Abstract
The problem of the motion of a load at a constant velocity over an infinitely long beam that rests on a solid, nonlocally viscoelastic foundation is investigated. The load is considered to be a Gaussian random homogeneous function of the longitudinal coordinate with a constant mathematical expectation. The influence of the nonlocality and viscoelasticity characteristics of the foundation on the value of the critical velocity of the load and the root-mean-square variance in the deflection of the beam has been analyzed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Fryba, L., Random vibration of a beam on elastic foundation under moving force, in Random Vibration Status and Recent Development, Amsterdam, 1986, pp. 127–147.
Fryba, L., Vibration of Solids and Structures under Moving Loads, Prague: Thomas Telford, 1999.
Ivanchenko, I.I., Dinamika transportnykh sooruzhenii (Transport Constructions Dynamics), Moscow: Nauka, 2011.
Siu-Seong Law and Xin-Qun Zhu, Moving Loads Dynamic Analysis and Identification Techniques, Boca Raton, London, New York, Leiden, 2011.
Potapov, V.D., Effect of movable random loading onto infinitely long beam laying at continuous elastic-plastic foundation, Probl. Mashinostr. Nadezhn. Mash., 2017 (in press).
Winkler, E., Die Lehre von der Elastizitat und Festigkeit, Prague, 1867.
Friswell, M.I., Adhikari, S.A., and Lei, Y., Vibration analysis of beams with non-local foundations using the finite element method, Int. J. Num. Methods Eng., 2006, vol. 43, no. 3, pp. 3381–3400.
Potapov, V.D., Fimkin, A.I., and Pepanyan, A.R., Experimental verification for non-local elastic foundation model, Stroit. Mekh. Inzh. Konstrukts. Sooruzh., 2015, no. 5, pp. 63–68.
Potapov, V.D., On bending and stability of beams and plates laying on a continuous nonlocally elastic foundation, J. Mach. Manuf. Reliab., 2016, vol. 45, no. 3, pp. 199–205.
Sveshnikov, A.A., Prikladnye metody teorii sluchainykh funktsii (Applied Methods for the Theory of Random Functions), Moscow: Nauka, 1968.
Atanackovic, T.M. and Stankovic, B., Stability of an elastic rod on a fractional derivative type of foundation, J. Sound Vibrat., 2004, vol. 277, pp. 149–161.
Muravskii, G.B., Oscillation of the beam laying on elastic-inherited foundation, Stroit. Mekh. Raschet Sooruzh., 1976, no. 3, pp. 38–41.
Rabotnov, Yu.N., Elementy nasledstvennoi mekhaniki tverdykh tel (Elements of Hereditary Mechanics for Solids), Moscow: Nauka, 1977.
Gradtshtein, I.S. and Ryzhik, I.M., Tablitsy integralov, summ, ryadov i proizvedenii (Tables of Integrals, Sums, Series and Products), Moscow: Nauka, 1971.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.D. Potapov, M. Treckmann, 2017, published in Problemy Mashinostroeniya i Nadezhnosti Mashin, 2017, No. 2, pp. 40–46.
About this article
Cite this article
Potapov, V.D., Treckmann, M. Impact of a random moving load on an infinitely long beam that rests on a solid, nonlocally vicsoelastic foundation. J. Mach. Manuf. Reliab. 46, 120–127 (2017). https://doi.org/10.3103/S1052618817020145
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1052618817020145