can be controlled. Utilizing the nonlinear harden characteristics of the EBMG system, when the AC voltage is applied in the thickness direction of exponential beam, the EBMG system can obtain better bandwidth performance and linear measurable range by choosing the appropriate ESF, damping ratio, and AC voltage; when the AC voltage is applied in the width direction of the exponential beam, the EBMG can not only obtain the higher sensitivity performance, but also increase the linear detectable range by choosing an appropriate ESF.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Chang, Zhaomin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Hao, Shuying</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Zhang, Qichang</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Feng, Jingjing</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Acta mechanica Sinica</subfield><subfield code="d">Berlin : Springer, 1985</subfield><subfield code="g">39(2023), 3 vom: 16. 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Zhang, Kunpeng Nonlinear characteristics and analysis of an exponential variable cross-section beam-based micro-gyroscope with electrostatic driven |
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nonlinear characteristics and analysis of an exponential variable cross-section beam-based micro-gyroscope with electrostatic driven |
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Nonlinear characteristics and analysis of an exponential variable cross-section beam-based micro-gyroscope with electrostatic driven |
| abstract |
Abstract In this paper, a novel vibrating beam gyroscope with exponential variable cross-section is designed. Relationship between the width and length of the variable cross-section exponential beam is in the form of an exponential function change. The exponential shape factor (ESF) of beam is less than or equal to zero, and the thickness of the beam remains constant with the beam length. The effects of curvature nonlinearity and inertia nonlinearity on the system are considered. The vibration control equations, boundary conditions, and nonlinear discretization model of the exponential beam micro-gyroscope (EBMG) are developed by using the extended Hamiltonian principle, the single-mode approximation method, and the Lagrange differential equations. The effects of direct current (DC) and alternating current (AC) voltages on the system response in both the drive and sense directions of the gyroscope are analyzed. The static response of the gyroscope system under the different ESF is solved by the Adomian decomposition method (ADM). The nonlinear discretization model is solved by the multi-scale method to analyze the influence of each parameter on the dynamic response of the gyroscope. The results show that with the increase of the ESF, the pull-in voltage and the first-order natural frequency of the EBMG increase gradually, and have a linear change pattern approximately. By adjusting the ESF, the difference between the peak frequency of Coriolis force response and the sense peak frequency can be controlled. Utilizing the nonlinear harden characteristics of the EBMG system, when the AC voltage is applied in the thickness direction of exponential beam, the EBMG system can obtain better bandwidth performance and linear measurable range by choosing the appropriate ESF, damping ratio, and AC voltage; when the AC voltage is applied in the width direction of the exponential beam, the EBMG can not only obtain the higher sensitivity performance, but also increase the linear detectable range by choosing an appropriate ESF. © The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2023 |
| abstractGer |
Abstract In this paper, a novel vibrating beam gyroscope with exponential variable cross-section is designed. Relationship between the width and length of the variable cross-section exponential beam is in the form of an exponential function change. The exponential shape factor (ESF) of beam is less than or equal to zero, and the thickness of the beam remains constant with the beam length. The effects of curvature nonlinearity and inertia nonlinearity on the system are considered. The vibration control equations, boundary conditions, and nonlinear discretization model of the exponential beam micro-gyroscope (EBMG) are developed by using the extended Hamiltonian principle, the single-mode approximation method, and the Lagrange differential equations. The effects of direct current (DC) and alternating current (AC) voltages on the system response in both the drive and sense directions of the gyroscope are analyzed. The static response of the gyroscope system under the different ESF is solved by the Adomian decomposition method (ADM). The nonlinear discretization model is solved by the multi-scale method to analyze the influence of each parameter on the dynamic response of the gyroscope. The results show that with the increase of the ESF, the pull-in voltage and the first-order natural frequency of the EBMG increase gradually, and have a linear change pattern approximately. By adjusting the ESF, the difference between the peak frequency of Coriolis force response and the sense peak frequency can be controlled. Utilizing the nonlinear harden characteristics of the EBMG system, when the AC voltage is applied in the thickness direction of exponential beam, the EBMG system can obtain better bandwidth performance and linear measurable range by choosing the appropriate ESF, damping ratio, and AC voltage; when the AC voltage is applied in the width direction of the exponential beam, the EBMG can not only obtain the higher sensitivity performance, but also increase the linear detectable range by choosing an appropriate ESF. © The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2023 |
| abstract_unstemmed |
Abstract In this paper, a novel vibrating beam gyroscope with exponential variable cross-section is designed. Relationship between the width and length of the variable cross-section exponential beam is in the form of an exponential function change. The exponential shape factor (ESF) of beam is less than or equal to zero, and the thickness of the beam remains constant with the beam length. The effects of curvature nonlinearity and inertia nonlinearity on the system are considered. The vibration control equations, boundary conditions, and nonlinear discretization model of the exponential beam micro-gyroscope (EBMG) are developed by using the extended Hamiltonian principle, the single-mode approximation method, and the Lagrange differential equations. The effects of direct current (DC) and alternating current (AC) voltages on the system response in both the drive and sense directions of the gyroscope are analyzed. The static response of the gyroscope system under the different ESF is solved by the Adomian decomposition method (ADM). The nonlinear discretization model is solved by the multi-scale method to analyze the influence of each parameter on the dynamic response of the gyroscope. The results show that with the increase of the ESF, the pull-in voltage and the first-order natural frequency of the EBMG increase gradually, and have a linear change pattern approximately. By adjusting the ESF, the difference between the peak frequency of Coriolis force response and the sense peak frequency can be controlled. Utilizing the nonlinear harden characteristics of the EBMG system, when the AC voltage is applied in the thickness direction of exponential beam, the EBMG system can obtain better bandwidth performance and linear measurable range by choosing the appropriate ESF, damping ratio, and AC voltage; when the AC voltage is applied in the width direction of the exponential beam, the EBMG can not only obtain the higher sensitivity performance, but also increase the linear detectable range by choosing an appropriate ESF. © The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2023 |
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Nonlinear characteristics and analysis of an exponential variable cross-section beam-based micro-gyroscope with electrostatic driven |
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https://dx.doi.org/10.1007/s10409-022-22371-x |
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Chang, Zhaomin Hao, Shuying Zhang, Qichang Feng, Jingjing |
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Chang, Zhaomin Hao, Shuying Zhang, Qichang Feng, Jingjing |
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10.1007/s10409-022-22371-x |
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2024-07-03T21:54:29.625Z |
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| score |
7.400571 |