Engineering Transactions, 67, 2, pp. 243–252, 2019
10.24423/EngTrans.1010.20190530

### Vibrations of a Double-Beam System with Intermediate Elastic Restraints Due to a Moving Force

Filip ZAKĘŚ
Wroclaw University of Environmental and Life Sciences
Poland

Wroclaw University of Environmental and Life Sciences
Poland

In this paper, we investigate the problem of the dynamic behaviour of a double-beam system with intermediate elastic restraints subjected to a moving point force. Problem is solved by replacing this type of structure with two single-span beams loaded with a given moving force and redundant forces representing reactions in the intermediate restraints. Redundant forces are obtained by solving Volterra integral equations of the second order which are compatibility equations corresponding to each redundant. Solutions for the arbitrarily supported singlespan beam loaded with a moving point force and concentrated time-varying force are given. Difficulties in analytically solving Volterra integral equations are bypassed by applying a simple numerical procedure. Finally, a numerical example of a double-beam system with two elastic restraints is presented in order to show the effectiveness of the presented method.
Keywords: double-beam system; vibrations; moving load; Volterra integral equations
Full Text: PDF

#### References

Fryba L., Vibrations of solids and structures under moving load, Telford, London, 1999.

Abu-Hilal M., Dynamic response of a double Euler-Bernoulli beam due to a moving constant load, Journal of Sound and Vibration, 297(3–5): 477–491, 2006.

Oniszczuk Z., Forced transverse vibrations of an elastically connected simply supported double-beam system, Journal of Sound and Vibration, 264(2): 273–286, 2003.

Zakes F., Sniady P., Application of Volterra integral equations in dynamics of multispan uniform continuous beams subjected to a moving load, Shock and Vibration, 2016, article ID 4070627, 12 pages, 2016, http://dx.doi.org/10.1155/2016/4070627.

Krylov A.N., Mathematical collection of papers of the Academy of Sciences, Vol. 61, St. Petersburg, 1905.

Clough R.W., Penzien J., Dynamics of Structures, McGraw-Hill, New York, 1993.

Weaver W., Timoshenko S., Young D.H., Vibration Problems in Engineering, Wiley, New York, 1990.

DOI: 10.24423/EngTrans.1010.20190530