Exact solutions for free vibration analysis of train body by Carrera unified formulation (CUF) and dynamic stiffness method (DSM)

Abstract. A novel approach for free vibration analysis of train body structures is introduced by using the Carrera Unified Formulation (CUF) and Dynamic Stiffness Method (DSM). Higher-order kinematic fields are developed Formulation, which allows straightforward implementation any-order theory without need ad hoc formulations, in case beam theories. In particular, parallel axis theorem on basis Taylor expansion cross-sectional displacement variables, unifies different shape subsections into same coordinate system. The Principle Virtual Displacements used to derive governing differential equations associated natural boundary conditions. An exact dynamic stiffness matrix then relating amplitudes harmonically varying loads those responses. Finally, Wittrick–Williams (WW) algorithm was carry out frequencies corresponding modal shapes presented.