Free Vibration of Stepped Horizontally Curved Members Supported by Two-Parameter Elastic Foundation

The main purpose of this paper is to present an analytical method for free vibration of stepped horizontally curved members on two-parameter elastic foundation. The ordinary differential equations governing the free vibration of such beams are derived as non-dimensional forms including the effects of rotatory inertia and shear deformation. The governing equations are solved numerically for the circular, parabolic, sinusoidal and elliptic curved beams with hinged-hinged, hinged-clamped and clamped-clamped end constraints. As the numerical results, the lowest four natural frequency parameters are presented as the functions of various non-dimensional system parameters. Also the typical mode shapes are presented.