LATERAL VIBRATION OF CANTILEVERS ON VISCOELASTIC FOUNDATIONS | ||||
| The International Conference on Applied Mechanics and Mechanical Engineering | ||||
| Article 10, Volume 1, 2nd Conference on Applied Mechanical Engineering., May 1986, Page 13-22 PDF (3.07 MB) | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/amme.1986.51793 | ||||
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| Author | ||||
| S. A. KASSEM | ||||
| Associate Professor, Mechanical Design and Production Department, Faculty of Engineering, Cairo University, Cairo, Egypt. | ||||
| Abstract | ||||
| Lateral vibrations of uniform cantilevers resting on viscoelastic foundations are investigated. Effect of foundation parameters and a follower force applied at the cantilever free end, on natural frequencies and vibration stability is studied. The system governing equations reduced to a dimension less form, is solved using variational method, with three modes of vibrations taken into account. The second and third natural frequencies are shown to increase with the increase of either the foundation elastic and shear rigidities or the applied external tensile force. The first natural frequency increases with increasing the foundation elastic rigidity, while it decreases with the increase of the foundation shear rigidity and/or the tensile follower force, till it vanishes indicating vibration instability. Regions of stable vibrations are determined when the cantilever is subjected to a tensile or compressive follower force. Results obtained can be used for design purposes to determine the foundation parameters that should be guaranteed for stable vibrations when a certain follower force is applied to the beam, or alternatively to determine the limits to be imppsed on this force when the cantilever is mounted on a viscoelastic medium of known parameters. | ||||
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