Large Amplitude Forced Vibrations of Restrained Beams Resting on Elastic Point Supports
The present paper concerns the study of geometrically non-linear forced vibrations of beams resting on two different types of springs: rotational and translational. Assuming that the motion is harmonic, the displacement is extended as a series of spatial functions determined by solving the linear pr...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Institute of Fundamental Technological Research
2021-07-01
|
| Series: | Engineering Transactions |
| Subjects: | |
| Online Access: | https://et.ippt.pan.pl/index.php/et/article/view/1290 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849321045610201088 |
|---|---|
| author | Hatim FAKHREDDINE Ahmed ADRI Mohcine CHAJDI Said RIFAI Rhali BENAMAR |
| author_facet | Hatim FAKHREDDINE Ahmed ADRI Mohcine CHAJDI Said RIFAI Rhali BENAMAR |
| author_sort | Hatim FAKHREDDINE |
| collection | DOAJ |
| description | The present paper concerns the study of geometrically non-linear forced vibrations of beams resting on two different types of springs: rotational and translational. Assuming that the motion is harmonic, the displacement is extended as a series of spatial functions determined by solving the linear problem. Hamilton’s principle and spectral analysis are used to reduce the problem to a non-linear algebraic system solved using a previously developed approximate method. The effects of the nature of the added springs and their location on the non-linear behaviour of the beam are examined. A multimode approach is used in the forced case to obtain results over a wide range of vibration amplitudes. This leads to examining the non-linear forced dynamic response for different positions of each spring and different levels of excitations. Following a parametric study, the non-linear forced mode shapes and their associated bending moments are presented for different levels of excitations and for different vibration amplitudes to give an estimation of the stress distribution over the beam length. |
| format | Article |
| id | doaj-art-ec300e1b574840c2a81cf342b29b34ea |
| institution | Kabale University |
| issn | 0867-888X 2450-8071 |
| language | English |
| publishDate | 2021-07-01 |
| publisher | Institute of Fundamental Technological Research |
| record_format | Article |
| series | Engineering Transactions |
| spelling | doaj-art-ec300e1b574840c2a81cf342b29b34ea2025-08-20T03:49:51ZengInstitute of Fundamental Technological ResearchEngineering Transactions0867-888X2450-80712021-07-0169310.24423/EngTrans.1290.20210709Large Amplitude Forced Vibrations of Restrained Beams Resting on Elastic Point SupportsHatim FAKHREDDINE0Ahmed ADRI1Mohcine CHAJDI2Said RIFAI3Rhali BENAMAR4Hassan II University of CasablancaHassan II University of CasablancaMohammed V University in RabatHassan II University of CasablancaMohammed V University in RabatThe present paper concerns the study of geometrically non-linear forced vibrations of beams resting on two different types of springs: rotational and translational. Assuming that the motion is harmonic, the displacement is extended as a series of spatial functions determined by solving the linear problem. Hamilton’s principle and spectral analysis are used to reduce the problem to a non-linear algebraic system solved using a previously developed approximate method. The effects of the nature of the added springs and their location on the non-linear behaviour of the beam are examined. A multimode approach is used in the forced case to obtain results over a wide range of vibration amplitudes. This leads to examining the non-linear forced dynamic response for different positions of each spring and different levels of excitations. Following a parametric study, the non-linear forced mode shapes and their associated bending moments are presented for different levels of excitations and for different vibration amplitudes to give an estimation of the stress distribution over the beam length.https://et.ippt.pan.pl/index.php/et/article/view/1290geometrical non-linearityforced vibrationsmultimode approachstress distributionelastic supports |
| spellingShingle | Hatim FAKHREDDINE Ahmed ADRI Mohcine CHAJDI Said RIFAI Rhali BENAMAR Large Amplitude Forced Vibrations of Restrained Beams Resting on Elastic Point Supports Engineering Transactions geometrical non-linearity forced vibrations multimode approach stress distribution elastic supports |
| title | Large Amplitude Forced Vibrations of Restrained Beams Resting on Elastic Point Supports |
| title_full | Large Amplitude Forced Vibrations of Restrained Beams Resting on Elastic Point Supports |
| title_fullStr | Large Amplitude Forced Vibrations of Restrained Beams Resting on Elastic Point Supports |
| title_full_unstemmed | Large Amplitude Forced Vibrations of Restrained Beams Resting on Elastic Point Supports |
| title_short | Large Amplitude Forced Vibrations of Restrained Beams Resting on Elastic Point Supports |
| title_sort | large amplitude forced vibrations of restrained beams resting on elastic point supports |
| topic | geometrical non-linearity forced vibrations multimode approach stress distribution elastic supports |
| url | https://et.ippt.pan.pl/index.php/et/article/view/1290 |
| work_keys_str_mv | AT hatimfakhreddine largeamplitudeforcedvibrationsofrestrainedbeamsrestingonelasticpointsupports AT ahmedadri largeamplitudeforcedvibrationsofrestrainedbeamsrestingonelasticpointsupports AT mohcinechajdi largeamplitudeforcedvibrationsofrestrainedbeamsrestingonelasticpointsupports AT saidrifai largeamplitudeforcedvibrationsofrestrainedbeamsrestingonelasticpointsupports AT rhalibenamar largeamplitudeforcedvibrationsofrestrainedbeamsrestingonelasticpointsupports |