Some physical insights for active control of sound radiated from a clamped ribbed plate

An analytical study of mechanisms of active control of sound radiation from a rib stiffened plate is presented in this letter. Using the well-known modal expansion method to solve the beam/plate coupling vibration response, the physical mechanisms are interpreted in an analytical way similar as that used in the unribbed plate case. But some special rules are discovered for the ribbed plate case. The primary characteristic for the ribbed plate is that its new resonant modes are essentially the superposition of a couple of specific base plate modes that possess the same vibration pattern along the rib. These modes should be all suppressed in controlled condition to achieve on-resonances noise reduction. A large number of base plate modes contribute to off-resonances sound radiation such that multi-point forces are needed to rearrange their amplitudes and phases to guarantee their sound radiation being canceled each other. The imperfect control effects when control force acting on nodal areas of the mode of the ribbed plate are due to the opposite vibration states of the corresponding base plate modes where the control force applied for suppressing one mode may consequentially excite another.