Dynamic stiffness method for free vibration analysis of a two-part beam-mass system

Using the dynamic stiffness method, the free vibration characteristics of a two-part beam-mass system have been investigated in this paper. The procedure allows an exact free vibration analysis of the system without making any approximation en route. The governing differential equations of motion of the combined system for flexural motion are used in formulating the theory. For harmonic oscillation, these equations are solved in closed analytical form in terms of arbitrary constants. The kinematic boundary conditions are imposed and the arbitrary constants are eliminated so that the force-displacement relationship is expressed in terms of the frequency dependent dynamic stress matrix. Once the dynamic stiffness matrix is obtained, the well-established algorithm of Wittrick-Williams is applied to compute the natural frequencies of the system. The theory is demonstrated by numerical results. The method is exact and thus can be used to validate finite element and other approximate methods.