Some qualitative properties of frequency spectrum and modes of difference discrete system of multibearing beam

The qualitative properties of the frequency spectrum and modes were studied extensively for the nonhomogeneous single span beams, in which the discrete and continuous systems were included. However, the qualitative properties about the multispan beams were studied and only shown in the book 'Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems' published by Gantmakher, F. P. and Krein, M. G. The discrete model given in this book was formed by adding several masses to massless continuous system of the multispan beam, and the adopted method was based on the influence function of the beam, related to the positive systems. Nevertheless, the conditions about the positive systems were not discussed in the above-mentioned book. In this paper the difference discrete models of the multispan beam with arbitrary supports at two ends are established. According to the above book, the flexibility coefficient of the above models corresponding to the positive single span beam systems is given. The oscillating property of the flexibility matrix of the multispan beam is determined based on that of the positive single span beam systems by introducing an auxiliary system. A series of qualitative properties of the frequency spectrum and modes of the multispan beams are obtained.EI06947-9524