Free vibration analysis of segmented Timoshenko beams on Pasternak foundation by using transfer matrix

The aim of this study is performing free vibration analysis segmented Timoshenko beams on two parameter elastic foundation by using the transfer matrix method (TMM). Pasternak model which has an incompressible shear layer vertical elements attached to Winkler springs was considered. formulations are based closed-form solutions equations motion were obtained. natural frequencies calculated equating determinant global structure zero after reduction according boundary conditions. mode shapes plotted normalising state vectors at ends. Firstly, that obtained proposed approach validated data in literature for a simply supported beam where very good agreement observed. Then, three-segmented models having various conditions namely simple-simple (S-S), simple-fixed (S-F), fixed-simple (F-S) and fixed-fixed (F-F) considered numerical analysis. For models, TMM compared results finite element (FEM) from SAP2000 ignoring effects foundation. as well stiffness revealed S-S, S-F, F-S F-F conditions, respectively. presented. show can be used effective tool multi-segmented