In-plane and out-of-plane waves' power transmission through an L-plate junction using the mobility power flow approach

摘要

The structural power flow through the junction between two flat plates, coupled in an L-shaped configuration, is considered using the mobility power flow (MPF) approach, for both in-plane (longitudinal and shear) and out-of-plane (bending) waves' propagation. Power flow by both types of waves is included by considering the junction edge between the two plates, when uncoupled, to be free. Mobility expressions are then derived for both in-plane and out-of-plane degrees of freedom forces and responses. The results of the analysis show that the in-plane waves do not significantly contribute to the structural power flow at relatively low frequencies, that is, for frequencies below a bending wave number and plate thickness product of approximately 0.1. In this case, the power flow results are not different from those obtained if the junction is assumed to be pinned, and power is transmitted by only the out-of-plane waves. However, as the frequency increases, the significance of the in-plane waves' contribution increases, and for a bending wave number and plate thickness product greater than approximately 1.0, the contribution from the in-plane waves dominates. This condition is different from the well-known result that if the thickness is greater than approximately 10% of the bending wavelength, simple bending theory does not apply. This condition deals with the significance of the in-plane waves. In the frequency region where the in-plane waves dominate, the in-plane longitudinal waves are more significant than the in-plane shear waves, although this has some dependence on the selected L-shaped configuration. The in-plane longitudinal waves couple directly to the out-of-plane waves because of the 90 degree junction.