Free Vibration Analyses of Functionally Graded CNT Reinforced Nanocomposite Sandwich Plates Resting on Elastic Foundation
محورهای موضوعی : Engineering
R Moradi-Dastjerdi
1
(Young Researchers and Elite Club, Khomeinishahr Branch, Islamic Azad University)
Gh Payganeh
2
(School of Mechanical Engineering, Shahid Rajaee Teacher Training University)
H Malek-Mohammadi
3
(School of Mechanical Engineering, Shahid Rajaee Teacher Training University)
کلید واژه: Carbon nanotubes, Refined plate theory, Sandwich plates, Mori–Tanaka approach, Navier’s solution,
چکیده مقاله :
In this paper, a refined plate theory is applied to investigate the free vibration analysis of functionally graded nanocomposite sandwich plates reinforced by randomly oriented straight carbon nanotube (CNT). The refined shear deformation plate theory (RSDT) uses only four independent unknowns and accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The motion equations are derived using Hamilton’s energy principle and Navier’s method and is applied to solve this equation. The sandwich plates are considered simply supported and resting on a Winkler/Pasternak elastic foundation. The material properties of the functionally graded carbon nanotube reinforced composites (FG-CNTRCs) are graded along the thickness and estimated though the Mori–Tanaka method. Effects of CNT volume fraction, geometric dimensions of sandwich plate, and elastic foundation parameters are investigated on the natural frequency of the FG-CNTRC sandwich plates.
[1] Wagner H.D., Lourie O., Feldman Y., 1997, Stress-induced fragmentation of multiwall carbon nanotubes in a polymer matrix, Applied Physics Letters 72: 188-190.
[2] Griebel M., Hamaekers J., 2004, Molecular dynamic simulations of the elastic moduli of polymer-carbon nanotube composites, Computer Methods in Applied Mechanics and Engineering 193: 1773-1788.
[3] Fidelus J.D., Wiesel E., Gojny F.H., Schulte K., Wagner H.D., 2005, Thermo-mechanical properties of randomly oriented carbon/epoxy nanocomposites, Composite Part A 36: 1555-1561.
[4] Song Y.S., Youn J.R., 2006, Modeling of effective elastic properties for polymer based carbon nanotube composites, Polymer 47:1741-1748.
[5] Han Y., Elliott J., 2007, Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites, Computational Materials Science 39: 315-323.
[6] Zhu R., Pan E., Roy A.K., 2007, Molecular dynamics study of the stress–strain behavior of carbon-nanotube reinforced Epon 862 composites, Materials Science and Engineering A 447: 51-57.
[7] Manchado M.A.L., Valentini L., Biagiotti J., Kenny J.M., 2005, Thermal and mechanical properties of single-walled carbon nanotubes-polypropylene composites prepared by melt processing, Carbon 43: 1499-1505.
[8] Qian D., Dickey E.C., Andrews R., Rantell T., 2000, Load transfer and deformation mechanisms in carbon nanotube–polystyrene composites, Applied Physics Letters 76: 2868-2870.
[9] Mokashi V.V., Qian D., Liu Y.J., 2007, A study on the tensile response and fracture in carbon nanotube-based composites using molecular mechanics, Composites Science and Technology 67: 530-540.
[10] Wuite J., Adali S., 2005, Deflection and stress behaviour of nanocomposite reinforced beams using a multiscale analysis, Composite Structures 71: 388-396.
[11] Reddy J.N., 2000, Analysis of functionally graded plates, International Journal for Numerical Methods in Engineering
47: 663-684.
[12] Cheng Z.Q., Batra R.C., 2000, Deflection relationships between the homogeneous Kirchhoff plate theory and different functionally graded plate theories, Archive of Mechanics 52:143-158.
[13] Cheng Z.Q., Batra R.C., 2000, Exact correspondence between eigenvalues of membranes and functionallygraded simplysupported polygonal plates, Journal of Sound and Vibration 229: 879-895.
[14] Shen H.S., 2011, Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part I: Axially-loaded shells, Composite Structures 93: 2096-2108.
[15] Ke L.L., Yang J., Kitipornchai S., 2010, Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams, Composite Structures 92: 676-683.
[16] Mori T., Tanaka K., 1973, Average stress in matrix and average elastic energy of materials with Misfitting inclusions, Acta Metallurgica 21: 571-574.
[17] Yas M.H., Heshmati M., 2012, Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load, Applied Mathematical Modelling 36: 1371-1394.
[18] Sobhani Aragh B., Nasrollah Barati A.H., Hedayati H., 2012, Eshelby–Mori–Tanaka approach for vibrational behavior of continuously graded carbon nanotube–reinforced cylindrical panels, Composites Part B 43: 1943-1954.
[19] Pourasghar A., Yas M.H., Kamarian S., 2013, Local aggregation effect of CNT on the vibrational behavior of four-parameter continuous grading nanotube-reinforced cylindrical panels, Polymer Composites 34: 707-721.
[20] Moradi-Dastjerdi R., Pourasghar A., Foroutan M., 2013, The effects of carbon nanotube orientation and aggregation on vibrational behavior of functionally graded nanocomposite cylinders by a mesh-free method, Acta Mechanica 224: 2817-2832.
[21] Pasternak P.L., 1954, On a New Method of Analysis of an Elastic Foundation by Means of Two Foundation Constants, Cosudarstrennoe Izdatelstvo Literaturi po Stroitelstvu i Arkhitekture, Moscow, USSR.
[22] Pourasghar A., Kamarian S., 2013, Three-dimensional solution for the vibration analysis of functionally graded multiwalled carbon nanotubes/phenolic nanocomposite cylindrical panels on elastic foundation, Polymer Composites 34: 2040-2048.
[23] Zenkour AM., 2006, Generalized shear deformation theory for bending analysis of functionally graded plates, Applied Mathematical Modelling 30: 67-84.
[24] Zenkour AM., 2009, The refined sinusoidal theory for FGM plates on elastic foundations, International Journal of Mechanical Sciences 51: 869-880.
[25] Merdaci S., Tounsi A., A.Houari M.S., Mechab I., Hebali H., Benyoucef S., 2011, Two new refined shear displacement models for functionally graded sandwich plates, Archive of Applied Mechanics 81:1507-1522.
[26] Thai H.T., Choi D.H., 2011, A refined plate theory for functionally graded plates resting on elastic foundation, Composites Science and Technology 71: 1850-1858.
[27] Akavci SS., 2007, Buckling and free vibration analysis of symmetric and antisymmetric laminated composite plates on an elastic foundation, Journal of Reinforced Plastics and Composites 26: 1907-1919.
[28] Benyoucef S., Mechab I., Tounsi A., Fekrar A., Ait Atmane H., Adda Bedia EA., 2010, Bending of thick functionally graded plates resting on Winkler-Pasternak elastic foundations, Mechanics of Composite Materials 46: 425-434.
[29] Ait Atmane H., Tounsi A., Mechab I., Adda Bedia EA., 2010, Free vibration analysis of functionally graded plates resting on Winkler-Pasternak elastic foundations using a new shear deformation theory, International Journal of Mechanics and Materials in Design 6: 113-121.
[30] Shi D.L., Feng X.Q., Yonggang Y.H., Hwang K.C., Gao H., 2004, The effect of nanotube waviness and agglomeration on the elasticproperty of carbon nanotube reinforced composites, Journal of Engineering Materials and Technology 126: 250-257.
[31] Matsunaga H., 2008, Free vibration and stability of functionally graded plates according to a 2D higher-order deformation theory, Composite Structures 82: 499-512.
[32] Akhavan H., Hosseini-Hashemi Sh., Rokni Damavandi Taher H., Alibeigloo A., Vahabi Sh., 2009, Exact solutions for rectangular Mindlin plates under in-plane loads resting on Pasternak elastic foundation. Part II: Frequency analysis, Computational Materials Science 44: 951-961.