Free vibration analysis of nanocomposite sandwich plates reinforced with CNT aggregates

Abstract

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...

Stress distributions in nanocomposite sandwich cylinders reinforced by aggregated carbon nanotube

“…They used higher‐order shear deformation theory (HSDT) and reported natural frequencies of the panels at different environment temperatures. Moradi‐Dastjerdi et al developed a refined shear deformation plate theory to evaluate the natural frequencies of sandwich plates with nanocomposite face sheets reinforced by FG distribution of randomly oriented straight CNT. Zafarmand and Kadkhodayan utilized axisymmetric theory of elasticity to study nonlinear static behavior of FG‐CNT‐reinforced rotating thick disks.…”

“…Pourasghar et al utilized Eshelby–Mori–Tanaka approach and 3D theory of elasticity to examine the effects of CNT orientation and aggregation on the natural frequencies of FG‐CNTRC cylinders. The effect of formation of CNT agglomeration on the sandwich buckling and vibration behaviors of sandwich plates with two face sheets made of FG‐CNTRC were investigated . Sobhaniaragh et al examined the effect of CNT agglomeration formation on the stress distribution of ceramic based FG‐CNTRC cylindrical shells subjected to thermo‐mechanical loads.…”

Nonlinear vibration and modal analysis of FG nanocomposite sandwich beams reinforced by aggregated CNTs

“…The nonlinear and linear vibration of sandwich beams, plates, and panels has been an object of many studies [20][21][22][23][24][25][26][27]. Nanocomposite FG sandwich structures are widely used in the field of transportation (helicopter blades, ship's hull, etc.)…”

“…is used to solve Eq (25). and the associated boundary conditions to determine the nonlinear frequencies of FGS-CNTR beam resting on Pasternak foundation.…”

New analytic bending, buckling, and free vibration solutions of rectangular nanoplates by the symplectic superposition method

“…Jamalpoor et al 41 adopted the Navier approach to solve free vibration and biaxial buckling of double-magneto-electro-elastic nanoplate-systems subjected to initial external electric and magnetic potentials. Moradi-Dasjerdi et al 42 applied the Navier approach at the free vibration analysis of nanocomposite sandwich plates reinforced with CNT aggregates. Arefi et al 43 adopted the Navier-form solutions to analyze the free vibration of a sandwich nano-plate including FG core and piezoelectric face-sheets.…”