In this research, the dynamic stability of the double-bonded annular sandwich microplate is investigated. Face sheets are made from composite materials reinforced by carbon nanotubes in which mechanical properties are obtained by the extended rule of the mixture. Also, the core layer is made from a honeycomb aluminum which is defined by the geometric parameters of the unit cell and mechanical properties of the virgin core material. The equations of motion are derived from Hamilton’s principle and solved by the differential quadrature method (DQM) based on higher order shear deformation theory (HSDT) and modified couple stress theory (MCST). The results are compared with the obtained results by the other literature to examine the accuracy of the present formulation. The dynamic stability of the double-bonded annular sandwich microplate with hexagonal honeycomb core including variations of core thickness, inclined angle, and aspect ratio of the unit cell are discussed. Also, the effects of motion direction of the structure, viscoelastic foundation, material length scale parameter, volume fractions of CNTs in face sheets, and the core thickness to total thickness ratio on dynamic instability region are presented.
ReissnerE.Finite deflections of sandwich plates. J Aeronaut Sci1948; 15: 435–440.
4.
NguyenDDKimSEPhamHC, et al. Dynamic response and vibration of composite double curved shallow shells with negative poisson's ratio in auxetic honeycombs core layer on elastic foundations subjected to blast and damping loads. Int J Mech Sci2017; 133: 504–512; DOI:10.1016/j.ijmecsci.2017.09.009.
5.
Qing-TianDZhi-ChunY.Wave propagation in sandwich panel with auxetic core. J Solid Mech2010; 2: 393–402.
6.
GrimaJNOliveriLAttardD, et al. Hexagonal honeycombs with zero Poisson’s ratios and enhances stiffness. Adv Eng Mater2010; 12: 855–862.
7.
YangYMaceBRKinganMJ.A wave and finite element based homogenized model for predicting sound transmission through honeycomb panels. J Sound Vib2019; 463: 114963.
8.
MalekSGibsonL.Effective elastic properties of periodic hexagonal honeycombs.Mech Mat2015; 91: 226–240.
9.
MukhopadhyayTAdhikariS.Free-vibration analysis of sandwich panels with randomly irregular honeycomb core. J Eng Mech2016; 142: 06016008.
10.
MukhopadhyayTAdhikariS.Effective in-plane elastic moduli of quasi-random spatially irregular hexagonal lattices. Int J Eng Sci2017; 119: 142–179.
11.
MohammadimehrMNaviBGorbanpourA.Biaxial buckling and bending of smart nanocomposite plate reinforced by CNTs using extended mixture rule approach. Mech Adv Compos Struct2014; 1: 17–26.
12.
Khoddami MaraghiZ.Flutter and divergence instability of nanocomposite sandwich plate with magnetostrictive face sheets. J Sound Vib2019; 457: 240–260.
13.
MohammadimehrMEmdadiMAfshariH, et al. Bending, buckling and vibration analyses of MSGT microcomposite circular-annular sandwich plate under hydro-thermo-magneto-mechanical loadings using DQM. Int J Smart Nan Mat2018; 9: 233–260.
14.
AlipourMMShariyatM.Analytical layerwise free vibration analysis of circular/annular composite sandwich plates with auxetic cores. Int J Mech Mater Des2017; 13: 125–157.
15.
JalaliSKNaeiMHPoorsolhjouyA.Buckling of circular sandwich plates of variable core thickness and FGM face sheets. Int J Str Stab Dyn2011; 11: 273–295.
16.
BolotinVV.The dynamic stability of elastic systems. San Francisco: Holden-Day, 1964.
WangXYangWDYangS.Dynamic stability of carbon nanotubes reinforced composite. Appl Math Model2014; 38: 2934–2945.
19.
MarynowskiK.Dynamic analysis of an axially moving sandwich beam with viscoelastic core. Compos Struct2012; 94: 2931–2936.
20.
DeySMukhopadhyayTSahuSK, et al. Stochastic dynamic stability analysis of composite curved panels subjected to non-uniform partial edge loading. Euro J Mech A/Solids2018; 67: 108–122.
21.
ChenLQTangYQLimCW.Dynamic stability in parametric resonance of axially accelerating viscoelastic Timoshenko beams. J Sound Vib2010; 329: 547–565.
22.
LeeSY.Finite element dynamic stability analysis of laminated composite skew plates containing cutouts based on HSDT. Compos Sci Technol2010; 70: 1249–1125.
23.
SahuSKDattaPK.Dynamic stability of laminated composite curved panels with cutouts. J Eng Mech2003; 129: 1245–1253.
24.
SalehiMMarashizadehPAbshiriniM.Dynamic relaxation analysis of composite sandwich annular sector plate with viscoelastic core. J Sandw Struct Mater2015; 17(6): 721–747
25.
MohammadimehrMEmdadiMRoustaNB.Dynamic stability analysis of microcomposite annular sandwich plate with CNT reinforced composite facesheets based on MSGT. J Sandw Struct Mater2020; 22(4): 1199–1234
26.
AifantisEC.Gradient deformation models at nano, micro and macro scales. J Eng Mater Technol1999; 121: 189–202.
27.
EringenAC.Theory of micropolar plates. J Appl Math Physics (ZAMP)1967; 18: 12–30.
28.
EringenAC.Nonlocal polar elastic continua. Int J Eng Sci1972; 10: 1–16.
29.
FleckNAHutchinsonJW.A phenomenological theory for strain gradient effects in plasticity. J Mech Phys Solids1993; 41: 1825–1857.
KoiterWT.Couple stresses in the theory of elasticity, I and II. Proc K Ned Akad Wet1964; 67: 17–44.
32.
ShaatMAbdelkefiA.Pull-in instability of multi-phase nano crystalline silicon beams under distributed electrostatic force. Int J Mech Sci2015; 90: 58–75.
33.
KryskoVAAwrejcewiczJDobriyanV, et al. Size-dependent parameter cancels chaotic vibrations of flexible shallow nano-shells. J Sound Vib2019; 446: 374–386.
34.
KeLLWangYSYangJ, et al. Free vibration of size-dependent mindlin microplates based on the modified couple stress theory. J Vib Control2012; 331: 94–106.
35.
MohammadimehrMMohandesMMoradiM.Size dependent effect on the buckling and vibration analysis of double-bonded nanocomposite piezoelectric plate reinforced by boron nitride nanotube based on modified couple stress theory. J Vib Control2016; 22: 1790–1807.
36.
KeLLWangYS.Size effect on dynamic stability of functionally graded microbeams based on a modified couple stress theory. Compos Struct2011; 93: 342–350.
37.
MohammadimehrMRousta NaviBGhorbanpourA.Dynamic stability of MSGT sinusoidal viscoelastic piezoelectric polymeric FG-SWNT reinforced nanocomposite plate considering surface stress and agglomeration effects under hydro-thermoelectro-magneto-mechanical loadings. Mech Adv Mat Struct2017; 24: 1325–1342.
38.
Ghorbanpour AraniAHashemianMLoghmanA, et al. Study of dynamic stability of the double-walled carbon nanotube under axial loading embedded in an elastic medium by the energy method. J Appl Mech Tech Phy2011; 52: 815–824.
39.
ArefiMPourjamshidianMGhorbanpour AraniA.Nonlinear free and forced vibration analysis of embedded functionally graded sandwich micro beam with moving mass. J Sandw Struct Mater2018; 20: 462–492.
40.
SedighiHMBozorgmehriA.Dynamic instability analysis of doubly clamped cylindrical nanowires in the presence of casimir attraction and surface effects using modified couple stress theory. Acta Mech2016; 227: 1575–1517.
41.
EmdadiMMohammadimehrMRoustaNB.Free vibration of an annular sandwich plate with CNTRC facesheets and FG porous cores using ritz method. Adv Nan Res2019; 7: 109–123.
42.
NatarajanSHaboussiMManickamG.Application of higher-order structural theory to bending and free vibration analysis of sandwich plates with CNT reinforced composite facesheets. Compos Struct2014; 113: 197–207.
43.
MinghuiYJ.Equivalent elastic parameters of the honeycomb core. Act Mech1999; 31: 113–118.
44.
MojahedinAJabbariMKhorshidvandAR, et al. Buckling analysis of functionally graded circular plates made of saturated porous materials based on higher order shear deformation theory. Thin Wall Struct2016; 99: 83–90.
45.
LamDCCYangFChongACM, et al. Experiments and theory in strain gradient elasticity. J Mech Phys Solids2003; 51: 1477–1508.
46.
JalaeiMHGhorbanpourAANguyen-XuanH.Investigation of thermal and magnetic field effects on the dynamic instability of FG Timoshenko nanobeam employing nonlocal strain gradient theory. Int J Mech Sci2019; 161–162: 105043.
47.
ZhongRWangQTangJ, et al. Vibration analysis of functionally graded carbon nanotube reinforced composites (FG-CNTRC) circular, annular and sector plates. Compos Struct2018; 194: 49–67. DOI: DOI: https://doi.org/10.1016/j.compstruct.2018.03.104.
48.
BrushODAlmorothBO.Buchking of bars, plates and shells. New York: McGraw – Hill, 1975.
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