Abstract
The contributions of compressive load and support damping are included into the formulation of flexural wave motion in beams lying on elastic (Winkler) foundation. The beam is modeled by both Euler–Bernoulli’s and Timoshenko’s theories. First, dispersion analysis is performed, which reveals that, for a fixed wavenumber, phase velocity decreases as the intensity of the compressive force or the value of the support damping is increased. Secondly, the transverse displacement of a semi-infinite beam excited by a velocity step pulse at its finite end is examined in the transient regime by adopting Laplace transform approach. This latter study sustains the validity of the dispersion analysis outcomes and shows that compressive load and support damping cause an amplification and a diminution, respectively, of the displacement amplitudes at the various positions of the beam.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Timoshenko S.P.: On the correction for shear of the differential equation for transverse vibrations of prismatic bars. Phil. Mag. 41, 744–746 (1921)
Graff K.F.: Wave Motion in Elastic Solids. Dover Publications, Inc., New York (1975)
Yu C.-P., Chiang C.-H.: Prediction of dispersion relation for elastic stress waves in prestressed tendons using 1-D member theories. Int. J. Appl. Sci. Eng. 1, 1–16 (2003)
Chen F., Wilcox P.D.: The effect of load on guided wave propagation. Ultrasonics 47, 111–122 (2007)
Loveday P.W.: Semi-analytical finite element analysis of elastic waveguides subjected to axial loads. Ultrasonics 49, 298–300 (2009)
Frikha A., Treyssède F., Cartraud P.: Effect of axial load on the propagation of elastic waves in helical beams. Wave Motion 48, 83–92 (2011)
Metrikine A.V., Popp K.: Steady-state vibrations of an elastic beam on a visco-elastic layer under moving load. Arch. Appl. Mech. 70, 399–408 (2000)
McGhie R.D.: Flexural wave motion in infinite beam. J. Eng. Mech. 116, 531–548 (1990)
Chen Y.-H., Huang. Y.-H., Shih C.-T.: Response of an infinite Timoshenko beam on a viscoelastic foundation to a harmonic moving load. J. Sound Vib. 241, 809–824 (2001)
Sun L.: A closed-form solution of a Bernoulli-Euler beam on a viscoelastic foundation under harmonic line loads. J. Sound Vib. 242, 619–627 (2001)
Kim S.-M.: Vibration and stability of axial loaded beams on elastic foundation under moving harmonic loads. Eng. Struct. 26, 95–105 (2004)
Kien N.D.: Dynamic response of prestressed Timoshenko beams resting on two-parameter foundation to moving harmonic load. Tech. Mech. 28, 237–258 (2008)
Hagedorn P., DasGupta A.: Vibrations and Waves in Continuous Mechanical Systems. Wiley, England (2007)
Valkó P.P., Abate J.: Comparison of sequence accelerators for the Gaver method of numerical Laplace transform inversion. Comp. Math. Appl. 48, 629–636 (2004)
Wolfram Library Archive. http://library.wolfram.com/infocenter/MathSource/4738. Accessed 12 May 2011
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Carta, G. Effects of compressive load and support damping on the propagation of flexural waves in beams resting on elastic foundation. Arch Appl Mech 82, 1219–1232 (2012). https://doi.org/10.1007/s00419-012-0611-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-012-0611-y