Vibration stability of a cantilevered thin plate with inner fluid circulation

The vibration of a cantilevered thin plate with inner fluid circulation is a typical situation in engineering. The plate's vibration can be considered a combination of bending motion and torsional motion. With the force generated by the inner fluid circulation on the plate, these two types of motion affect each other and raise the problem of stability. In the present study, the vibration stability of different vibrating pattern thus generated is investigated. It is found that with the increase of the flow velocity, torsional mode frequencies decrease synchronously, whereas their modal shapes remain unchanged, which results in the buckling of the plate. Under the circumstance of coupled vibration, because both bending and torsional modal frequencies vary with the flow velocity, a phenomenon of coupled-mode flutter occurs between a certain pair of modes with frequency orders of (2k) and (2k - 1) and vibration becomes unstable.