## 1 Introduction  
The rib stiffened double-panel structure is the most common form of bulkhead structure used in aviation and navigation [1]. Such structure has predominant sound insulation performance in mid and high frequency range. It can effectively isolate noise, induced by uncertain dynamic loads or turbulent flow loads, transmitting into the cabin. However, the level of sound insulation declines remarkably in the low frequency range. Excessive heavy damping materials are required if the passive noise control approach is applied, which, however, do not always achieve remarkable effects. In order to further effectively improve low frequency sound insulation performance, an active control approach may then be applied [2]. Much research work has been carried out on the unribbed double-panel structure [3; 4; 5; 6; 7], and little attention [2] has been given to the ribbed case. In order to fill these theoretical gaps, [PERSON] [8] presents an analytical investigation on the physical mechanism of active control of sound transmission through a single rib stiffened double-panel system, using the cavity control approach. Only a single rib stiffened case is involved in this research to simplify the model. Such an approach allows the authors to pay close attention to distinctly explore the elementary physical nature of active control. However, the double-layer cabin walls are usually the classical orthogonally n-ribbed plate. In order to improve the engineering relevance of the analytical research, this study further presents a more practical structure which refers to the orthogonally two ribs stiffened double-panel system. Hence, this research is continued from the work in Ref. [8]. The aim of this paper is to further explore the active control mechanisms of such a structure, which may support engineering application of this technique in the future. The orthogonal ribbed case is only concerned with one horizontal and one vertical rib. Although such a structure is not in accord with the engineering applications, it seems to be more practical. The purpose of this is to simplify the investigation. Understanding the physical nature of active control in orthogonal ribbed cases may provide better understanding of complicated mechanisms involved in an orthogonal n-ribbed case [9]. Many techniques [10; 11; 12; 13; 14; 15] have been proposed to accurately predict free vibration of the ribbed plate. Some other techniques [2; 16] have been also applied to model complicated double-panel structures composed of rib stiffened plates. These contributions deepen the comprehending of the vibration characteristics of the rib stiffened plate and rule of sound energy transmission through these structures, which offers assistance for noise and vibration control engineering. One new modeling approach proposed recently is the modal expansion method [1; 8; 17], which can clearly reflect the coupling effects between the rib and plate. Therefore, [PERSON] [18] applies this model to investigate the active control of noise radiation from the single rib stiffened plate. Some original mechanisms which differ from these of the unribbed plate case have been obtained. [PERSON] [8] further applies modal expansion and vibro-acoustic coupling methods to model the single rib stiffened double-panel structure. It provides a good understanding of the rule of sound energy transmission between the cavity and radiating ribbed plate, and also the original mechanisms of active control triggered by the coupling effects of the rib. As a continuous work, the model for the orthogonally two ribs stiffened case in this research is also established using the method involved in Ref. [8]. Compared with the unribbed double-panel system [4; 5; 6; 19; 20; 21], the physical mechanism of active control of noise transmission presents additional prominent differences for the single ribbed case.