Abstract
In this paper the free oscillations of a simply supported Euler-Bernoulli beam resting on a nonlinear spring bed with linear and cubic stiffness are studied. The system is discretized by means of the classical Galerkin procedure and its nonlinear dynamic behaviour is analyzed using the Optimal Auxiliary Functions Method (OAFM). Frequency responses are presented in a closed form and their sensitivity with respect to the initial amplitudes are investigated. It is proved that OAFM is a reliable and straightforward approach to solve a set of coupled nonlinear differential equations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
T. Horibe, N. Asano, Large deflection analysis of beams on two-parameter elastic foundation using the boundary integral equation method. JSME Int. J. Series A 44(2), 231–236 (2001)
V. Rao, Large amplitude vibration of slender, uniform beams on elastic foundation. Indian J. Eng. Mater. Sci. 10, 87–91 (2003)
M. Ansari, E. Esmailzadeh, D. Younesian, Internal resonance of finite beams on nonlinear foundations traversed by a moving load, in ASME Proceedings of IMECE 2008. Paper no. IMECE2008–68188 (2016), pp. 321–2329
A.D. Senalp, A. Arikoglu, I. Ozkol, V.Z. Dogan, Dynamic response of a finite length Euler-Bernoulli beam on linear and nonlinear viscoelastic foundation to a concentrated moving force. J. Mech. Sci. Tech. 24(10), 19579961 (2010)
G.C. Tsiatas, Nonlinear analysis of non-uniform beams on nonlinear elastic foundation. Acta Mech. 209, 141–152 (2010)
U. Bhattiprolu, P. Davies, Response of a beam on nonlinear viscoelastic unilateral foundation and numerical challenges, in ASME Proceedings of IDETC/CIE, Paper no. DETC2011-48776 (2011), pp. 813–819
H. Ding, L.-Q. Chen, S.-P. Yang, Convergence of Galerkin truncation for dynamic response of finite beams on nonlinear foundation under a moving load. J. Sound Vibr. 331, 2426–2442 (2012)
D. Younesian, B. Saadatnia, H. Askari, Analytical solutions for free oscillations of beams on nonlinear elastic foundation using the variational iteration method. J. Theor. Appl. Mech. 50(2), 639–692 (2012)
P. Koziol, Z. Hryniewicz, Dynamic response of a beam resting on a nonlinear foundation to a moving load: coiflet-based solution. Shock. Vibr. 19, 995–1007 (2012)
G. Sari, M. Pakdemirli, Vibration of a slightly curved microbeam resting on an elastic foundation with nonideal boundary conditions. Math. Probl. Eng. ID736148 (2013)
S.M. Abdelghany, K.M. Ewis, A.A. Mahmoud, M.M. Nassar, Dynamic response of non uniform beam subjected to moving load and resting on a nonlinear viscoelastic foundation. J. Basic Appl. Sci. 4, 192–199 (2015)
F. Pellicano, F. Mastrodi, Nonlinear dynamics of a beam on elastic foundation. Nonlinear Dyn. 14(4), 335–355 (1997)
N. Herisanu, V. Marinca, Approximate analytical solutions to Jerk equations, in Springer Proceedings in Mathematics and Statistics, vol. 182 (2016), pp. 169–176
V. Marinca, N. Herisanu, Nonlinear Dynamical Systems in Engineering. Some approximate Approaches (Springer, Berlin, 2011)
V. Marinca, N. Herisanu, The Optimal Homotopy Asymptotic Method. Engineering Applications (Springer, Berlin, 2015)
N. Herisanu, V. Marinca, Gh Madescu, An analytical approach to non-linear dynamical model of a permanent magnet synchronous generator. Wind Energy 18, 1657–1670 (2015)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Herisanu, N., Marinca, V. (2018). Free Oscillations of Euler-Bernoulli Beams on Nonlinear Winkler-Pasternak Foundation. In: Herisanu, N., Marinca, V. (eds) Acoustics and Vibration of Mechanical Structures—AVMS-2017. Springer Proceedings in Physics, vol 198. Springer, Cham. https://doi.org/10.1007/978-3-319-69823-6_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-69823-6_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-69822-9
Online ISBN: 978-3-319-69823-6
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)