Dynamic Characteristics of a Beam with a Shallow Crack Using Alternative Admissible Functions
The presence of a crack in a beam leads to changes in its dynamic characteristics and hence changes in its natural frequencies and mode shapes. In this paper, Alternative Admissible Functions (<i>AAF</i>) with penalties for extracting the dynamic characteristics of a Euler–Bernoulli Beam...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-02-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/2/311 |
| _version_ | 1797476406736715776 |
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| author | Srividyadhare Kateel Natalie Baddour |
| author_facet | Srividyadhare Kateel Natalie Baddour |
| author_sort | Srividyadhare Kateel |
| collection | DOAJ |
| description | The presence of a crack in a beam leads to changes in its dynamic characteristics and hence changes in its natural frequencies and mode shapes. In this paper, Alternative Admissible Functions (<i>AAF</i>) with penalties for extracting the dynamic characteristics of a Euler–Bernoulli Beam with a shallow crack is proposed and validated. The proposed method has two key advantages. First, the alternative admissible function choice is independent of the boundary conditions, which are modelled via boundary penalty terms. Second, the crack is treated as a penalty function to account for the local stiffness reduction while ensuring beam continuity. The approach is validated with different crack depth ratios and locations. The mass, stiffness, and penalty function matrices for Simply Supported (<i>SS</i>), Clamped–Clamped (<i>CC</i>), and Clamped–Free (<i>CF</i>) are developed and are used in the analysis of a beam with a shallow crack. The proposed method demonstrates results in good agreement with published literature for shallow cracks. A significant advantage of the proposed method is the ease of applicability, eliminating the need for remodeling with changes in boundary conditions or crack parameters. The results show that the crack introduces asymmetry to the beam and may require changing the boundary penalty values, depending on the location and depth of the crack. |
| first_indexed | 2024-03-09T20:57:21Z |
| format | Article |
| id | doaj.art-56f5f26c2e9d41a5b480f9d93d87a82a |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T20:57:21Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-56f5f26c2e9d41a5b480f9d93d87a82a2023-11-23T22:16:34ZengMDPI AGSymmetry2073-89942022-02-0114231110.3390/sym14020311Dynamic Characteristics of a Beam with a Shallow Crack Using Alternative Admissible FunctionsSrividyadhare Kateel0Natalie Baddour1Department of Mechanical Engineering, University of Ottawa, Ottawa, ON K1N 6N5, CanadaDepartment of Mechanical Engineering, University of Ottawa, Ottawa, ON K1N 6N5, CanadaThe presence of a crack in a beam leads to changes in its dynamic characteristics and hence changes in its natural frequencies and mode shapes. In this paper, Alternative Admissible Functions (<i>AAF</i>) with penalties for extracting the dynamic characteristics of a Euler–Bernoulli Beam with a shallow crack is proposed and validated. The proposed method has two key advantages. First, the alternative admissible function choice is independent of the boundary conditions, which are modelled via boundary penalty terms. Second, the crack is treated as a penalty function to account for the local stiffness reduction while ensuring beam continuity. The approach is validated with different crack depth ratios and locations. The mass, stiffness, and penalty function matrices for Simply Supported (<i>SS</i>), Clamped–Clamped (<i>CC</i>), and Clamped–Free (<i>CF</i>) are developed and are used in the analysis of a beam with a shallow crack. The proposed method demonstrates results in good agreement with published literature for shallow cracks. A significant advantage of the proposed method is the ease of applicability, eliminating the need for remodeling with changes in boundary conditions or crack parameters. The results show that the crack introduces asymmetry to the beam and may require changing the boundary penalty values, depending on the location and depth of the crack.https://www.mdpi.com/2073-8994/14/2/311vibrationbeamcracked beamsassumed modeseigenvaluesnatural frequencies |
| spellingShingle | Srividyadhare Kateel Natalie Baddour Dynamic Characteristics of a Beam with a Shallow Crack Using Alternative Admissible Functions Symmetry vibration beam cracked beams assumed modes eigenvalues natural frequencies |
| title | Dynamic Characteristics of a Beam with a Shallow Crack Using Alternative Admissible Functions |
| title_full | Dynamic Characteristics of a Beam with a Shallow Crack Using Alternative Admissible Functions |
| title_fullStr | Dynamic Characteristics of a Beam with a Shallow Crack Using Alternative Admissible Functions |
| title_full_unstemmed | Dynamic Characteristics of a Beam with a Shallow Crack Using Alternative Admissible Functions |
| title_short | Dynamic Characteristics of a Beam with a Shallow Crack Using Alternative Admissible Functions |
| title_sort | dynamic characteristics of a beam with a shallow crack using alternative admissible functions |
| topic | vibration beam cracked beams assumed modes eigenvalues natural frequencies |
| url | https://www.mdpi.com/2073-8994/14/2/311 |
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