Series solution for dynamical characteristic of spatial beam system structure in offshore platform

Abstract

In engineering, the beam system is often used as a support element for large shell structures to improve the support stiffness of the shell and its vibration characteristics are worth being investigated. In this paper, the dynamics of the beam system is modeled and its vibration characteristics are investigated. This paper develops a 6-degree-of-freedom beam theory to describe the displacements of the basic cells of a beam system. This facilitates the solution of the problem of coupling failure of the beam system. The strain potential energy, the boundary spring potential energy, Energy generated by external forces and the structural kinetic energy of the beam system are derived from the energy principle. The above energy expression is then used to construct a Lagrangian energy functional. The displacement function of the beam cells is constructed by improving the Fourier series. It is substituted into the energy functional. The functional is also processed using the Rayleigh Ritz method to finally obtain a dynamic analysis model of the beam system. Then convergence analysis and correctness verification are carried out to ensure the correctness of the model. Finally, the parametric analysis is carried out to investigate the effect of the geometry on its frequency characteristics.