A Modified FEM for Transverse and Lateral Vibration Analysis of Thin Beams Under a Mass Moving with a Variable Acceleration
Abstract In this paper, a new modified finite element method that can be used in the analysis of transverse and lateral vibrations of the thin beams under a point mass moving with a variable acceleration and constant jerk is presented. Jerk is the change in acceleration over time. In this method, th...
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| Format: | Article |
| Language: | English |
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Marcílio Alves
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| Series: | Latin American Journal of Solids and Structures |
| Subjects: | |
| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252017000300485&lng=en&tlng=en |
| _version_ | 1811283526011584512 |
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| author | Ismail Esen |
| author_facet | Ismail Esen |
| author_sort | Ismail Esen |
| collection | DOAJ |
| description | Abstract In this paper, a new modified finite element method that can be used in the analysis of transverse and lateral vibrations of the thin beams under a point mass moving with a variable acceleration and constant jerk is presented. Jerk is the change in acceleration over time. In this method, the classical finite element of the beam is modified by the inclusion of the inertial effects of the moving mass. This modification is made using the relations between nodal forces and nodal deflections and shape functions of six DOF beam element. The mass, stiffness, and damping matrices of the modified finite element are determined by forces caused by the corresponding transverse and lateral accelerations and jerks, and transverse Coriolis and centripetal accelerations and jerks, respectively. This method was first applied on a simply supported beam plate to provide a comparison with the previous studies in literature, and it was proved that the results were within acceptable limits. Secondly, it was applied on a CNC type box-framed beam to analyse the dynamic response of the beam in terms of variable acceleration and jerk as well as constant velocity and mass ratios. |
| first_indexed | 2024-04-13T02:13:07Z |
| format | Article |
| id | doaj.art-d09a46932e214bd09c8060f92a461646 |
| institution | Directory Open Access Journal |
| issn | 1679-7825 |
| language | English |
| last_indexed | 2024-04-13T02:13:07Z |
| publisher | Marcílio Alves |
| record_format | Article |
| series | Latin American Journal of Solids and Structures |
| spelling | doaj.art-d09a46932e214bd09c8060f92a4616462022-12-22T03:07:14ZengMarcílio AlvesLatin American Journal of Solids and Structures1679-782514348551110.1590/1679-78253180S1679-78252017000300485A Modified FEM for Transverse and Lateral Vibration Analysis of Thin Beams Under a Mass Moving with a Variable AccelerationIsmail EsenAbstract In this paper, a new modified finite element method that can be used in the analysis of transverse and lateral vibrations of the thin beams under a point mass moving with a variable acceleration and constant jerk is presented. Jerk is the change in acceleration over time. In this method, the classical finite element of the beam is modified by the inclusion of the inertial effects of the moving mass. This modification is made using the relations between nodal forces and nodal deflections and shape functions of six DOF beam element. The mass, stiffness, and damping matrices of the modified finite element are determined by forces caused by the corresponding transverse and lateral accelerations and jerks, and transverse Coriolis and centripetal accelerations and jerks, respectively. This method was first applied on a simply supported beam plate to provide a comparison with the previous studies in literature, and it was proved that the results were within acceptable limits. Secondly, it was applied on a CNC type box-framed beam to analyse the dynamic response of the beam in terms of variable acceleration and jerk as well as constant velocity and mass ratios.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252017000300485&lng=en&tlng=enFinite elementbeam vibrationsaccelerating massjerk |
| spellingShingle | Ismail Esen A Modified FEM for Transverse and Lateral Vibration Analysis of Thin Beams Under a Mass Moving with a Variable Acceleration Latin American Journal of Solids and Structures Finite element beam vibrations accelerating mass jerk |
| title | A Modified FEM for Transverse and Lateral Vibration Analysis of Thin Beams Under a Mass Moving with a Variable Acceleration |
| title_full | A Modified FEM for Transverse and Lateral Vibration Analysis of Thin Beams Under a Mass Moving with a Variable Acceleration |
| title_fullStr | A Modified FEM for Transverse and Lateral Vibration Analysis of Thin Beams Under a Mass Moving with a Variable Acceleration |
| title_full_unstemmed | A Modified FEM for Transverse and Lateral Vibration Analysis of Thin Beams Under a Mass Moving with a Variable Acceleration |
| title_short | A Modified FEM for Transverse and Lateral Vibration Analysis of Thin Beams Under a Mass Moving with a Variable Acceleration |
| title_sort | modified fem for transverse and lateral vibration analysis of thin beams under a mass moving with a variable acceleration |
| topic | Finite element beam vibrations accelerating mass jerk |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252017000300485&lng=en&tlng=en |
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