The following paper addresses the applicability and the advantages of finite elements for the study of transmission and reflection of waves impinging upon beam junctions. It will be shown that it is possible to simulate travelling waves on general beams by using a wave-absorbing element at each end of the beam. The stiffness matrix of the wave-absorbing element is determined by the characteristic stiffness of the beam. A general procedure to identify the characteristic stiffness is given in the appendix. Next, by performing a direct frequency response analysis on the finite element model of the junction (including the wave-absorbing elements at either end), it is possible to calculate the energy absorbed by the wave-absorbing elements. Along with some additional calculations, one can easily deduce the energy transmission characteristics of the junction. The method will be explained in detail in the case of beam junction. The applicability, which is mainly situated in the higher frequency dynamic range, will be highlighted through some relevant examples. One of the main advantages of using finite elements is the possibility of evaluating the transmission characteristics of whatever junction, including all essential geometrical details, in a straightforward way.
Semiring optimizations: dynamic elision of expressions with identity and absorbing elements