The main purpose of this paper is to present both the fundamental and some higher natural frequencies of Timeshenko beams testing on the Winkler-type foundation. The nondimensional differential equation governing the free vibrations for this beam is d...
The main purpose of this paper is to present both the fundamental and some higher natural frequencies of Timeshenko beams testing on the Winkler-type foundation. The nondimensional differential equation governing the free vibrations for this beam is derived in which the effects of rotatory inertia and shear deformation are included. The Improved Euler method and Determinant Search method are used to perform the integration of the differential equation and to determine the natural frequencies, respectively. The hinged-hinged, hinged-clamped, clamped-clamped and free-clamped end constraints are applied in numerical examples. The relations between frequency parameter and foundation parameter, slenderness ratio are presented in figures. The effects of cross-sectional shapes and material properties are also investigated.