APPLICATION OF GDQ METHOD FOR FREE VIBRATION BEHAVIOR OF AN AUXETIC SANDWICH BEAM WITH FG CNT-REINFORCED NANOCOMPOSITE FACE SHEETS RESTING ON AN ELASTIC SUBSTRATE

In this study, the free vibration behavior of an embedded sandwich beam consisting of an aluminum auxetic core and two polymer nanocomposite face sheets reinforced with carbon nanotubes (CNTs) was investigated. The CNTs were dispersed along the thickness of the face sheets through various functionally graded (FG) and uniformly distributed (UD) patterns (i.e., FG-X, FG-V, FG-O, and UD). In addition, the structure was embedded on a Winkler-Pasternak elastic substrate in order to make the problem more realistic. The effective material properties of the face sheets and the core were estimated using the extended rule of mixtures and the relations of the auxetic materials, respectively. Next, the governing differential equations were derived based on the incorporation of the first-order shear deformation theory and Hamilton's principle. To obtain the natural frequencies of the structure, the differential equations were solved by implementing the generalized differential quadrature method, which is a well-known numerical strategy. In addition, the results were validated by comparing them with the results obtained in a reputed literature study, in which perfect agreement was achieved. Finally, the influences of various parameters such as the length-tothickness ratio, cell inclined angle, substrate parameters, CNT volume fractions, various boundary conditions, and core-to-face sheet ratio on the first natural frequency of the sandwich beam were investigated.