Vibrations of complex flexible structures at mid- to high- frequencies have important applications in automotive, aerospace and ship engineering, as well as in high-tech developments. In this paper, a new method is proposed for mid- and high-frequency vibration analyses of complex flexible beam structures. In this method, the vibration of a multi-body beam structure is modeled by an augmented formulation of the Distributed Transfer Function Method (DTFM). This formulation does not rely on discretization, treats beam members, different types of connection, and general boundary conditions in a unified manner, and does not need to adjust algorithms of calculation as the excitation frequency varies from low to high. A highlight of the new method is that it delivers frequency response solutions with detailed information on local displacement, slope, bending moment and shear force in mid- to high-frequency regions, which otherwise might be difficult to obtain by conventional analyses. The proposed method is illustrated on two-dimensional Euler-Bernoulli beam frames in numerical simulation. The new method is validated with the finite element analysis (FEA), the statistical energy analysis (SEA) and the energy flow analysis (EFA), and good agreement is seen in all the examples. Moreover, the new method can certainly go higher than those frequencies that have been reported in the literature. Indeed, the new method is numerically efficient and delivers highly accurate solutions in frequency regions from 102 to 108 Hz, and beyond. It is believed that the proposed DTFM is a useful tool for design and optimization of complex structures in engineering applications.