A study of ribbing effect on the vibration response and transmission of an L-shaped plate

This paper presents an analytical solution for the vibration response of a ribbed L-shaped plate using a modal expansion solution approach. The analytical model is then employed to study the ribbing effect on vibration reduction and transmission between the two plate components of the L-shaped plate. It is found that for the system considered in the study, a rib inserted between the excitation force and the source plate can lead to a large vibration reduction for both source and receiving plates except at a frequency band near the fundamental resonant frequency of the rib where the rib's flexural stiffness is negligible. A reduced vibration transmission to the receiving plate can also be achieved by placing a rib near the plate/plate junction, attributed to the increased moment impedance at the coupling after the rib insertion. Increasing the rib's flexural stiffness under this condition can further reduce vibration transmission in the low frequency bands while increasing the rib's mass can lead to a reduced vibration transmission in the higher frequency bands. The insights obtained from this study are relevant to vibration control of structures such as transformer tanks and machine covers.