In this article, a first-order shear deformable model is expanded based on the nonlocal strain gradient theory to vibration analysis of smart nanostructures under different boundary conditions. The governing equations of motion of rotating magneto-viscoelastic functionally graded cylindrical nanoshell in the magnetic field and corresponding boundary conditions are obtained using Hamilton’s principle. To discretize the equations of motion, the generalized differential quadrature method is applied. The aim of this work is to investigate the effects of the temperature changes, nonlocal parameter, material length scale, viscoelastic coefficient, various boundary conditions, and the rotational speed of this smart structure on natural frequencies of rotating cylindrical nanoshell made of magneto-viscoelastic functionally graded material.
AbazidMASobhyM (2018) Thermo-electro-mechanical bending of FG piezoelectric microplates on Pasternak foundation based on a four-variable plate model and the modified couple stress theory. Microsystem Technologies24(2): 1227–1245.
2.
AkgözBCivalekÖ (2011) Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams. International Journal of Engineering Science49(11): 1268–1280.
3.
AlibeiglooAShabanM (2013) Free vibration analysis of carbon nanotubes by using three-dimensional theory of elasticity. Acta Mechanica224(7): 1415–1427.
4.
AlibeiglooAZanoosiAAP (2017) Thermo-electro-elasticity solution of functionally graded carbon nanotube reinforced composite cylindrical shell embedded in piezoelectric layers. Composite Structures173: 268–280.
5.
BeniYTMehralianFZeighampourH (2016) The modified couple stress functionally graded cylindrical thin shell formulation. Mechanics of Advanced Materials and Structures23(7): 791–801.
6.
BhangaleRKGanesanNÃ (2005) Free vibration studies of simply supported non-homogeneous functionally graded magneto-electro-elastic finite cylindrical shells. Journal of Sound and Vibration288: 412–422.
7.
BorjalilouVAsghariM (2018) Small-scale analysis of plates with thermoelastic damping based on the modified couple stress theory and the dual-phase-lag heat conduction model. Acta Mechanica229(9): 3869–3884.
8.
DaneshjouKTalebitootiMTalebitootiR, et al. (2013) Dynamic analysis and critical speed of rotating laminated conical shells with orthogonal stiffeners using generalized differential quadrature method. Latin American Journal of Solids and Structures10(2): 349–390.
9.
EbrahimiF (2016) Dynamic modeling of a thermo—piezo-electrically actuated nanosize beam subjected to a magnetic field. Applied Physics A122(4): 451.
10.
EbrahimiFBaratiMR (2016a) Flexural wave propagation analysis of embedded S-FGM nanobeams under longitudinal magnetic field based on nonlocal strain gradient theory. Arabian Journal for Science and Engineering42(5): 1715–1726.
11.
EbrahimiFBaratiMR (2016b) Thermal environment effects on wave dispersion behavior of inhomogeneous strain gradient nanobeams based on higher order refined beam theory. Journal of Thermal Stresses39(12): 1560–1571.
12.
EbrahimiFBaratiMR (2017) A nonlocal strain gradient refined beam model for buckling analysis of size-dependent shear-deformable curved FG nanobeams. Composite Structures159: 174–182.
13.
EbrahimiFDabbaghA (2016) On flexural wave propagation responses of smart FG magneto-electro-elastic nanoplates via nonlocal strain gradient theory. Composite Structures162: 281–293.
14.
EringenAC (2012) On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of Applied Physics54: 4703–4710.
15.
EringenACWegnerJ (2003) Nonlocal continuum field theories. Applied Mechanics Reviews56: B20–B22.
16.
FarajpourAYazdiMRastgooA, et al. (2016) A higher-order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment. Acta Mechanica227(7): 1849–1867.
17.
GhadiriMSafarpourH (2016) Free vibration analysis of embedded magneto-electro-thermo- elastic cylindrical nanoshell based on the modified couple stress theory. Applied Physics A122: 833.
18.
GhadiriMSafarpourH (2017) Free vibration analysis of size-dependent functionally graded porous cylindrical microshells in thermal environment. Journal of Thermal Stresses40(1): 55–71.
19.
HasheminejadSMMotaaleghiMA (2015) Aeroelastic analysis and active flutter suppression of an electro-rheological sandwich cylindrical panel under yawed supersonic flow. Aerospace Science and Technology42: 118–127.
20.
KeLWangYYangJ, et al. (2012) Free vibration of size-dependent Mindlin microplates based on the modified couple stress theory. Journal of Sound and Vibration331(1): 94–106.
21.
KongSZhouSNieZ, et al. (2009) Static and dynamic analysis of micro beams based on strain gradient elasticity theory. International Journal of Engineering Science47(4): 487–498.
LamDCCYangFChongACM, et al. (2003) Experiments and theory in strain gradient elasticity. Journal of the Mechanics and Physics of Solids51: 1477–1508.
24.
LeeHKwakMK (2015) Free vibration analysis of a circular cylindrical shell using the Rayleigh—Ritz method and comparison of different shell theories. Journal of Sound and Vibration353: 344–377.
25.
LiLHuYLingL (2015a) Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory. Composite Structures133: 1079–1092.
26.
LiLHuYLiX, et al. (2016a) Longitudinal vibration of size-dependent rods via nonlocal strain gradient theory. International Journal of Mechanical Sciences115: 135–144.
27.
LiLHuYLingL, et al. (2015b) Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory. Physica E: Low-Dimensional Systems and Nanostructures75: 118–124.
28.
LiLLiXHuY (2016b) Free vibration analysis of nonlocal strain gradient beams made of functionally graded material. International Journal of Engineering Science102: 77–92.
29.
LimCWZhangGReddyJN (2015) A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. Journal of the Mechanics and Physics of Solids78: 298–313.
30.
LuLGuoXZhaoJ (2017) Size-dependent vibration analysis of nanobeams based on the nonlocal strain gradient theory. International Journal of Engineering Science116: 12–24.
31.
MaHMGaoXÃReddyJN (2008) A microstructure-dependent Timoshenko beam model based on a modified couple stress theory. Journal of the Mechanics and Physics of Solids56: 3379–3391.
32.
MaLHKeLLReddyJN, et al. (2018) Wave propagation characteristics in magneto-electro-elastic nanoshells using nonlocal strain gradient theory. Composite Structures199: 10–23.
33.
MaaniENejatHYouseA, et al. (2014) Polysilicon nano-beam model based on modified couple stress and Eringen’s nonlocal elasticity theories. Physica E: Low-Dimensional Systems and Nanostructures63: 223–228.
34.
MahinzareMMohammadiKGhadiriM, et al. (2017) Size-dependent effects on critical flow velocity of a SWCNT conveying viscous fluid based on nonlocal strain gradient cylindrical shell model. Microfluidics and Nanofluidics21: 123.
35.
MohammadiKMahinzareMGhorbaniK (2017a) Cylindrical functionally graded shell model based on the first order shear deformation nonlocal strain gradient elasticity theory. Microsystem Technologies24: 1133–1146.
36.
MohammadiKMahinzareMRajabpourA, et al. (2017b) Comparison of modeling a conical nanotube resting on the Winkler elastic foundation based on the modified couple stress. The European Physical Journal Plus132(3): 115.
37.
Nguyen-ThanhNValizadehNNguyenMN, et al. (2015) An extended isogeometric thin shell analysis based on Kirchhoff–Love theory. Computer Methods in Applied Mechanics and Engineering284: 265–291.
38.
RazaviHBabadiAFBeniYT (2016) Free vibration analysis of functionally graded piezoelectric cylindrical nanoshell based on consistent couple stress theory. Composite Structures160: 1299–1309.
39.
ReddyJN (2004) Mechanics of Laminated Composite Plates and Shells. Theory and Analysis. Boca Raton, FL: CRC Press.
40.
RouhiHAnsariRDarvizehM (2017) Size-dependent large amplitude vibration analysis of nanoshells using the Gurtin–Murdoch model. International Journal of Nanoscience and Nanotechnology13(3): 241–252.
41.
SchöllhammerDFriesT (2019) Kirchhoff–Love shell theory based on tangential differential calculus. Computational Mechanics64(1): 113–131.
42.
SoedelW (2004) Vibrations of Shells and Plates. 3rd ed.New York: Marcel Dekker.
43.
SofiyevAH (2018) On the solution of the dynamic stability of heterogeneous orthotropic visco-elastic cylindrical shells. Composite Structures206: 124–130.
44.
SongZGZhangLWLiewKM (2016) Vibration analysis of CNT-reinforced functionally graded composite cylindrical shells in thermal environments. International Journal of Mechanical Sciences115: 339–347.
45.
StölkenJSEvansAG (1998) A microbend test method for measuring the plasticity length scale. Acta Materialia46(14): 5109–5115.
46.
TaatiE (2016) Analytical solutions for the size dependent buckling and postbuckling behavior of functionally graded micro-plates. International Journal of Engineering Science100: 45–60.
47.
TepoleABKabariaHBletzingerK-U, et al. (2015) Isogeometric Kirchhoff–Love shell formulations for biological membranes. Computer Methods in Applied Mechanics and Engineering293: 328–347.
48.
TooraniMHLakisAA (2000) General equations of anisotropic plates and shells including transverse shear deformations, rotary inertia and initial curvature effects. Journal of Sound and Vibration237: 561–615.
49.
TornabeneFFantuzziNViolaE, et al. (2014) Winkler—Pasternak foundation effect on the static and dynamic analyses of laminated doubly-curved and degenerate shells and panels. Composites Part B57: 269–296.
50.
TsiatasGC (2009) A new Kirchhoff plate model based on a modified couple stress theory. International Journal of Solids and Structures46(13): 2757–2764.
51.
Van DungDKhaL (2013) Nonlinear buckling and post-buckling analysis of eccentrically stiffened functionally graded circular cylindrical shells under external pressure. Thin Walled Structures63: 117–124.
52.
VinyasMKattimaniSC (2017) Static analysis of stepped functionally graded magneto-electro-elastic plates in thermal environment: a finite element study. Composite Structures178: 63–86.
53.
ViolaETornabeneFFantuzziN (2013) Static analysis of completely doubly-curved laminated shells and panels using general higher-order shear deformation theories. Composite Structures101: 59–93.
54.
WagnerHNRHühneCRohwerK, et al. (2017) Stimulating the realistic worst case buckling scenario of axially compressed unstiffened cylindrical composite shells. Composite Structures160: 1095–1104.
55.
WangBZhaoJZhouS (2010) A micro scale Timoshenko beam model based on strain gradient elasticity theory. European Journal of Mechanics-A/Solids29(4): 591–599.
56.
WuCTsaiY (2007) Static behavior of functionally graded magneto-electro-elastic shells under electric displacement and magnetic flux. International Journal of Engineering Science45: 744–769.
57.
XuXWangXZhengM, et al. (2016) Bending and buckling of nonlocal strain gradient elastic beams. Composite Structures160: 366–377.
58.
ZandekarimiSAsadiBRahaeifardM (2018) Size dependent thermal buckling and postbuckling of functionally graded circular microplates based on modified couple stress theory. Journal of Thermal Stresses41(1): 1–16.
59.
ZeighampourH (2017) Size-dependent vibration of sandwich cylindrical nanoshells with functionally graded material based on the couple stress theory. Journal of the Brazilian Society of Mechanical Sciences and Engineering39: 2789–2800.
60.
ZhangLWSongZGQiaoP, et al. (2017) Modeling of dynamic responses of CNT-reinforced composite cylindrical shells under impact loads. Computer Methods in Applied Mechanics and Engineering313: 889–903.
