Pretensioners Structural Frequency Based On The Dynamic Stiffness Method

The pre-tensioned structures are commonly used in bridge engineering. Due to their special structural type, the pre-tensioned structures are sensitive to the dynamic loadings, and the loss of pre-tension affects the structural safety and durability. Therefore, the accurate calculation of dynamic characteristics for those structures is a key issue in the health monitoring and condition assessment. The dynamic stiffness method has been an effective approach to solve the vibration problems in structural engineering, particularly when higher order natural frequencies and better accuracy are required. Unlike the traditional finite element method and other approximate methods, this method allows an infinite number of natural frequencies and normal modes of structure to be accounted for with few degrees of freedom.The present work is aimed at presenting a dynamic stiffness matrix based method to accurately calculate the natural frequencies of axial eccentrically forced beams, beams considering dead load effect and parabolic cables. The main work and conclusions are:1. According to the relationship between the force increment and displacement, the dynamic stiffness matrix of axial eccentrically forced Euler beams is derived combining the governing differential equation and the boundary conditions. The Wittick-Williams algorithm is implemented to calculate the natural frequencies of such a beam and the parametric study is also carried out.2. The vibration stress-strain relationship of the beam considering dead load effect is studied. By using Hamilton principle, the vibration control differential equation and corresponding boundary conditions of such a beam are presented. After converting the boundary value problems into a set of equivalent initial value problems, the dynamic stiffness matrix of the beam considering dead load effect is derived with the help of the fourth-order Runge-Kutta method. The Wittick-Williams algorithm is then used to calculate the natural frequencies and the results are compared with those obtained from finite element method and analytical solution. It is demonstrated that the current results are more close to the analytical solutions.3. Starting from the cable vibration control equations in the in-plane the dynamic stiffness matrix of a parabolic cable is derived. Again, the Wittick-Williams algorithm is then used to calculate the natural frequencies of a sagging cable. The dynamic stiffness matrix based procedure to calculate the cable frequencies is clear and physically meaningful.