# Acoustic and Dynamic Response of Unbaffled Plates of Arbitrary Shape
## 1 Introduction  
Spacecraft structures, such as communication reflectors and solar arrays, are excited by an intense acoustic field during launcher lift-off. The acceleration levels induced by the acoustic loads can be very high, because of the very low densities of these structures. Acoustic loads can damage sensitive parts of a structure and the electronic equipment attached to it. Therefore, light aerospace structures are subjected to intense acoustic tests in large reverberant chambers. The aerospace industry requires a method to predict the acceleration levels reached when the acoustic loads excite these structures. Therefore, the catastrophic damage that occurs when acoustic tests are performed in the reverberant chamber can be prevented during the design phase. Two effects need to be considered when the dynamic response of the structure under acoustic loads is investigated: Plate radiation and external sources generated acoustic wavediffraction when the loads impinge on the structure. These effects are coupled and thus produce continuous feedback between the structural and acoustic behaviors. The dynamic behavior of these types of structures has recently received attention from several investigators. Therefore, the stress level and concentration for glass fiber reinforced polymer composites has been studied by [PERSON] et al. [1] and the behaviour under impact loads by [PERSON] et al. [2] and [PERSON] et al. [3]. The problem of coupling between a baffled plate and an acoustic field has been investigated extensively, e.g., [PERSON] et al. [4], [PERSON] et al. [5], [PERSON] and [PERSON] [6], [PERSON] [7], [PERSON] [8], [PERSON] et al. [9] and [PERSON] and [PERSON] [10; 11]. Unbaffled plates have been studied recently because of some additional difficulties identified by [PERSON] et al. [12], [PERSON] and [PERSON]. [13], [PERSON] et al. [14], [PERSON] [15], and [PERSON] and [PERSON] [16]. For all cases examined in this study, the plate is assumed to be unbaffled. The effect of the surrounding air on the dynamic characteristics of these types of structures cannot be ignored. There may be significant differences between the analysis and vibration tests, owing to the presence of air. Therefore, the effect of the surrounding air must be considered during the modeling to validate mathematical models of structural dynamics. A fluid (including a light fluid, such as air) influences the natural frequency, damping coefficient, and normal modes when the structure is made of a very low-density material. [PERSON] et al. [17], [PERSON] [18], [PERSON] [19], and [PERSON] [20] provided some examples of this phenomenon. The assumption of light coupling cannot be applied therefore for this case. For complex structures, the governing equations of the fluid-structure interaction must be solved numerically. Among the different numerical techniques, the boundary element method (BEM) and the finite element method (FEM) are the most widely used to solve this type of problem. The advantages of the BEM for solving a vibrating plate surrounded by the fluid include the satisfaction of the far-field radiation conditions and the relatively low number of discretization elements. However, the main disadvantage is that the matrix of influence coefficients is complete with no zeros. Therefore, the BEM method is more expensive than the FEM method in solving a linear system of equations where the matrix has a bandwidth diagonal. [PERSON] and [PERSON] [21], [PERSON] [22], [PERSON] et al. [23], and [PERSON] and [PERSON] [16] used the BEM/FEM model to solve acoustical problems. In relation to the use of FEM models for solving acoustic problems, there are several commercial software programs based on this method. Among them, it is worth mentioning COMSOL Multiphysics, whose acoustic module allows modeling acoustic propagation problems in both solids and fluids (see for example, [PERSON] et al. [24]). Both the FEM and the BEM are only valid for low- to medium-frequency ranges to solve fluid-structure interaction problems.