Dynamic Stiffness Matrix Of Partial-interaction Composite Beams And Its Applications

Dynamic stiffness matrix method is theoretically exact for the dynamic characteristics of structures and therefore it is applicable for broad frequency range. Based on Euler-Bernoulli and Timoshenko beam theories, the dynamic stiffness matrices of composite beams are derived by taking into account the interface slip as well as the influence of axial forces. This paper then develops the method for calculating dynamic characteristics and critical buckling loads of composite beams with single-span and multi-span. The free vibration frequencies and the corresponding mode shapes are obtained for composite beams of single-span, two-span and three-span. The effect of the axial force on the frequencies of vibration is investigated in detail. The critical loads of buckling of the composite beams with different boundary conditions are also obtained compared with those in the literatures. It shows that the present method is convenient to use and of high precision. As an example of application in a practical project, the present method is used to analysis the frequencies and mode shapes of the north access of the Jiubao Bridge. The results are also compared with the measured values for validation.It is noticeable that the numerical instability usually occurs for conventional dynamic stiffness matrix method in the case of the high order frequencies of structures. To solve this problem, this paper adopts the exponential functions with special parameters instead of hyperbolic functions, which are used in conventional dynamic stiffness matrix. The improved dynamic stiffness matrix can solve the problem of numerical instability and therefor realize the full potential to obtain accurate results of the high order frequencies without the consideration of the number of the elements. This method could be extended for the dynamic stiffness matrix of other structural members to overcome the numerical instability.