Browse > Article
http://dx.doi.org/10.12989/sem.2019.69.5.487

On exact wave propagation analysis of triclinic material using three-dimensional bi-Helmholtz gradient plate model  

Karami, Behrouz (Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University)
Janghorban, Maziar (Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University)
Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Publication Information
Structural Engineering and Mechanics / v.69, no.5, 2019 , pp. 487-497 More about this Journal
Abstract
Rapid advances in the engineering applications can bring further areas to provide the opportunity to manipulate anisotropic structures for direct productivity in design of micro/nano-structures. For the first time, magnetic affected wave characteristics of nanosize plates made of anisotropic material is investigated via the three-dimensional bi-Helmholtz nonlocal strain gradient theory. Three small scale parameters are used to predict the size-dependent behavior of the nanoplates more accurately. After owing governing equations of wave motion, an analytical approach based harmonic series is utilized to fine the wave frequency as well as phase velocity. It is observed that the small scale parameters, magnetic field and wave number have considerable influence on the wave characteristics of anisotropic nanoplates. Due to the lack of any study on the mechanics of three-dimensional bi-Helmholtz gradient plates made of anisotropic materials, it is hoped that the present exact model may be used as a benchmark for future works of such nanostructures.
Keywords
wave propagation; anisotropic materials; three dimensional elasticity theory; magnetic field;
Citations & Related Records
Times Cited By KSCI : 16  (Citation Analysis)
연도 인용수 순위
1 Mehralian, F., Beni, Y.T. and Zeverdejani, M.K. (2017), "Nonlocal strain gradient theory calibration using molecular dynamics simulation based on small scale vibration of nanotubes", Phys. B: Condens. Matt., 514, 61-69.   DOI
2 Mohammadi, K., Mahinzare, M., Ghorbani, K. and Ghadiri, M. (2018), "Cylindrical functionally graded shell model based on the first order shear deformation nonlocal strain gradient elasticity theory", Microsyst. Technol., 24(2), 1133-1146.   DOI
3 Karami, B., Janghorban, M. and Tounsi, A. (2017), "Effects of triaxial magnetic field on the anisotropic nanoplates", Steel Compos. Struct., 25(3), 361-374.   DOI
4 Karami, B., Janghorban, M. and Tounsi, A. (2018c), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Eng. Comput., 1-20.
5 Karami, B., Janghorban, M. and Tounsi, A. (2018d), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct., 27(2), 201-216.   DOI
6 Karami, B., Shahsavari, D. and Janghorban, M. (2018g), "Wave propagation analysis in functionally graded (FG) nanoplates under in-plane magnetic field based on nonlocal strain gradient theory and four variable refined plate theory", Mech. Adv. Mater. Struct., 25(12), 1047-1057.   DOI
7 Mouli, C.B., Ramji, K., Kar, V.R., Panda, S.K., Anil, L.K. and Pandey, H.K. (2018), "Numerical study of temperature dependent eigenfrequency responses of tilted functionally graded shallow shell structures", Struct. Eng. Mech., 68(5), 527-536.   DOI
8 Murmu, T., McCarthy, M. and Adhikari, S. (2013), "In-plane magnetic field affected transverse vibration of embedded singlelayer graphene sheets using equivalent nonlocal elasticity approach", Compos. Struct., 96, 57-63.   DOI
9 Nami, M.R. and Janghorban, M. (2014a), "Resonance behavior of FG rectangular micro/nano plate based on nonlocal elasticity theory and strain gradient theory with one gradient constant", Compos. Struct., 111, 349-353.   DOI
10 Karami, B., Shahsavari, D., Janghorban, M., Dimitri, R. and Tornabene, F. (2019a), "Wave propagation of porous nanoshells", Nanomater., 9(1), 22.   DOI
11 Karami, B., Shahsavari, D., Janghorban, M. and Li, L. (2018h), "Wave dispersion of mounted graphene with initial stress", Thin-Wall. Struct., 122, 102-111.   DOI
12 Karami, B., Shahsavari, D., Li, L., Karami, M. and Janghorban, M. (2019b), "Thermal buckling of embedded sandwich piezoelectric nanoplates with functionally graded core by a nonlocal second-order shear deformation theory", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 233(1), 287-301.   DOI
13 Karami, B., Janghorban, M. and Tounsi, A. (2018e), "Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory", Thin-Wall. Struct., 129, 251-264.
14 Karami, B., Shahsavari, D. and Janghorban, M. (2018f), "A comprehensive analytical study on functionally graded carbon nanotube-reinforced composite plates", Aerosp. Sci. Technol., 82, 499-512.   DOI
15 Karami, B., Shahsavari, D., Karami, M. and Li, L. (2018i), "Hygrothermal wave characteristic of nanobeam-type inhomogeneous materials with porosity under magnetic field", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science.
16 Karami, B., Shahsavari, D. and Li, L. (2018j), "Hygrothermal wave propagation in viscoelastic graphene under in-plane magnetic field based on nonlocal strain gradient theory", Phys. E: Low-Dimens. Syst. Nanostruct., 97, 317-327.   DOI
17 Karami, B., Shahsavari, D. and Li, L. (2018k), "Temperaturedependent flexural wave propagation in nanoplate-type porous heterogenous material subjected to in-plane magnetic field", J. Therm. Stress., 41(4), 483-499.   DOI
18 Karami, B., Shahsavari, D., Nazemosadat, S.M.R., Li, L. and Ebrahimi, A. (2018l), "Thermal buckling of smart porous functionally graded nanobeam rested on Kerr foundation", Steel Compos. Struct., 29(3), 349-362.   DOI
19 Katariya, P.V. and Panda, S.K. (2018), "Frequency and deflection responses of shear deformable skew sandwich curved shell panel: A finite element approach", Arab. J. Sci. Eng., 1-18.
20 Khaniki, H.B. (2018), "On vibrations of nanobeam systems", Int. J. Eng. Sci., 124, 85-103.   DOI
21 Barati, M.R. (2017b), "Vibration analysis of FG nanoplates with nanovoids on viscoelastic substrate under hygro-thermomechanical loading using nonlocal strain gradient theory", Struct. Eng. Mech., 64(6), 683-693.   DOI
22 Khetir, H., Bouiadjra, M.B., Houari, M.S.A., Tounsi, A. and Mahmoud, S. (2017), "A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates", Struct. Eng. Mech., 64(4), 391-402.   DOI
23 Kocaturk, T. and Akbas, S.D. (2013), "Wave propagation in a microbeam based on the modified couple stress theory", Struct. Eng. Mech., 46(3), 417-431.   DOI
24 Li, L. and Hu, Y. (2015), "Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory", Int. J. Eng. Sci., 97, 84-94.   DOI
25 Li, L. and Hu, Y. (2016), "Wave propagation in fluid-conveying viscoelastic carbon nanotubes based on nonlocal strain gradient theory", Comput. Mater. Sci., 112, 282-288.   DOI
26 Barati, M.R. (2017a), "On wave propagation in nanoporous materials", Int. J. Eng. Sci., 116, 1-11.   DOI
27 Barati, M.R. (2018), "Vibration analysis of porous FG nanoshells with even and uneven porosity distributions using nonlocal strain gradient elasticity", Acta Mech., 229(3), 1183-1196.   DOI
28 Barretta, R., Faghidian, S.A. and Luciano, R. (2018), "Longitudinal vibrations of nano-rods by stress-driven integral elasticity", Mech. Adv. Mater. Struct., 1-9.
29 She, G.L., Yan, K.M., Zhang, Y.L., Liu, H.B. and Ren, Y.R. (2018b), "Wave propagation of functionally graded porous nanobeams based on non-local strain gradient theory", Eur. Phys. J. Plus, 133(9), 368.   DOI
30 She, G.L., Ren, Y.R., Yuan, F.G. and Xiao, W.S. (2018a), "On vibrations of porous nanotubes", Int. J. Eng. Sci., 125, 23-35.   DOI
31 She, G.L., Yuan, F.G., Karami, B., Ren, Y.R. and Xiao, W.S. (2019), "On nonlinear bending behavior of FG porous curved nanotubes", Int. J. Eng. Sci., 135, 58-74.   DOI
32 She, G.L., Yuan, F.G. and Ren, Y.R. (2018c), "On wave propagation of porous nanotubes", Int. J. Eng. Sci., 130, 62-74.   DOI
33 She, G.L., Yuan, F.G., Ren, Y.R., Liu, H.B. and Xiao, W.S. (2018d), "Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory", Compos. Struct., 203, 614-623.   DOI
34 She, G.L., Yuan, F.G., Ren, Y.R. and Xiao, W.S. (2017), "On buckling and postbuckling behavior of nanotubes", Int. J. Eng. Sci., 121, 130-142.   DOI
35 Srinivas, S., Rao, C.J. and Rao, A. (1970), "An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates", J. Sound Vibr., 12(2), 187-199.   DOI
36 Trofimov, A., Abaimov, S., Akhatov, I. and Sevostianov, I. (2018), "On the bounds of applicability of two-step homogenization technique for porous materials", Int. J. Eng. Sci., 123, 117-126.   DOI
37 Shahsavari, D., Karami, B. and Li, L. (2018b), "Damped vibration of a graphene sheet using a higher-order nonlocal strain-gradient Kirchhoff plate model", Compt. Rend. Mecaniq., 346(12), 1216-1232.   DOI
38 Shahsavari, D. and Janghorban, M. (2017), "Bending and shearing responses for dynamic analysis of single-layer graphene sheets under moving load", J. Brazil. Soc. Mech. Sciv Eng., 39(10), 3849-3861.   DOI
39 Shahsavari, D., Karami, B., Fahham, H.R. and Li, L. (2018a), "On the shear buckling of porous nanoplates using a new sizedependent quasi-3D shear deformation theory", Acta Mech., 229(11), 4549-4573.   DOI
40 Shahsavari, D., Karami, B., Janghorban, M. and Li, L. (2017), "Dynamic characteristics of viscoelastic nanoplates under moving load embedded within visco-Pasternak substrate and hygrothermal environment", Mater. Res. Expr., 4(8), 085013.   DOI
41 Shahsavari, D., Karami, B. and Li, L. (2018c), "A high-order gradient model for wave propagation analysis of porous FG nanoplates", Steel Compos. Struct., 29(1), 53-66.   DOI
42 Shahsavari, D., Karami, B. and Mansouri, S. (2018d), "Shear buckling of single layer graphene sheets in hygrothermal environment resting on elastic foundation based on different nonlocal strain gradient theories", Eur. J. Mech.-A/Sol., 67, 200-214.   DOI
43 Zhu, X. and Li, L. (2017), "On longitudinal dynamics of nanorods", Int. J. Eng. Sci., 120, 129-145.   DOI
44 Aguiar, A.R., Bravo-Castillero, J. and Da Silva, U.P. (2018), "Application of Mori-Tanaka method in 3-1 porous piezoelectric medium of crystal class 6", Int. J. Eng. Sci., 123, 36-50.   DOI
45 Alibeigloo, A. and Liew, K. (2014), "Free vibration analysis of sandwich cylindrical panel with functionally graded core using three-dimensional theory of elasticity", Compos. Struct., 113, 23-30.   DOI
46 Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S. (2017), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., 62(6), 695-702.   DOI
47 Xu, X.J., Zheng, M.L. and Wang, X.C. (2017), "On vibrations of nonlocal rods: Boundary conditions, exact solutions and their asymptotics", Int. J. Eng. Sci., 119, 217-231.   DOI
48 Zeighampour, H., Beni, Y.T. and Dehkordi, M.B. (2018), "Wave propagation in viscoelastic thin cylindrical nanoshell resting on a visco-Pasternak foundation based on nonlocal strain gradient theory", Thin-Wall. Struct., 122, 378-386.   DOI
49 Nami, M.R. and Janghorban, M. (2014b), "Wave propagation in rectangular nanoplates based on strain gradient theory with one gradient parameter with considering initial stress", Mod. Phys. Lett. B, 28(3), 1450021.
50 Sahmani, S. and Aghdam, M. (2017a), "Nonlocal strain gradient beam model for nonlinear vibration of prebuckled and postbuckled multilayer functionally graded GPLRC nanobeams", Compos. Struct., 179, 77-88.   DOI
51 Sahmani, S. and Aghdam, M. (2017b), "A nonlocal strain gradient hyperbolic shear deformable shell model for radial postbuckling analysis of functionally graded multilayer GPLRC nanoshells", Compos. Struct., 178, 97-109.   DOI
52 Sahmani, S. and Aghdam, M. (2018), "Nonlocal strain gradient beam model for postbuckling and associated vibrational response of lipid supramolecular protein micro/nano-tubules", Math. Biosci., 295, 24-35.   DOI
53 Sahmani, S., Bahrami, M. and Aghdam, M. (2015), "Surface stress effects on the postbuckling behavior of geometrically imperfect cylindrical nanoshells subjected to combined axial and radial compressions", Int. J. Mech. Sci., 100, 1-22.   DOI
54 Boumia, L., Zidour, M., Benzair, A. and Tounsi, A. (2014), "A Timoshenko beam model for vibration analysis of chiral singlewalled carbon nanotubes", Phys. E Low-Dimens. Syst. Nanostruct., 59, 186-191.   DOI
55 Shahsavari, D., Shahsavari, M., Li, L. and Karami, B. (2018e), "A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation", Aerosp. Sci. Technol., 72, 134-149.   DOI
56 Shahverdi, H. and Barati, M.R. (2017), "Vibration analysis of porous functionally graded nanoplates", Int. J. Eng. Sci., 120, 82-99.   DOI
57 Li, L., Li, X. and Hu, Y. (2016), "Free vibration analysis of nonlocal strain gradient beams made of functionally graded material", Int. J. Eng. Sci., 102, 77-92.   DOI
58 Shafiei, N. and She, G.L. (2018), "On vibration of functionally graded nano-tubes in the thermal environment", Int. J. Eng. Sci., 133, 84-98.   DOI
59 Besseghier, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S. (2017), "Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory", Smart Struct. Syst., 19(6), 601-614.   DOI
60 Besseghier, A., Tounsi, A., Houari, M.S.A., Benzair, A., Boumia, L. and Heireche, H. (2011), "Thermal effect on wave propagation in double-walled carbon nanotubes embedded in a polymer matrix using nonlocal elasticity", Phys. E: Low-Dimens. Syst. Nanostruct., 43(7), 1379-1386.   DOI
61 Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., 20(2), 227-249.   DOI
62 Brach, S., Dormieux, L., Kondo, D. and Vairo, G. (2017), "Strength properties of nanoporous materials: a 3-layered based non-linear homogenization approach with interface effects", Int. J. Eng. Sci., 115, 28-42.   DOI
63 Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710.   DOI
64 Ebrahimi, F. and Barati, M.R. (2018), "Wave propagation analysis of smart strain gradient piezo-magneto-elastic nonlocal beams", Struct. Eng. Mech., 66(2), 237-248.   DOI
65 Ebrahimi, F. and Dabbagh, A. (2018), "Wave dispersion characteristics of nonlocal strain gradient double-layered graphene sheets in hygro-thermal environments", Struct. Eng. Mech., 65(6), 645-656.   DOI
66 Ehyaei, J. and Akbarizadeh, M.R. (2017), "Vibration analysis of micro composite thin beam based on modified couple stress", Struct. Eng. Mech., 64(4), 403-411.   DOI
67 Malekzadeh, P. and Heydarpour, Y. (2015), "Mixed Navierlayerwise differential quadrature three-dimensional static and free vibration analysis of functionally graded carbon nanotube reinforced composite laminated plates", Meccan., 50(1), 143-167.   DOI
68 Li, L., Tang, H. and Hu, Y. (2018), "The effect of thickness on the mechanics of nanobeams", Int. J. Eng. Sci., 123, 81-91.   DOI
69 Lim, C., Zhang, G. and Reddy, J. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Sol., 78, 298-313.   DOI
70 Malekzadeh, P. (2009), "Three-dimensional free vibration analysis of thick functionally graded plates on elastic foundations", Compos. Struct., 89(3), 367-373.   DOI
71 Mehar, K., Mahapatra, T.R., Panda, S.K., Katariya, P.V. and Tompe, U.K. (2018), "Finite-element solution to nonlocal elasticity and scale effect on frequency behavior of shear deformable nanoplate structure", J. Eng. Mech., 144(9), 04018094.   DOI
72 Mehralian, F. and Beni, Y.T. (2018), "Vibration analysis of sizedependent bimorph functionally graded piezoelectric cylindrical shell based on nonlocal strain gradient theory", J. Brazil. Soc. Mech. Sci. Eng., 40(1), 27.   DOI
73 Mehar, K. and Panda, S.K. (2018a), Dynamic esponse of Functionally Graded Carbon Nanotube Reinforced Sandwich Plate, IOP Conference Series: Materials Science and Engineering, IOP Publishing.
74 Mehar, K. and Panda, S.K. (2018b), "Theoretical deflection analysis of multi-walled carbon nanotube reinforced sandwich panel and experimental verification", Compos. Part B: Eng.
75 Mehrabian, A. (2018), "The poroelastic constants of multipleporosity solids", Int. J. Eng. Sci., 132, 97-104.   DOI
76 Ghayesh, M.H. (2018b), "Functionally graded microbeams: Simultaneous presence of imperfection and viscoelasticity", Int. J. Mech. Sci., 140, 339-350.   DOI
77 Eringen, A.C. and Edelen, D. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248.   DOI
78 Faleh, N.M., Ahmed, R.A. and Fenjan, R.M. (2018), "On vibrations of porous FG nanoshells", Int. J. Eng. Sci., 133, 1-14.   DOI
79 Ghayesh, M.H. (2018a), "Dynamics of functionally graded viscoelastic microbeams", Int. J. Eng. Sci., 124, 115-131.   DOI
80 Ghayesh, M.H. (2018c), "Nonlinear vibration analysis of axially functionally graded shear-deformable tapered beams", Appl. Math. Modell., 59, 583-596.   DOI
81 Ghayesh, M.H. and Farokhi, H. (2015), "Chaotic motion of a parametrically excited microbeam", Int. J. Eng. Sci., 96, 34-45.   DOI
82 Karami, B., Janghorban, M. and Li, L. (2018a), "On guided wave propagation in fully clamped porous functionally graded nanoplates", Acta Astronaut., 143, 380-390.   DOI
83 Gholipour, A., Farokhi, H. and Ghayesh, M.H. (2015), "In-plane and out-of-plane nonlinear size-dependent dynamics of microplates", Nonlin. Dyn., 79(3), 1771-1785.   DOI
84 Kaghazian, A., Hajnayeb, A. and Foruzande, H. (2017), "Free vibration analysis of a piezoelectric nanobeam using nonlocal elasticity theory", Struct. Eng. Mech., 61(5), 617-624.   DOI
85 Karami, B. and Janghorban, M. (2016), "Effect of magnetic field on the wave propagation in nanoplates based on strain gradient theory with one parameter and two-variable refined plate theory", Mod. Phys. Lett. B, 30(36), 1650421.   DOI
86 Karami, B., Janghorban, M., Shahsavari, D. and Tounsi, A. (2018b), "A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates", Steel Compos. Struct., 28(1), 99-110.   DOI