In-Plane Free Vibration Analysis of a Scimitar-Type Rotating Curved Beam Using the Adomian Modified Decomposition Method
Free in-plane vibrations of a scimitar-type nonprismatic rotating curved beam, with a variable cross-section and increasing sweep along the leading edge, are calculated using an innovative, efficient and accurate solver called the Adomian modified decomposition method (AMDM). The equation of motion...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Mathematical and Computational Applications |
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| Online Access: | https://www.mdpi.com/2297-8747/25/4/68 |
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| author | Desmond Adair Martin Jaeger |
| author_facet | Desmond Adair Martin Jaeger |
| author_sort | Desmond Adair |
| collection | DOAJ |
| description | Free in-plane vibrations of a scimitar-type nonprismatic rotating curved beam, with a variable cross-section and increasing sweep along the leading edge, are calculated using an innovative, efficient and accurate solver called the Adomian modified decomposition method (AMDM). The equation of motion includes the axial force resulting from centrifugal stiffening, and the boundary conditions imposed are those of a cantilever beam, i.e., clamped-free and simple-free. The AMDM allows the governing differential equation to become a recursive algebraic equation suitable for symbolic computation, and, after additional simple mathematical operations, the natural frequencies and corresponding closed-form series solution of the mode shapes are obtained simultaneously. Two main advantages of the application of the AMDM are its fast convergence rate to a solution and its high degree of accuracy. The design shape parameters of the beam, such as transitioning from a straight beam pattern to a curved beam pattern, are investigated. The accuracy of the model is investigated using previously reported investigations and using an innovative error analysis procedure. |
| first_indexed | 2024-03-10T15:36:50Z |
| format | Article |
| id | doaj.art-c68c83211aef4afb990e2973c5a7b1a6 |
| institution | Directory Open Access Journal |
| issn | 1300-686X 2297-8747 |
| language | English |
| last_indexed | 2024-03-10T15:36:50Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj.art-c68c83211aef4afb990e2973c5a7b1a62023-11-20T17:13:18ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472020-10-012546810.3390/mca25040068In-Plane Free Vibration Analysis of a Scimitar-Type Rotating Curved Beam Using the Adomian Modified Decomposition MethodDesmond Adair0Martin Jaeger1Department of Mechanical & Aerospace Engineering, Nazarbayev University, Nur-Sultan, KazakhstanDepartment of Civil Engineering, Australian College of Kuwait, West Mishref, KuwaitFree in-plane vibrations of a scimitar-type nonprismatic rotating curved beam, with a variable cross-section and increasing sweep along the leading edge, are calculated using an innovative, efficient and accurate solver called the Adomian modified decomposition method (AMDM). The equation of motion includes the axial force resulting from centrifugal stiffening, and the boundary conditions imposed are those of a cantilever beam, i.e., clamped-free and simple-free. The AMDM allows the governing differential equation to become a recursive algebraic equation suitable for symbolic computation, and, after additional simple mathematical operations, the natural frequencies and corresponding closed-form series solution of the mode shapes are obtained simultaneously. Two main advantages of the application of the AMDM are its fast convergence rate to a solution and its high degree of accuracy. The design shape parameters of the beam, such as transitioning from a straight beam pattern to a curved beam pattern, are investigated. The accuracy of the model is investigated using previously reported investigations and using an innovative error analysis procedure.https://www.mdpi.com/2297-8747/25/4/68non-prismatic beamAdomian modified decomposition methodrotationcurved beamerror analysis |
| spellingShingle | Desmond Adair Martin Jaeger In-Plane Free Vibration Analysis of a Scimitar-Type Rotating Curved Beam Using the Adomian Modified Decomposition Method Mathematical and Computational Applications non-prismatic beam Adomian modified decomposition method rotation curved beam error analysis |
| title | In-Plane Free Vibration Analysis of a Scimitar-Type Rotating Curved Beam Using the Adomian Modified Decomposition Method |
| title_full | In-Plane Free Vibration Analysis of a Scimitar-Type Rotating Curved Beam Using the Adomian Modified Decomposition Method |
| title_fullStr | In-Plane Free Vibration Analysis of a Scimitar-Type Rotating Curved Beam Using the Adomian Modified Decomposition Method |
| title_full_unstemmed | In-Plane Free Vibration Analysis of a Scimitar-Type Rotating Curved Beam Using the Adomian Modified Decomposition Method |
| title_short | In-Plane Free Vibration Analysis of a Scimitar-Type Rotating Curved Beam Using the Adomian Modified Decomposition Method |
| title_sort | in plane free vibration analysis of a scimitar type rotating curved beam using the adomian modified decomposition method |
| topic | non-prismatic beam Adomian modified decomposition method rotation curved beam error analysis |
| url | https://www.mdpi.com/2297-8747/25/4/68 |
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