A Dynamic Stiffness Element for Free Vibration Analysis of Delaminated Layered Beams
A dynamic stiffness element for flexural vibration analysis of delaminated multilayer beams is developed and subsequently used to investigate the natural frequencies and modes of two-layer beam configurations. Using the Euler-Bernoulli bending beam theory, the governing differential equations are ex...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Modelling and Simulation in Engineering |
| Online Access: | http://dx.doi.org/10.1155/2012/492415 |
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| author | Nicholas H. Erdelyi Seyed M. Hashemi |
| author_facet | Nicholas H. Erdelyi Seyed M. Hashemi |
| author_sort | Nicholas H. Erdelyi |
| collection | DOAJ |
| description | A dynamic stiffness element for flexural vibration analysis of delaminated multilayer beams is developed and subsequently used to investigate the natural frequencies and modes of two-layer beam configurations. Using the Euler-Bernoulli bending beam theory, the governing differential equations are exploited and representative, frequency-dependent, field variables are chosen based on the closed form solution to these equations. The boundary conditions are then imposed to formulate the dynamic stiffness matrix (DSM), which relates harmonically varying loads to harmonically varying displacements at the beam ends. The bending vibration of an illustrative example problem, characterized by delamination zone of variable length, is investigated. Two computer codes, based on the conventional Finite Element Method (FEM) and the analytical solutions reported in the literature, are also developed and used for comparison. The intact and defective beam natural frequencies and modes obtained from the proposed DSM method are presented along with the FEM and analytical results and those available in the literature. |
| format | Article |
| id | doaj-art-b003127b107a490d87bf79bb0ca907d9 |
| institution | Kabale University |
| issn | 1687-5591 1687-5605 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Modelling and Simulation in Engineering |
| spelling | doaj-art-b003127b107a490d87bf79bb0ca907d92025-02-03T06:11:47ZengWileyModelling and Simulation in Engineering1687-55911687-56052012-01-01201210.1155/2012/492415492415A Dynamic Stiffness Element for Free Vibration Analysis of Delaminated Layered BeamsNicholas H. Erdelyi0Seyed M. Hashemi1Department of Aerospace Engineering, Ryerson University, 350 Victoria Street, Toronto, ON, M5B 2K3, CanadaDepartment of Aerospace Engineering, Ryerson University, 350 Victoria Street, Toronto, ON, M5B 2K3, CanadaA dynamic stiffness element for flexural vibration analysis of delaminated multilayer beams is developed and subsequently used to investigate the natural frequencies and modes of two-layer beam configurations. Using the Euler-Bernoulli bending beam theory, the governing differential equations are exploited and representative, frequency-dependent, field variables are chosen based on the closed form solution to these equations. The boundary conditions are then imposed to formulate the dynamic stiffness matrix (DSM), which relates harmonically varying loads to harmonically varying displacements at the beam ends. The bending vibration of an illustrative example problem, characterized by delamination zone of variable length, is investigated. Two computer codes, based on the conventional Finite Element Method (FEM) and the analytical solutions reported in the literature, are also developed and used for comparison. The intact and defective beam natural frequencies and modes obtained from the proposed DSM method are presented along with the FEM and analytical results and those available in the literature.http://dx.doi.org/10.1155/2012/492415 |
| spellingShingle | Nicholas H. Erdelyi Seyed M. Hashemi A Dynamic Stiffness Element for Free Vibration Analysis of Delaminated Layered Beams Modelling and Simulation in Engineering |
| title | A Dynamic Stiffness Element for Free Vibration Analysis of Delaminated Layered Beams |
| title_full | A Dynamic Stiffness Element for Free Vibration Analysis of Delaminated Layered Beams |
| title_fullStr | A Dynamic Stiffness Element for Free Vibration Analysis of Delaminated Layered Beams |
| title_full_unstemmed | A Dynamic Stiffness Element for Free Vibration Analysis of Delaminated Layered Beams |
| title_short | A Dynamic Stiffness Element for Free Vibration Analysis of Delaminated Layered Beams |
| title_sort | dynamic stiffness element for free vibration analysis of delaminated layered beams |
| url | http://dx.doi.org/10.1155/2012/492415 |
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