Some Qualitative Properties of the Vibration Modes of the Continuous System of a Beam with One or Two Overhangs

Green’s functions for the continuous system of a beam with overhangs are constructed in this paper. Green’s functions for the corresponding mathematically transformed system are proven to be of oscillating kernels. The basic oscillating properties with respect to the natural frequencies and modes of the corresponding systems are revealed and proven. The number of the nodes of the flexural moment modes of the system is determined by analyzing its conjugated system. Furthermore, some qualitative properties of its displacement modes, rotational modes, moment modes, and shearing force modes are also obtained.