TY - JOUR N2 - Complex structures used in various engineering applications are made up of simple structural members like beams, plates and shells. The fundamental frequency is absolutely essential in determining the response of these structural elements subjected to the dynamic loads. However, for short beams, one has to consider the effect of shear deformation and rotary inertia in order to evaluate their fundamental linear frequencies. In this paper, the authors developed a Coupled Displacement Field method where the number of undetermined coefficients 2n existing in the classical Rayleigh-Ritz method are reduced to n, which significantly simplifies the procedure to obtain the analytical solution. This is accomplished by using a coupling equation derived from the static equilibrium of the shear flexible structural element. In this paper, the free vibration behaviour in terms of slenderness ratio and foundation parameters have been derived for the most practically used shear flexible uniform Timoshenko Hinged-Hinged, Clamped-Clamped beams resting on Pasternak foundation. The findings obtained by the present Coupled Displacement Field Method are compared with the existing literature wherever possible and the agreement is good. L1 - http://www.czasopisma.pan.pl/Content/104244/PDF/ame-2017-0022.pdf L2 - http://www.czasopisma.pan.pl/Content/104244 PY - 2017 IS - No 3 EP - 373 DO - 10.1515/meceng-2017-0022 KW - free vibration KW - Coupled Displacement Field method KW - uniform Timoshenko beam KW - Pasternak foundation A1 - Rajesh, Korabathina A1 - Saheb, Koppanati Meera PB - Polish Academy of Sciences, Committee on Machine Building VL - vol. 64 DA - 2017 T1 - Free vibrations of uniform Timoshenko beams on Pasternak foundation using Coupled Displacement Field method SP - 359 UR - http://www.czasopisma.pan.pl/dlibra/publication/edition/104244 T2 - Archive of Mechanical Engineering ER -