Document Type : Research Paper


Power Mechanics Engineering Techniques, Technical Engineering College/ Mosul, Northern Technical University, Mosul, Iraq


Tapered beams are more effective than uniform beams because they offer a superior distribution of mass and strength and also satisfy unique functional requirements in many engineering applications. This study calculates the mode shapes and natural frequencies of straight and various tapered Euler-Bernoulli beams by finite elements using ANSYS 16.5 software. The dynamic response for a cantilever beam was obtained for different taper angles. The results were compared with the dynamic response of a straight cantilever beam, to show the effect of the taper ratio on the dynamic response of the cantilever beam, when its volume and mass are constant. The results showed that the natural frequencies were increased as the taper angle increases, and the torsional natural frequencies were shifted from the fourth natural frequency to the fifth one as the taper angle increases.


Main Subjects

  1. De’nan, N. S. Hashim, and X. Y. Sua, “Parametrical analysis of the tapered steel section with elliptical perforation: Shear behaviour effects,” World Journal of Engineering, 2022. doi:10.1108/wje-03-2022-0107
  2. Boreyri, P. Mohtat, M. J. Ketabdari, and A. Moosavi, “Vibration analysis of a tapered beam with exponentially varying thickness resting on Winkler Foundation using the Differential Transform Method,” International Journal of Physical Research, vol. 2, no. 1, 2014. doi:10.14419/ijpr.v2i1.2152
  3. Rajesh and K.M. Saheb," Large amplitude free vibration analysis of tapered timoshenko beams using coupled displacement field method" Int. J. of Applied Mechanics and Engineering, 2018, vol.23, No.3, pp.673-688.
  4. Bazoune, “Effect of tapering on natural frequencies of rotating beams,” Shock and Vibration, vol. 14, no. 3, pp. 169–179, 2007. doi:10.1155/2007/865109
  5. Attarnejad, N. Manavi, and A. Farsad, “Exact solution for the free vibration of a tapered beam with elastic end rotational restraints,” Computational Methods, pp. 1993–2003. doi:10.1007/978-1-4020-3953-9_146
  6. Luay S. Al-Ansari, Ali M. H. Al-Hajjar, Husam Jawad A. " Calculating the natural frequency of cantilever tapered beam using classical Rayleigh, modified Rayleigh and finite element methods" International Journal of Engineering & Technology, 7 (4) (2018) 4866-4872.
  7. Byoung Koo Lee, et al. “Free vibrations of tapered Beams with general boundary condition". Journal of Civil Engineering, Vol. 6, Issue 3, p. 283-288, 2002.
  8. Firouz-Abadi R. D, et al. "An asymptotic solution to transverse free vibrations of variable-section beams". Journal of Sound and Vibration, Vol. 304, p. 530-540, 2007.
  9. Bayat, I. Pakar, and M. Bayat, “Analytical study on the vibration frequencies of tapered beams,” Latin American Journal of Solids and Structures, vol. 8, no. 2, pp. 149–162, 2011. doi:10.1590/s1679-78252011000200003
  10. V. Maganti and M. R. Nalluri, “Flapwise bending vibration analysis of functionally graded rotating double-tapered beams,” International Journal of Mechanical and Materials Engineering, vol. 10, no. 1, 2015. doi:10.1186/s40712-015-0040-0
  11. Raju L.S., Raju K. and Rao G.V. "Large amplitude free vibrations of tapered beams", AIAA Journal, (1976) vol.14, No.2, pp.280-282.
  12. Rishi Kumar Shukla " Vibration Analysis of Tapered Beam" Master thesis, Department of Mechanical Engineering National Institute of Technology, Rourkela Rourkela-769008, Odisha, INDIA May 2013.
  13. S. AlAli, M. B. Abdulrahman, and B. A. Tayeh, “Response of reinforced concrete tapered beams strengthened using NSM-CFRP laminates,” Tikrit Journal of Engineering Sciences, vol. 29, no. 1, pp. 99–110, 2022. doi:10.25130/tjes.29.1.08.
  14. Haskul and M. Kisa, “Free vibration of the double tapered cracked beam,” Inverse Problems in Science and Engineering, vol. 29, no. 11, pp. 1537–1564, 2021. doi:10.1080/17415977.2020.1870971
  15. El Hantati, A. Adri, H. Fakhreddine, S. Rifai, and R. Benamar, “Multimode analysis of geometrically nonlinear transverse free and forced vibrations of tapered beams,” Shock and Vibration, vol. 2022, pp. 1–22, 2022. doi:10.1155/2022/8464255
  16. Nawal H. Al – Raheimy," Transverse free vibrations of tapered cantilever beam" The Iraqi Journal for Mechanical and Material Engineering, Vol.13, No.2, 2013.
  17. Luay S. Al-Ansari, “Calculating of Natural Frequency of Step-ping Cantilever Beam”, International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:1 2 No:05, (2012).
  18. Luay S. Al-Ansari, “Calculating Static Deflection and Natural Frequency of Stepped Cantilever Beam Using Modified RAY-LEIGH Method”, International Journal of Mechanical and Production Engineering Research and Development (IJMPERD) 3, Issue 4, Oct 2013.
  19. Luay S. Al-Ansari, Muhannad Al-Waily and Ali M. H. Yusif, "Vibration Analysis of Hyper Composite Material Beam Utilizing Shear Deformation and Rotary Inertia Effects", International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS: 12 No: 04, (2012).