Vibration transmission through a junction connecting periodically stiffened thin plates

Abstract

There are many structures which are made of periodically stiffened, thin plates. Such stiffened plates are often connected to each other at a junction, and the purpose of this study is to provide the theoretical framework to predict the vibrational energy transmission at the junction. This is first done by setting up the governing equation for bending motion of stiffened plates, which is solved by using the spatial Fourier transform and the Floquet's theorem. The solutions to this equation are the free waves in the periodic plate. These are used to characterize wave transmission through a junction connecting two periodic structures for oblique wave angles, and also response of the periodic structure to external harmonic forces. Several numerical examples on the wave transmission and forced vibration problems are presented and discussed. For the wave transmission problem, transmission coefficient of a junction of interest, which is ratio of energy flux of incident wave to that of transmitted wave is obtained. This is obtained by first constructing wave field near the junction which comprises of incident, reflected and transmitted waves. Then, the transmission coefficient is obtained by applying the boundary conditions at the junction. For an L-junction connecting two stiffened plates, one observes that the transmission coefficient at an wave angle for the periodic plates shows significant difference when compared to the one for the uniform counterparts because energy propagates differently in the periodic plates. However, when the transmission coefficient is averaged over incident angles, the mean transmission coefficient for the case of the periodic plates becomes similar to that of the homogeneous plates. This is because there always exists a wave angle at which the waves can propagate freely. Furthermore, using the same principle of constructing wave field from the free wave solutions, wave field of a finite periodic plate subjected to a point harmonic force is obtained. It is observed that the analytical results agree very well with the FEM results which validate the methods of using free waves in describing wave fields of the periodic plates.