# Free Vibration Analysis of Functionally Graded Sandwich Plates with a Homogeneous Core
## 1 Introduction  
Conventional sandwich structures are characterized by a functional lamination construction of homogeneous layers. A representative example is a three-layered sandwich plate, which is composed of two thin, stiff face sheets and a relatively thick, lightweight core. Both the faces and core are firmly bonded to ensure the load transfer between constituent layers. Combining the superior performance qualities of each laminate, they have been broadly accepted in various engineering applications. For example, the high strength-to-weight ratio of sandwich structures greatly advanced composite-associated industries over several decades, particularly the transportation industry. However, conventional sandwich structures suffer from a major defect: the abrupt change in material properties across the lamina interfaces [1]. This inherent mismatch of material properties may degrade the target performance of the sandwich and even induce microcraking, which results in delamination. In order to resolve this problem, the concept of functionally graded materials, which was introduced by a group of Japanese scientists in 1980s [2], was extended to sandwich structures [3]. The concept of FGM was originally intended to minimize the thermal stress concentration at the interface of the conventional, bi-material-type, heat-resisting composites by inserting a graded layer. The graded layer is manufactured by mixing two constituent particles such that the volume fraction of one particle varies continuously from 100% atone side to 0% at the other side. Therefore, the conventional mismatch problem does not occur any longer; it is prevented through the insertion of a graded layer between two base homogeneous layers. Furthermore, the target performance of FGM could be maximized by optimally tailoring the thickness-wise distribution of volume fraction [4; 5]. Due to these excellent properties, the notion of FGM has received the considerable attention in various engineering fields. In heat-resisting FGMs, the two base materials are generally metal and ceramic, and this combination has been also adopted for other engineering applications [6]. Here, the FGM plates with this construction are known as a functionally graded sandwich plate with homogeneous faces and a FGM core [7; 8]. As a straightforward extension of three-layered metal-ceramic FGMs, this type of FG sandwich plate has been widely investigated. Another type is the functionally graded sandwich plate with FGM faces and a homogeneous core [9; 10; 11]. This type is, once again, divided into softcore and hardcore, based on whether the material composing the core is metal or ceramic. The FG sandwich structures have attained considerable attraction for their novel design of engineering structures, because they have a potential for exhibiting all the advantages of sandwich construction and FGM. Accordingly, extensive studies have been progressed to investigate the major mechanical behaviors of FG sandwich structures. In early studies, the bending, vibration, and buckling responses were analytically analyzed using the first-order shear deformation plate theory (FSDT) [3; 12; 13]. Later, a new refined plate theory for the simply supported FG sandwich plate was proposed by subsequent investigators [14; 15; 16]. Meanwhile, numerical studies using the refined finite element methods [9; 17] and a layerwise finite element approximation [18] have been also reported. Furthermore, a meshless method was introduced for the numerical investigation of free vibration of FG sandwich plates [19]. More recently, [PERSON] et al. [10] proposed a five-variable, refined plate theory for the accurate and effective vibration analysis of FG sandwich plates. [PERSON] and [PERSON] [20] assessed the performance of the refined zigzag theory to the analysis of bending and free vibration of FG sandwich plates. [PERSON] et al.