# Comparative Study of Sound Transmission Losses of Sandwich Composite Double Panel Walls
## 3 Double Panel Air Cavity, Sandwich and Composite Structures
### Functionally Graded Materials of Sandwich Structures  
Functionally graded materials (FGM) are materials whose composition or microstructures are graded and patterned to give specific functions. While the conventional composite laminates have sharp interface between their constituent materials (i.e., as shown in Figure 7b) which makes them susceptible to high stress concentration, the FGM, however, have smooth variation at their interface as shown in Figure 7a. As a result of this, their properties gradually change in the unit cell, therefore, giving them strong bonding and reduced stress concentration [83]. The vibro-acoustic response and STL of this type of material was studied by [PERSON] et al. [84]. The rectangular panel was graded with metal (i.e., aluminum) and ceramics (i.e., alumina and zirconia). The effects of incident angles with different power law indices on the STL were investigated. Their results before the resonance frequency indicated higher STL of the ceramic-rich graded material over the metal and metal-rich graded material. Moreover, at the resonance dip frequency, the STL curve of the ceramic-rich FGM shifted to a higher frequency than the metal and metal-rich FGM for all incident angles investigated. A three dimensional analytical model was developed by [PERSON] et al. [33] to estimate the STL of a FGM cylindrical shell as shown in Figure 8. The graded constituents were also metal (i.e., aluminum) and ceramics (i.e., alumina and zirconia) as material of choice previously used by [PERSON] et al. [84].  
Figure 6: Schematic representation of sandwich composite cylindrical shell [69] (reproduced with permission from [PERSON] et al. Composite Structures; published by Elsevier, 2016).  
Their result indicated enhancement in STL with judicious material distribution through the thickness of the FGM. In addition, the alumina was observed to be mostly efficient in the stiffness controlled zone while the zirconia was mostly efficient in the mass controlled zone due to mass law effect. It should be noted that for thin-walled cylindrical structures, increase in their densities causes the STL to increase especially in the mass controlled zone. However, for thick-walled cylindrical structures, increased densities do not necessarily increase the STL because during transmission loss of the structure, the mass controlled region disappears [85]. Moreover, the authors [33] took into consideration the external flow effect and various Mach numbers from \(-0.5\) to \(0.5\) were studied. It was observed that the STL increased with Mach number at stiffness and coincidence controlled zones especially when the Mach numbers were negative. To further study the effect of some parameters on the STL of double panel with FGM, an analytical investigation was performed by [PERSON] and [PERSON] [86]. The structure consisted of an enclosed acoustic cavity with double-wall FGM piezoelectric plate. The power law distribution was used to gradually alter the material properties in the direction of the thickness of the plate. In the aforementioned double wall investigations, only the panels or shells were made with FGM. However, the core of the DPS can be made of FGM as demonstrated by [PERSON] et al. [87]. Other notable authors [88; 89; 90; 91; 92] have adopted the FGM to model the vibro-acoustic response of structural panels.  
Figure 8: Functionally graded multi-layered cylindrical/curved wall [33] (reproduced with permission from [PERSON] et al. International Journal of Mechanical Sciences; published by Elsevier, 2017).  
Figure 7: Comparison between (**a**) functionally graded material with smooth graded variations and (**b**) composite laminates with sharp interfaces.