Forced vibration analysis of a Timoshenko beam featuring bending-torsion on Pasternak foundation

Abstract

• Orthogonality conditions of mode shapes of a Timoshenko beam on a Pasternak foundation are obtained. • The system response for DTF and STF and their differences are assessed. • The related time functions in DTF and STF are almost identical for transverse displacement and bending angle. • The differences between DTF and STF in the torsion angle are significant. • Applying DTF is recommended when bending-torsion coupling is of concern. Free and forced vibration analysis of a Timoshenko beam on viscoelastic Pasternak foundation featuring coupling between flapwise bending and torsional vibrations is studied in this article. The system motion is described through a coupled set of three partial differential equations. The differential transform method, DTM, as an efficient mathematical technique is adopted to obtain the natural frequencies and the mode shapes. The system force response is assessed for a moving concentrated load with a constant velocity. Two different methods are studied and applied in obtaining forced vibration response of the system: (1) the same time functions, STF, by setting out the orthogonality conditions derived in this article and (2) the different time functions, DTF. The difference between the responses of the system is assessed by applying STF and DTF for a constant moving load. The effects of some parameters on the system response are probed. A numerical example is solved to validate the results obtained here with the available ones and a close agreement is found. It is observed that the time functions in DTF and STF are almost identical for transverse displacement and bending angle and are significant for torsion angle, recommending the application of DTF when the bending-torsion coupling is of concern.