## 1 Introduction  
Thin plates stiffened by a set of beams form a class of structural elements that are widely applied in various engineering applications [1]. The rib-stiffened structure is most commonly applied in aerospace, the aircraft industry, ground vehicles and so on. The structure has a naturally predominant sound insulation performance in mid and high frequency range, which is beneficial for noise and vibration control. For instance, the fuselage shells of the aircraft are usually the complicated rib stiffened plate, which can effectively isolate the mid and high frequency noise outside the cabin induced by the air-dynamic excitation or aircraft engine transmitting into the cabin. However, the sound insulation performance of such a structure in the low frequency range declines remarkably. In order to further improve the low frequency sound insulation, noise and vibration reduction technic should be introduced. The traditional method--or the so called passive approach--applies the sound absorbing material [2, 3] or structure (such as the micro-perforated plate) [4, 5], the vibration absorption [6] and resistance structure [7] to absorb the sound and vibration energy. The absorbed energy is then dissipated due to the resistance characteristic of these materials or structures. This work mechanism means that the passive control approach can only be effective in mid and high frequency range. It will require excessive heavy damping material for the low frequency control and can not always gain remarkable effects. These insufficient aspects have prompted the research into applying active control techniques [8]. This method applies secondary sound or vibration sources to generate an anti-phase signal to actively cancel the primary noise and vibration [9]--which is effective for controlling low frequency noise and vibration. The active control system normally contains the digital controller, control sources and error sensors. As mentioned above, structural vibration, noise radiation and its influences on itself is an important issue in engineering. High levels of structural vibration can not only radiate a high level of noise--which will pollute the sound filed environment--but also cause structural fatigue, which is attached great importance to the fuselage shells of aircrafts. Accordingly, investigations on structural vibration and noise radiation, and its control approach have been paid close attention. For instance, [PERSON] et al. [10] used numerical and experimental methods to quantifiably investigate the energy losses within linear motion devices (one kW two-stroke free piston linear engine alternator) that included flexural springs as the main suspension component. There are also many research works carried out for using different methods for vibration modeling and control. [PERSON] et al. [11] investigated the non-linear vibration of Euler-Bernoulli beams using the VAM method. [PERSON] et al. [12] presented an analytical and experimental investigation of modified tuned liquid dampers to control structural vibration. This passive control approach mainly works in mid and high frequency range. For further controlling of the low frequency vibration and noise, active control technic is applied. [PERSON] et al. [13] investigated the active vibration control of a cantilever beam using a genetic algorithm. [PERSON] et al. [14] and [PERSON] et al. [15] analytically and experimentally investigated the active vibration and sound transmission control of double-wall structure. For the rib stiffened plate used in practice, in order to further explore the physical nature of the active control of vibration and sound radiation of ribbed structure, [PERSON] et al. [16] investigated the mechanism of active control of sound radiation from the single ribbed plate using the single point force as the control source. Then, for further exploration of the physical nature of active control in complex double panel case, [PERSON] et al.