Explicit Novel Nonlinear Regression Method to Find Radial Natural Frequencies of Hemispherical Resonator

Background Hemispherical shells are commonly used in percussion instruments such as Hang, Bell, and Singing Bowls as well as other engineering applications. The dynamic properties of a hemispherical shell are important, especially for music which demands close control of the natural frequencies. Pur...
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Autor*in:	Limkar, Beena [verfasserIn] Vaidya, Vinay Chandekar, Gautam

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	Hemispherical resonator Nonlinear regression Natural frequency Experimental modal analysis Operational modal analysis

Anmerkung:	© Krishtel eMaging Solutions Private Limited 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Übergeordnetes Werk:	Enthalten in: Journal of vibration engineering & technologies - Singapore : Springer Singapore, 2018, 11(2022), 5 vom: 17. Okt., Seite 2419-2428
Übergeordnetes Werk:	volume:11 ; year:2022 ; number:5 ; day:17 ; month:10 ; pages:2419-2428

Links:	Volltext

DOI / URN:	10.1007/s42417-022-00712-8

Katalog-ID:	SPR052298086

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520			\|a Background Hemispherical shells are commonly used in percussion instruments such as Hang, Bell, and Singing Bowls as well as other engineering applications. The dynamic properties of a hemispherical shell are important, especially for music which demands close control of the natural frequencies. Purpose Theoretically, the dynamic behavior of hemispherical shell is studied by solving very complex differential equations and mostly results are available for thin shells. Finite element analysis (FEA) is thus favored but it requires costly software and special expertise. FEA is also mesh-sensitive and mesh-independent analysis is required. Considering these facts, in this paper, an explicit nonlinear equation is formulated, which is a function of the geometry and material parameters. Methodology In this paper, the proposed explicit nonlinear equation is formulated using nonlinear regression with 4000 simulated data points generated using software. It obeys dimensional homogeneity and is validated using numerical and experimental methods. Results Validation of this equation using numerical data shows RMS error mostly less than 6% and 5% for geometry and material parameters, respectively. Frequency values of two manufactured hemispherical shells are extracted using audio analysis as well as experimental and operational modal analysis. The validation of these experimentally obtained frequencies with the proposed explicit equation gives a maximum absolute error of less than 5%, except in a few higher modes it is up to 7%. Conclusion The proposed nonlinear explicit equation predicts the first four radial mode frequencies of a hemispherical shell just by entering a few physically significant parameters. It can be used to design shells demanding close control of the frequency values. The model can also be used in optimization.
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700	1		\|a Vaidya, Vinay \|4 aut
700	1		\|a Chandekar, Gautam \|4 aut
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912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
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allfields	10.1007/s42417-022-00712-8 doi (DE-627)SPR052298086 (SPR)s42417-022-00712-8-e DE-627 ger DE-627 rakwb eng Limkar, Beena verfasserin (orcid)0000-0002-0055-4068 aut Explicit Novel Nonlinear Regression Method to Find Radial Natural Frequencies of Hemispherical Resonator 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Krishtel eMaging Solutions Private Limited 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Background Hemispherical shells are commonly used in percussion instruments such as Hang, Bell, and Singing Bowls as well as other engineering applications. The dynamic properties of a hemispherical shell are important, especially for music which demands close control of the natural frequencies. Purpose Theoretically, the dynamic behavior of hemispherical shell is studied by solving very complex differential equations and mostly results are available for thin shells. Finite element analysis (FEA) is thus favored but it requires costly software and special expertise. FEA is also mesh-sensitive and mesh-independent analysis is required. Considering these facts, in this paper, an explicit nonlinear equation is formulated, which is a function of the geometry and material parameters. Methodology In this paper, the proposed explicit nonlinear equation is formulated using nonlinear regression with 4000 simulated data points generated using software. It obeys dimensional homogeneity and is validated using numerical and experimental methods. Results Validation of this equation using numerical data shows RMS error mostly less than 6% and 5% for geometry and material parameters, respectively. Frequency values of two manufactured hemispherical shells are extracted using audio analysis as well as experimental and operational modal analysis. The validation of these experimentally obtained frequencies with the proposed explicit equation gives a maximum absolute error of less than 5%, except in a few higher modes it is up to 7%. Conclusion The proposed nonlinear explicit equation predicts the first four radial mode frequencies of a hemispherical shell just by entering a few physically significant parameters. It can be used to design shells demanding close control of the frequency values. The model can also be used in optimization. Hemispherical resonator (dpeaa)DE-He213 Nonlinear regression (dpeaa)DE-He213 Natural frequency (dpeaa)DE-He213 Experimental modal analysis (dpeaa)DE-He213 Operational modal analysis (dpeaa)DE-He213 Vaidya, Vinay aut Chandekar, Gautam aut Enthalten in Journal of vibration engineering & technologies Singapore : Springer Singapore, 2018 11(2022), 5 vom: 17. Okt., Seite 2419-2428 (DE-627)1030123837 (DE-600)2941414-3 2523-3939 nnns volume:11 year:2022 number:5 day:17 month:10 pages:2419-2428 https://dx.doi.org/10.1007/s42417-022-00712-8 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_105 GBV_ILN_110 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 11 2022 5 17 10 2419-2428
spelling	10.1007/s42417-022-00712-8 doi (DE-627)SPR052298086 (SPR)s42417-022-00712-8-e DE-627 ger DE-627 rakwb eng Limkar, Beena verfasserin (orcid)0000-0002-0055-4068 aut Explicit Novel Nonlinear Regression Method to Find Radial Natural Frequencies of Hemispherical Resonator 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Krishtel eMaging Solutions Private Limited 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Background Hemispherical shells are commonly used in percussion instruments such as Hang, Bell, and Singing Bowls as well as other engineering applications. The dynamic properties of a hemispherical shell are important, especially for music which demands close control of the natural frequencies. Purpose Theoretically, the dynamic behavior of hemispherical shell is studied by solving very complex differential equations and mostly results are available for thin shells. Finite element analysis (FEA) is thus favored but it requires costly software and special expertise. FEA is also mesh-sensitive and mesh-independent analysis is required. Considering these facts, in this paper, an explicit nonlinear equation is formulated, which is a function of the geometry and material parameters. Methodology In this paper, the proposed explicit nonlinear equation is formulated using nonlinear regression with 4000 simulated data points generated using software. It obeys dimensional homogeneity and is validated using numerical and experimental methods. Results Validation of this equation using numerical data shows RMS error mostly less than 6% and 5% for geometry and material parameters, respectively. Frequency values of two manufactured hemispherical shells are extracted using audio analysis as well as experimental and operational modal analysis. The validation of these experimentally obtained frequencies with the proposed explicit equation gives a maximum absolute error of less than 5%, except in a few higher modes it is up to 7%. Conclusion The proposed nonlinear explicit equation predicts the first four radial mode frequencies of a hemispherical shell just by entering a few physically significant parameters. It can be used to design shells demanding close control of the frequency values. The model can also be used in optimization. Hemispherical resonator (dpeaa)DE-He213 Nonlinear regression (dpeaa)DE-He213 Natural frequency (dpeaa)DE-He213 Experimental modal analysis (dpeaa)DE-He213 Operational modal analysis (dpeaa)DE-He213 Vaidya, Vinay aut Chandekar, Gautam aut Enthalten in Journal of vibration engineering & technologies Singapore : Springer Singapore, 2018 11(2022), 5 vom: 17. Okt., Seite 2419-2428 (DE-627)1030123837 (DE-600)2941414-3 2523-3939 nnns volume:11 year:2022 number:5 day:17 month:10 pages:2419-2428 https://dx.doi.org/10.1007/s42417-022-00712-8 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_105 GBV_ILN_110 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 11 2022 5 17 10 2419-2428
allfields_unstemmed	10.1007/s42417-022-00712-8 doi (DE-627)SPR052298086 (SPR)s42417-022-00712-8-e DE-627 ger DE-627 rakwb eng Limkar, Beena verfasserin (orcid)0000-0002-0055-4068 aut Explicit Novel Nonlinear Regression Method to Find Radial Natural Frequencies of Hemispherical Resonator 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Krishtel eMaging Solutions Private Limited 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Background Hemispherical shells are commonly used in percussion instruments such as Hang, Bell, and Singing Bowls as well as other engineering applications. The dynamic properties of a hemispherical shell are important, especially for music which demands close control of the natural frequencies. Purpose Theoretically, the dynamic behavior of hemispherical shell is studied by solving very complex differential equations and mostly results are available for thin shells. Finite element analysis (FEA) is thus favored but it requires costly software and special expertise. FEA is also mesh-sensitive and mesh-independent analysis is required. Considering these facts, in this paper, an explicit nonlinear equation is formulated, which is a function of the geometry and material parameters. Methodology In this paper, the proposed explicit nonlinear equation is formulated using nonlinear regression with 4000 simulated data points generated using software. It obeys dimensional homogeneity and is validated using numerical and experimental methods. Results Validation of this equation using numerical data shows RMS error mostly less than 6% and 5% for geometry and material parameters, respectively. Frequency values of two manufactured hemispherical shells are extracted using audio analysis as well as experimental and operational modal analysis. The validation of these experimentally obtained frequencies with the proposed explicit equation gives a maximum absolute error of less than 5%, except in a few higher modes it is up to 7%. Conclusion The proposed nonlinear explicit equation predicts the first four radial mode frequencies of a hemispherical shell just by entering a few physically significant parameters. It can be used to design shells demanding close control of the frequency values. The model can also be used in optimization. Hemispherical resonator (dpeaa)DE-He213 Nonlinear regression (dpeaa)DE-He213 Natural frequency (dpeaa)DE-He213 Experimental modal analysis (dpeaa)DE-He213 Operational modal analysis (dpeaa)DE-He213 Vaidya, Vinay aut Chandekar, Gautam aut Enthalten in Journal of vibration engineering & technologies Singapore : Springer Singapore, 2018 11(2022), 5 vom: 17. Okt., Seite 2419-2428 (DE-627)1030123837 (DE-600)2941414-3 2523-3939 nnns volume:11 year:2022 number:5 day:17 month:10 pages:2419-2428 https://dx.doi.org/10.1007/s42417-022-00712-8 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_105 GBV_ILN_110 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 11 2022 5 17 10 2419-2428
allfieldsGer	10.1007/s42417-022-00712-8 doi (DE-627)SPR052298086 (SPR)s42417-022-00712-8-e DE-627 ger DE-627 rakwb eng Limkar, Beena verfasserin (orcid)0000-0002-0055-4068 aut Explicit Novel Nonlinear Regression Method to Find Radial Natural Frequencies of Hemispherical Resonator 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Krishtel eMaging Solutions Private Limited 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Background Hemispherical shells are commonly used in percussion instruments such as Hang, Bell, and Singing Bowls as well as other engineering applications. The dynamic properties of a hemispherical shell are important, especially for music which demands close control of the natural frequencies. Purpose Theoretically, the dynamic behavior of hemispherical shell is studied by solving very complex differential equations and mostly results are available for thin shells. Finite element analysis (FEA) is thus favored but it requires costly software and special expertise. FEA is also mesh-sensitive and mesh-independent analysis is required. Considering these facts, in this paper, an explicit nonlinear equation is formulated, which is a function of the geometry and material parameters. Methodology In this paper, the proposed explicit nonlinear equation is formulated using nonlinear regression with 4000 simulated data points generated using software. It obeys dimensional homogeneity and is validated using numerical and experimental methods. Results Validation of this equation using numerical data shows RMS error mostly less than 6% and 5% for geometry and material parameters, respectively. Frequency values of two manufactured hemispherical shells are extracted using audio analysis as well as experimental and operational modal analysis. The validation of these experimentally obtained frequencies with the proposed explicit equation gives a maximum absolute error of less than 5%, except in a few higher modes it is up to 7%. Conclusion The proposed nonlinear explicit equation predicts the first four radial mode frequencies of a hemispherical shell just by entering a few physically significant parameters. It can be used to design shells demanding close control of the frequency values. The model can also be used in optimization. Hemispherical resonator (dpeaa)DE-He213 Nonlinear regression (dpeaa)DE-He213 Natural frequency (dpeaa)DE-He213 Experimental modal analysis (dpeaa)DE-He213 Operational modal analysis (dpeaa)DE-He213 Vaidya, Vinay aut Chandekar, Gautam aut Enthalten in Journal of vibration engineering & technologies Singapore : Springer Singapore, 2018 11(2022), 5 vom: 17. Okt., Seite 2419-2428 (DE-627)1030123837 (DE-600)2941414-3 2523-3939 nnns volume:11 year:2022 number:5 day:17 month:10 pages:2419-2428 https://dx.doi.org/10.1007/s42417-022-00712-8 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_105 GBV_ILN_110 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 11 2022 5 17 10 2419-2428
allfieldsSound	10.1007/s42417-022-00712-8 doi (DE-627)SPR052298086 (SPR)s42417-022-00712-8-e DE-627 ger DE-627 rakwb eng Limkar, Beena verfasserin (orcid)0000-0002-0055-4068 aut Explicit Novel Nonlinear Regression Method to Find Radial Natural Frequencies of Hemispherical Resonator 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Krishtel eMaging Solutions Private Limited 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Background Hemispherical shells are commonly used in percussion instruments such as Hang, Bell, and Singing Bowls as well as other engineering applications. The dynamic properties of a hemispherical shell are important, especially for music which demands close control of the natural frequencies. Purpose Theoretically, the dynamic behavior of hemispherical shell is studied by solving very complex differential equations and mostly results are available for thin shells. Finite element analysis (FEA) is thus favored but it requires costly software and special expertise. FEA is also mesh-sensitive and mesh-independent analysis is required. Considering these facts, in this paper, an explicit nonlinear equation is formulated, which is a function of the geometry and material parameters. Methodology In this paper, the proposed explicit nonlinear equation is formulated using nonlinear regression with 4000 simulated data points generated using software. It obeys dimensional homogeneity and is validated using numerical and experimental methods. Results Validation of this equation using numerical data shows RMS error mostly less than 6% and 5% for geometry and material parameters, respectively. Frequency values of two manufactured hemispherical shells are extracted using audio analysis as well as experimental and operational modal analysis. The validation of these experimentally obtained frequencies with the proposed explicit equation gives a maximum absolute error of less than 5%, except in a few higher modes it is up to 7%. Conclusion The proposed nonlinear explicit equation predicts the first four radial mode frequencies of a hemispherical shell just by entering a few physically significant parameters. It can be used to design shells demanding close control of the frequency values. The model can also be used in optimization. Hemispherical resonator (dpeaa)DE-He213 Nonlinear regression (dpeaa)DE-He213 Natural frequency (dpeaa)DE-He213 Experimental modal analysis (dpeaa)DE-He213 Operational modal analysis (dpeaa)DE-He213 Vaidya, Vinay aut Chandekar, Gautam aut Enthalten in Journal of vibration engineering & technologies Singapore : Springer Singapore, 2018 11(2022), 5 vom: 17. Okt., Seite 2419-2428 (DE-627)1030123837 (DE-600)2941414-3 2523-3939 nnns volume:11 year:2022 number:5 day:17 month:10 pages:2419-2428 https://dx.doi.org/10.1007/s42417-022-00712-8 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_105 GBV_ILN_110 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 11 2022 5 17 10 2419-2428
language	English
source	Enthalten in Journal of vibration engineering & technologies 11(2022), 5 vom: 17. Okt., Seite 2419-2428 volume:11 year:2022 number:5 day:17 month:10 pages:2419-2428
sourceStr	Enthalten in Journal of vibration engineering & technologies 11(2022), 5 vom: 17. Okt., Seite 2419-2428 volume:11 year:2022 number:5 day:17 month:10 pages:2419-2428
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Hemispherical resonator Nonlinear regression Natural frequency Experimental modal analysis Operational modal analysis
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container_title	Journal of vibration engineering & technologies
authorswithroles_txt_mv	Limkar, Beena @@aut@@ Vaidya, Vinay @@aut@@ Chandekar, Gautam @@aut@@
publishDateDaySort_date	2022-10-17T00:00:00Z
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Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Background Hemispherical shells are commonly used in percussion instruments such as Hang, Bell, and Singing Bowls as well as other engineering applications. The dynamic properties of a hemispherical shell are important, especially for music which demands close control of the natural frequencies. Purpose Theoretically, the dynamic behavior of hemispherical shell is studied by solving very complex differential equations and mostly results are available for thin shells. Finite element analysis (FEA) is thus favored but it requires costly software and special expertise. FEA is also mesh-sensitive and mesh-independent analysis is required. Considering these facts, in this paper, an explicit nonlinear equation is formulated, which is a function of the geometry and material parameters. Methodology In this paper, the proposed explicit nonlinear equation is formulated using nonlinear regression with 4000 simulated data points generated using software. It obeys dimensional homogeneity and is validated using numerical and experimental methods. Results Validation of this equation using numerical data shows RMS error mostly less than 6% and 5% for geometry and material parameters, respectively. Frequency values of two manufactured hemispherical shells are extracted using audio analysis as well as experimental and operational modal analysis. The validation of these experimentally obtained frequencies with the proposed explicit equation gives a maximum absolute error of less than 5%, except in a few higher modes it is up to 7%. 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author	Limkar, Beena
spellingShingle	Limkar, Beena misc Hemispherical resonator misc Nonlinear regression misc Natural frequency misc Experimental modal analysis misc Operational modal analysis Explicit Novel Nonlinear Regression Method to Find Radial Natural Frequencies of Hemispherical Resonator
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topic_title	Explicit Novel Nonlinear Regression Method to Find Radial Natural Frequencies of Hemispherical Resonator Hemispherical resonator (dpeaa)DE-He213 Nonlinear regression (dpeaa)DE-He213 Natural frequency (dpeaa)DE-He213 Experimental modal analysis (dpeaa)DE-He213 Operational modal analysis (dpeaa)DE-He213
topic	misc Hemispherical resonator misc Nonlinear regression misc Natural frequency misc Experimental modal analysis misc Operational modal analysis
topic_unstemmed	misc Hemispherical resonator misc Nonlinear regression misc Natural frequency misc Experimental modal analysis misc Operational modal analysis
topic_browse	misc Hemispherical resonator misc Nonlinear regression misc Natural frequency misc Experimental modal analysis misc Operational modal analysis
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title	Explicit Novel Nonlinear Regression Method to Find Radial Natural Frequencies of Hemispherical Resonator
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title_full	Explicit Novel Nonlinear Regression Method to Find Radial Natural Frequencies of Hemispherical Resonator
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author_browse	Limkar, Beena Vaidya, Vinay Chandekar, Gautam
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title_sort	explicit novel nonlinear regression method to find radial natural frequencies of hemispherical resonator
title_auth	Explicit Novel Nonlinear Regression Method to Find Radial Natural Frequencies of Hemispherical Resonator
abstract	Background Hemispherical shells are commonly used in percussion instruments such as Hang, Bell, and Singing Bowls as well as other engineering applications. The dynamic properties of a hemispherical shell are important, especially for music which demands close control of the natural frequencies. Purpose Theoretically, the dynamic behavior of hemispherical shell is studied by solving very complex differential equations and mostly results are available for thin shells. Finite element analysis (FEA) is thus favored but it requires costly software and special expertise. FEA is also mesh-sensitive and mesh-independent analysis is required. Considering these facts, in this paper, an explicit nonlinear equation is formulated, which is a function of the geometry and material parameters. Methodology In this paper, the proposed explicit nonlinear equation is formulated using nonlinear regression with 4000 simulated data points generated using software. It obeys dimensional homogeneity and is validated using numerical and experimental methods. Results Validation of this equation using numerical data shows RMS error mostly less than 6% and 5% for geometry and material parameters, respectively. Frequency values of two manufactured hemispherical shells are extracted using audio analysis as well as experimental and operational modal analysis. The validation of these experimentally obtained frequencies with the proposed explicit equation gives a maximum absolute error of less than 5%, except in a few higher modes it is up to 7%. Conclusion The proposed nonlinear explicit equation predicts the first four radial mode frequencies of a hemispherical shell just by entering a few physically significant parameters. It can be used to design shells demanding close control of the frequency values. The model can also be used in optimization. © Krishtel eMaging Solutions Private Limited 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
abstractGer	Background Hemispherical shells are commonly used in percussion instruments such as Hang, Bell, and Singing Bowls as well as other engineering applications. The dynamic properties of a hemispherical shell are important, especially for music which demands close control of the natural frequencies. Purpose Theoretically, the dynamic behavior of hemispherical shell is studied by solving very complex differential equations and mostly results are available for thin shells. Finite element analysis (FEA) is thus favored but it requires costly software and special expertise. FEA is also mesh-sensitive and mesh-independent analysis is required. Considering these facts, in this paper, an explicit nonlinear equation is formulated, which is a function of the geometry and material parameters. Methodology In this paper, the proposed explicit nonlinear equation is formulated using nonlinear regression with 4000 simulated data points generated using software. It obeys dimensional homogeneity and is validated using numerical and experimental methods. Results Validation of this equation using numerical data shows RMS error mostly less than 6% and 5% for geometry and material parameters, respectively. Frequency values of two manufactured hemispherical shells are extracted using audio analysis as well as experimental and operational modal analysis. The validation of these experimentally obtained frequencies with the proposed explicit equation gives a maximum absolute error of less than 5%, except in a few higher modes it is up to 7%. Conclusion The proposed nonlinear explicit equation predicts the first four radial mode frequencies of a hemispherical shell just by entering a few physically significant parameters. It can be used to design shells demanding close control of the frequency values. The model can also be used in optimization. © Krishtel eMaging Solutions Private Limited 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
abstract_unstemmed	Background Hemispherical shells are commonly used in percussion instruments such as Hang, Bell, and Singing Bowls as well as other engineering applications. The dynamic properties of a hemispherical shell are important, especially for music which demands close control of the natural frequencies. Purpose Theoretically, the dynamic behavior of hemispherical shell is studied by solving very complex differential equations and mostly results are available for thin shells. Finite element analysis (FEA) is thus favored but it requires costly software and special expertise. FEA is also mesh-sensitive and mesh-independent analysis is required. Considering these facts, in this paper, an explicit nonlinear equation is formulated, which is a function of the geometry and material parameters. Methodology In this paper, the proposed explicit nonlinear equation is formulated using nonlinear regression with 4000 simulated data points generated using software. It obeys dimensional homogeneity and is validated using numerical and experimental methods. Results Validation of this equation using numerical data shows RMS error mostly less than 6% and 5% for geometry and material parameters, respectively. Frequency values of two manufactured hemispherical shells are extracted using audio analysis as well as experimental and operational modal analysis. The validation of these experimentally obtained frequencies with the proposed explicit equation gives a maximum absolute error of less than 5%, except in a few higher modes it is up to 7%. Conclusion The proposed nonlinear explicit equation predicts the first four radial mode frequencies of a hemispherical shell just by entering a few physically significant parameters. It can be used to design shells demanding close control of the frequency values. The model can also be used in optimization. © Krishtel eMaging Solutions Private Limited 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
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title_short	Explicit Novel Nonlinear Regression Method to Find Radial Natural Frequencies of Hemispherical Resonator
url	https://dx.doi.org/10.1007/s42417-022-00712-8
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author2	Vaidya, Vinay Chandekar, Gautam
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up_date	2024-07-04T02:14:44.894Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">SPR052298086</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230719064738.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">230719s2022 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s42417-022-00712-8</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR052298086</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s42417-022-00712-8-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Limkar, Beena</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0002-0055-4068</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Explicit Novel Nonlinear Regression Method to Find Radial Natural Frequencies of Hemispherical Resonator</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2022</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Krishtel eMaging Solutions Private Limited 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Background Hemispherical shells are commonly used in percussion instruments such as Hang, Bell, and Singing Bowls as well as other engineering applications. The dynamic properties of a hemispherical shell are important, especially for music which demands close control of the natural frequencies. Purpose Theoretically, the dynamic behavior of hemispherical shell is studied by solving very complex differential equations and mostly results are available for thin shells. Finite element analysis (FEA) is thus favored but it requires costly software and special expertise. FEA is also mesh-sensitive and mesh-independent analysis is required. Considering these facts, in this paper, an explicit nonlinear equation is formulated, which is a function of the geometry and material parameters. Methodology In this paper, the proposed explicit nonlinear equation is formulated using nonlinear regression with 4000 simulated data points generated using software. It obeys dimensional homogeneity and is validated using numerical and experimental methods. Results Validation of this equation using numerical data shows RMS error mostly less than 6% and 5% for geometry and material parameters, respectively. Frequency values of two manufactured hemispherical shells are extracted using audio analysis as well as experimental and operational modal analysis. The validation of these experimentally obtained frequencies with the proposed explicit equation gives a maximum absolute error of less than 5%, except in a few higher modes it is up to 7%. Conclusion The proposed nonlinear explicit equation predicts the first four radial mode frequencies of a hemispherical shell just by entering a few physically significant parameters. It can be used to design shells demanding close control of the frequency values. The model can also be used in optimization.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hemispherical resonator</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nonlinear regression</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Natural frequency</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Experimental modal analysis</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Operational modal analysis</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Vaidya, Vinay</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Chandekar, Gautam</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of vibration engineering & technologies</subfield><subfield code="d">Singapore : Springer Singapore, 2018</subfield><subfield code="g">11(2022), 5 vom: 17. 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