Study of Forced Vibration of Variable Cross Section Bernoulli Beam Under Time Varying Moving Loads
Abstract
In this study, forced vibration characteristic of a variable cross section beam subjected to a time varying moving loads is examined. The Garlerkin’s method is employed to solve the equation of motion to obtain the dynamic response of the variable cross section beam. The pinned end condition for the beam is considered. Analyses of the solutions obtained were carried out and various results were displayed in plotted curve. It is concluded that with increasing in load factor, the dynamic response amplitudes of beam increases. Effect of foundational stiffness of the beam was also instituted.
References
[1] Fryba, L. (1972) Vibration of Solids and Structures under Moving Loads. Groningen: Noordhoff International, Groningen, The Netherlands.
[2] Wang, R.T. (1997). Vibration of multi-span Timoshenko beams to a moving force. Journal of Sound and Vibration, 207, 731–742.
[3] Fan, Z.J., Lee, J.H., Kang, K.H., Kim, K.J. (1998). The forced vibration of a beam with viscoelastic boundary supports, J. Sound Vib. 210 (5) ,673–682.
[4] Azrar, L., Benamar, R., White, R.G., (1999). A semi-analytical approach to the non-linear dynamic response problem of S-S and C-C beams at large vibration amplitudes Part I: general theory and application to the single mode approach to free and forced vibration analysis, J. Sound Vib. 224 (2), 183–207.
[5] Taha M.H, Abohadima S., (2008). Mathematical model for vibrations of non-uniform beams. Engineering MECHANICS, Vol. 15, No. 1, p. 3–11
[6] Majkut, L., (2009). Free and forced vibrations of Timoshenko beams described by single difference equation, J. Theor. Appl. Mech. 47 (1) ,193–210.
[7] Adedowole A., (2016). Flexural motions under moving distributed masses of Beam- type structures on Vlasoff foundation and having time dependent boundary conditions. Ph.D thesis. Federal University of Technology, Akure, Nigeria.
[8] Xie, K. Wang, Y., Fan, X., Fu, T. (2019). Nonlinear free vibration analysis of functionally graded beams by using different shear deformation theories, Appl. Math. Model. 77 , 1860–1880.
[9] Hosseini, S.M., Al-Jumaily, A. (2019). Analytical solution for forced vibration of Piezoelectrically actuated Timoshenko beam, J. Intell. Mater. Syst. Struct. 30 (8), 1276–1284.
[10] Omolofe, B., Adedowole, A. (2019). Transverse Response of a Structural Member with Time Dependent Boundary Conditions to Moving Distributed Mass. Journal of Applied Nonlinear Dynamics.; 8(2):167-187,. https://lhscientificpublishing.com/Journals/JAND-Default.aspx
[11] Sheng, G.G., Wang, X. (2019). Nonlinear forced vibration of functionally graded Timoshenko microbeams with thermal effect and parametric excitation, Int. J. Mech. Sci. 155 , 405–416.
[12] Adedowole, A. (2020).On The Transverse Vibrations of Rotating Timoshenko Beams Subjected to two Concentrated Moving Loads, The Coast Journal of The Faculty Of Science OSUSTECH Okitipupa 1(2) 211-221.
[13] Saheb , K. M., Kanneti , G., Sathujoda, P. (2022)., Large amplitude forced vibrations of Timoshenko beams using coupled displacement field method , Forces in Mechanics 7, 100079
[2] Wang, R.T. (1997). Vibration of multi-span Timoshenko beams to a moving force. Journal of Sound and Vibration, 207, 731–742.
[3] Fan, Z.J., Lee, J.H., Kang, K.H., Kim, K.J. (1998). The forced vibration of a beam with viscoelastic boundary supports, J. Sound Vib. 210 (5) ,673–682.
[4] Azrar, L., Benamar, R., White, R.G., (1999). A semi-analytical approach to the non-linear dynamic response problem of S-S and C-C beams at large vibration amplitudes Part I: general theory and application to the single mode approach to free and forced vibration analysis, J. Sound Vib. 224 (2), 183–207.
[5] Taha M.H, Abohadima S., (2008). Mathematical model for vibrations of non-uniform beams. Engineering MECHANICS, Vol. 15, No. 1, p. 3–11
[6] Majkut, L., (2009). Free and forced vibrations of Timoshenko beams described by single difference equation, J. Theor. Appl. Mech. 47 (1) ,193–210.
[7] Adedowole A., (2016). Flexural motions under moving distributed masses of Beam- type structures on Vlasoff foundation and having time dependent boundary conditions. Ph.D thesis. Federal University of Technology, Akure, Nigeria.
[8] Xie, K. Wang, Y., Fan, X., Fu, T. (2019). Nonlinear free vibration analysis of functionally graded beams by using different shear deformation theories, Appl. Math. Model. 77 , 1860–1880.
[9] Hosseini, S.M., Al-Jumaily, A. (2019). Analytical solution for forced vibration of Piezoelectrically actuated Timoshenko beam, J. Intell. Mater. Syst. Struct. 30 (8), 1276–1284.
[10] Omolofe, B., Adedowole, A. (2019). Transverse Response of a Structural Member with Time Dependent Boundary Conditions to Moving Distributed Mass. Journal of Applied Nonlinear Dynamics.; 8(2):167-187,. https://lhscientificpublishing.com/Journals/JAND-Default.aspx
[11] Sheng, G.G., Wang, X. (2019). Nonlinear forced vibration of functionally graded Timoshenko microbeams with thermal effect and parametric excitation, Int. J. Mech. Sci. 155 , 405–416.
[12] Adedowole, A. (2020).On The Transverse Vibrations of Rotating Timoshenko Beams Subjected to two Concentrated Moving Loads, The Coast Journal of The Faculty Of Science OSUSTECH Okitipupa 1(2) 211-221.
[13] Saheb , K. M., Kanneti , G., Sathujoda, P. (2022)., Large amplitude forced vibrations of Timoshenko beams using coupled displacement field method , Forces in Mechanics 7, 100079
Published
2023-07-30
How to Cite
ADEDOWOLE, A.; OGUNYEBI, S. N.; FAMUAGUN, K. S.
Study of Forced Vibration of Variable Cross Section Bernoulli Beam Under Time Varying Moving Loads.
International Journal of Advanced Research in Engineering Innovation, [S.l.], v. 5, n. 2, p. 24-36, july 2023.
Available at: <https://myjms.mohe.gov.my/index.php/ijarei/article/view/23349>. Date accessed: 09 sep. 2024.
Section
Articles
