Free Transverse Vibration Analysis of Axially Functionally Graded Tapered Euler-Bernoulli Beams through Spline Finite Point Method
A new model for the free transverse vibration of axially functionally graded (FG) tapered Euler-Bernoulli beams is developed through the spline finite point method (SFPM) by investigating the effects of the variation of cross-sectional and material properties along the longitudinal directions. In th...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2016/5891030 |
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| author | Peng Liu Kun Lin Hongjun Liu Rong Qin |
| author_facet | Peng Liu Kun Lin Hongjun Liu Rong Qin |
| author_sort | Peng Liu |
| collection | DOAJ |
| description | A new model for the free transverse vibration of axially functionally graded (FG) tapered Euler-Bernoulli beams is developed through the spline finite point method (SFPM) by investigating the effects of the variation of cross-sectional and material properties along the longitudinal directions. In the proposed method, the beam is discretized with a set of uniformly scattered spline nodes along the beam axis instead of meshes, and the displacement field is approximated by the particularly constructed cubic B-spline interpolation functions with good adaptability for various boundary conditions. Unlike traditional discretization and modeling methods, the global structural stiffness and mass matrices for beams of the proposed model are directly generated after spline discretization without needing element meshes, generation, and assembling. The proposed method shows the distinguished features of high modeling efficiency, low computational cost, and convenience for boundary condition treatment. The performance of the proposed method is verified through numerical examples available in the published literature. All results demonstrate that the proposed method can analyze the free vibration of axially FG tapered Euler-Bernoulli beams with various boundary conditions. Moreover, high accuracy and efficiency can be achieved. |
| format | Article |
| id | doaj-art-c6c81c4738f14c22a9e41438b2582801 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-c6c81c4738f14c22a9e41438b25828012025-02-03T01:12:01ZengWileyShock and Vibration1070-96221875-92032016-01-01201610.1155/2016/58910305891030Free Transverse Vibration Analysis of Axially Functionally Graded Tapered Euler-Bernoulli Beams through Spline Finite Point MethodPeng Liu0Kun Lin1Hongjun Liu2Rong Qin3Shenzhen Engineering Lab for Wind Environment and Technology, Shenzhen Key Lab of Urban & Civil Engineering Disaster Prevention & Reduction, Shenzhen Graduate School, Harbin Institute of Technology, Guangdong, Shenzhen 518055, ChinaShenzhen Engineering Lab for Wind Environment and Technology, Shenzhen Key Lab of Urban & Civil Engineering Disaster Prevention & Reduction, Shenzhen Graduate School, Harbin Institute of Technology, Guangdong, Shenzhen 518055, ChinaShenzhen Engineering Lab for Wind Environment and Technology, Shenzhen Key Lab of Urban & Civil Engineering Disaster Prevention & Reduction, Shenzhen Graduate School, Harbin Institute of Technology, Guangdong, Shenzhen 518055, ChinaCollege of Civil Engineering and Architecture, Guangxi University, Guangxi, Nanning 530004, ChinaA new model for the free transverse vibration of axially functionally graded (FG) tapered Euler-Bernoulli beams is developed through the spline finite point method (SFPM) by investigating the effects of the variation of cross-sectional and material properties along the longitudinal directions. In the proposed method, the beam is discretized with a set of uniformly scattered spline nodes along the beam axis instead of meshes, and the displacement field is approximated by the particularly constructed cubic B-spline interpolation functions with good adaptability for various boundary conditions. Unlike traditional discretization and modeling methods, the global structural stiffness and mass matrices for beams of the proposed model are directly generated after spline discretization without needing element meshes, generation, and assembling. The proposed method shows the distinguished features of high modeling efficiency, low computational cost, and convenience for boundary condition treatment. The performance of the proposed method is verified through numerical examples available in the published literature. All results demonstrate that the proposed method can analyze the free vibration of axially FG tapered Euler-Bernoulli beams with various boundary conditions. Moreover, high accuracy and efficiency can be achieved.http://dx.doi.org/10.1155/2016/5891030 |
| spellingShingle | Peng Liu Kun Lin Hongjun Liu Rong Qin Free Transverse Vibration Analysis of Axially Functionally Graded Tapered Euler-Bernoulli Beams through Spline Finite Point Method Shock and Vibration |
| title | Free Transverse Vibration Analysis of Axially Functionally Graded Tapered Euler-Bernoulli Beams through Spline Finite Point Method |
| title_full | Free Transverse Vibration Analysis of Axially Functionally Graded Tapered Euler-Bernoulli Beams through Spline Finite Point Method |
| title_fullStr | Free Transverse Vibration Analysis of Axially Functionally Graded Tapered Euler-Bernoulli Beams through Spline Finite Point Method |
| title_full_unstemmed | Free Transverse Vibration Analysis of Axially Functionally Graded Tapered Euler-Bernoulli Beams through Spline Finite Point Method |
| title_short | Free Transverse Vibration Analysis of Axially Functionally Graded Tapered Euler-Bernoulli Beams through Spline Finite Point Method |
| title_sort | free transverse vibration analysis of axially functionally graded tapered euler bernoulli beams through spline finite point method |
| url | http://dx.doi.org/10.1155/2016/5891030 |
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