In this paper, free and forced vibrations, and also resonance and pulse phenomena in sandwich plates with an isotropic core and composite reinforced by wavy carbon nanotube (CNT) face sheets are studied based on a mesh-free method and first order shear deformation theory (FSDT). The sandwich plates are resting on Pasternak elastic foundation and subjected to periodic loads. In the mesh-free analysis, moving least squares (MLS) shape functions are used for approximation of displacement field in the weak form of motion equation and the transformation method is used for imposition of essential boundary conditions. The distributions of CNTs are considered functionally graded (FG) or uniform along the thickness and their mechanical properties are estimated by an extended rule of mixture. Effects of CNT distribution, volume fraction, aspect ratio and waviness, and also effects of Pasternak’s elastic foundation coefficients, sandwich plate thickness, face sheets thickness, plate aspect ratio and time depended force are investigated on the free and forced vibrations, and resonance behavior of the sandwich plates with wavy CNT-reinforced face sheets.

In this article, free vibration analysis of simply supported sandwich plates with a flexible core and two functionally graded nanocomposite face sheets resting on two-parameter elastic foundation is carried out using Navier's solution. The nanocomposite face sheets are reinforced by randomly oriented and aggregated carbon nanotube (CNT). The material properties of the nanocomposites plates are graded along the thickness and are estimated though the Eshelby-Mori-Tanaka approach. In the proposed theory, 3-D elasticity theory and first order shear deformation theory are used for core and face sheets, respectively. Also, Hamilton's variational principle is used to derive the equations of motion. IntroductionHaving lighter mass and increased rigidity against bending, sandwich structures are widely used in aerospatial, naval and industrial applications [1]. Also, recently the use of CNT in polymer/CNT composites has attracted wide attention [2]. A high aspect ratio, low weight of CNTs and their extraordinary mechanical properties (strength and flexibility) provide the ultimate reinforcement for the next generation of extremely lightweight but highly elastic and very strong advanced composite materials [3]. On the other hand, by using of the polymer/CNT composites in advanced multilayered composite materials (sandwich structures) we can achieve structures with low weight, high strength and high stiffness in many structures of civil, mechanical and space engineering [4]. But, one of the common features of CNT morphology is the formation of aggregation in the matrix. Aggregation into bundles or ropes limits the overall effectiveness of nanotubes at improving the mechanical properties of the nanocomposite. The large aspect ratio (usually >1000), nanotube volume fraction, low bending rigidity of CNTs and interfacial bonding in the inter-phase region between embedded CNT and its surrounding polymer lead to their aggregation. Also, mechanical properties of CNTRC will become worse if the volume fraction of CNTs arises beyond certain limit [5]. Therefore, due to high cost of CNTs, in the modeling of CNTRC the concept of functionally graded materials (FGMs) might be incorporated to effectively make use of the CNTs. FGMs are classified as novel composite materials with gradient compositional variation. The concept of FGMs can be utilized for the management of a material's microstructure, so that the mechanical behavior of a structure made of such material can be improved. The composites, which are reinforced by CNTs with grading distribution, are called functionally graded carbon nanotube reinforced composites (FG-CNTRCs). Due to the mismatch of stiffness properties between the face sheets and core, sandwich panels are susceptible to delaminate at interfaces of the layers. Using FG-CNTRC in the layers of sandwich panels can solve the major problem in sandwich construction.Since the first-order shear deformation theory (FSDT) does not satisfy the condition of zero transverse shear stress at the top and bottom surfaces of plates, a...

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