An exact dynamic stiffness matrix for axially loaded double-beam systems

An exact dynamic stiffness method is presented in this paper to determine the natural frequencies and mode shapes of the axially loaded double-beam systems,which consist of two homogeneous and prismatic beams with a distributed spring in parallel between them. The effects of the axial force, shear deformation and rotary inertia are considered, as shown in the theoretical formulation. The dynamic stiffness influence coefficients are formulated from the governing differential equations of the axially loaded double-beam system in free vibration by using the Laplace transform method. An example is given to demonstrate the effectiveness of this method, in which ten boundary conditions are investigated and the effect of the axial force on the natural frequencies and mode shapes of the double-beam system are further discussed.