Closed form solution of nonlinear oscillation of a cantilever beam using λ-symmetry linearization criteria

Creative Commons License

Mara'Beh R. A., Al-Dweik A. Y., Yilbas B., SUNAR M.

Heliyon, cilt.8, sa.11, 2022 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 8 Sayı: 11
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1016/j.heliyon.2022.e11673
  • Dergi Adı: Heliyon
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, CAB Abstracts, Food Science & Technology Abstracts, Veterinary Science Database, Directory of Open Access Journals
  • Anahtar Kelimeler: Cantilever beam, Non-linear oscillation, Closed form solution, Lie-Tresse linearization
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Ankara Yıldırım Beyazıt Üniversitesi Adresli: Evet

Özet

© 2022 The Author(s)A mechanical system, in general, undergoes vibrational motion when the system is subjected to a tension or an external force. One of the examples of such a system is a cantilever beam when it is exposed to a bending action. When the tension is released, the cantilever beam suffers from the oscillations until the strain energy is totally released through the damping characteristics of the cantilever beam. Depending on the stiffness and damping factors of the beam, the vibrational motion can be non-linear; in which case, the analytical solution becomes challenging formulating the flexural characteristics of the beam. Although numerical solution for the non-linear problem is possible, the analytical solution provides useful information between the mechanical response and the cantilever beam characteristics. In the present study, the analytical solution of the non-linear equations governing the motion of the cantilever beam is presented. The governing equation is linearized incorporating the Lie-Tresse linearization method. The closed form solution for the displacement of the cantilever beam is reduced to a linear solution after introducing the appropriate beam characteristics. The dynamic behavior of the flexural motion due to non-linear and linear cantilever beams are compared.