Browse > Article
http://dx.doi.org/10.12989/scs.2019.32.2.225

Dynamic stability and nonlinear vibration of rotating sandwich cylindrical shell with considering FG core integrated with sensor and actuator  

Rostami, Rasoul (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
Mohamadimehr, Mehdi (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
Rahaghi, Mohsen Irani (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
Publication Information
Steel and Composite Structures / v.32, no.2, 2019 , pp. 225-237 More about this Journal
Abstract
In this research, the dynamic stability and nonlinear vibration behavior of a smart rotating sandwich cylindrical shell is studied. The core of the structure is a functionally graded material (FGM) which is integrated by functionally graded piezoelectric material (FGPM) layers subjected to electric field. The piezoelectric layers at the inner and outer surfaces used as actuator and sensor, respectively. By applying the energy method and Hamilton's principle, the governing equations of sandwich cylindrical shell derived based on first-order shear deformation theory (FSDT). The Galerkin method is used to discriminate the motion equations and the equations are converted to the form of the ordinary differential equations in terms of time. The perturbation method is employed to find the relation between nonlinear frequency and the amplitude of vibration. The main objective of this research is to determine the nonlinear frequencies and nonlinear vibration control by using sensor and actuator layers. The effects of geometrical parameters, power law index of core, sensor and actuator layers, angular velocity and scale transformation parameter on nonlinear frequency-amplitude response diagram and dynamic stability of sandwich cylindrical shell are investigated. The results of this research can be used to design and vibration control of rotating systems in various industries such as aircraft, biomechanics and automobile manufacturing.
Keywords
dynamic stability; nonlinear vibration; rotating sandwich cylindrical shell; functionally graded core; functionally graded piezoelectric layers; perturbation method;
Citations & Related Records
Times Cited By KSCI : 6  (Citation Analysis)
연도 인용수 순위
1 Tornabene, F. (2009), "Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution", Comput. Methods Appl. Mech. Engrg., 198, 2911-2935. https://doi.org/10.1016/j.cma.2009.04.011   DOI
2 Tornabene, F. and Reddy, J.N. (2013), "FGM and laminated doubly-curved and degenerate shells resting on nonlinear elastic foundations: a GDQ solution for static analysis with a posteriori stress and strain recovery", J. Indian Inst. Sci., 93(4), 635-688.
3 Zghal, S., Frikha, A. and Dammak, F. (2018), "Mechanical buckling analysis of functionally graded power-based and carbon nanotubes-reinforced composite plates and curved panels", Compos. Part B, 150, 165-183. https://doi.org/10.1016/j.compositesb.2018.05.037   DOI
4 Zhang, J., Li, G. and Li, S. (2015), "Analysis of transient displacements for a ceramic-metal functionally graded cylindrical shell under dynamic thermal loading", Ceram. Int., 41, 12378-2385. https://doi.org/10.1016/j.ceramint.2015.06.070   DOI
5 Mohammadimehr, M., Mehrabi, M., Hadizadeh, H. and Hadizadeh, H. (2018b), "Surface and size dependent effects on static, buckling, and vibration of micro composite beam under thermo-magnetic fields based on strain gradient theory", Steel Compos. Struct., Int. J., 26(4), 513-531. http://dx.doi.org/10.12989/scs.2018.26.4.513
6 Oh, I. and Lee, D. (2007), "Resonant frequency and instability of multi-layered microresonators with initial imperfection subject to piezoelectric loads", Microelectron Eng., 84, 1388-1392. https://doi.org/10.1016/j.mee.2007.01.103   DOI
7 Patel, B.P., Gupta, S.S., Loknath, M.S. and Kadu, C.P. (2005), "Free vibration analysis of functionally graded elliptical cylindrical shells using higher-order theory", Compos. Struct., 69, 259-270. https://doi.org/10.1016/j.compstruct.2004.07.002   DOI
8 Rajabi, J. and Mohammadimehr, M. (2019), "Bending analysis of a micro sandwich skew plate using extended Kantorovich method based on Eshelby-Mori-Tanaka approach", Comput. Concrete, Int. J., 23(5), 361-376. http://dx.doi.org/10.12989/cac.2019.23.5.361
9 Ghorbanpour Arani, A., Rousta Navi, B. and Mohammadimehr, M. (2016), "Surface stress and agglomeration effects on nonlocal biaxial buckling polymeric nanocomposite plate reinforced by CNT using various approaches", Adv. Compos. Mater., 25(5), 423-441. https://doi.org/10.1080/09243046.2015.1052189   DOI
10 Heydarpour, Y., Aghdam, M.M. and Malekzadeh, P. (2014), "Free vibration analysis of rotating functionally graded carbon nanotube-reinforced composite truncated conical shells", Compos. Struct., 117, 187-200. https://doi.org/10.1016/j.compstruct.2014.06.023   DOI
11 Hua, L. and Lam, K.Y. (1998), "Frequency characteristics of a thin rotating cylindrical in shell using the generalized differential quadrature method", Int. J. Mech. Sci., 40(5), 443-459. https://doi.org/10.1016/S0020-7403(97)00057-X   DOI
12 Irie, T., Yamada, G. and Kaneko, Y. (1982), "Free vibration of a conical shell with variable thickness", J. Sound Vibr., 82(1), 83-94. https://doi.org/10.1016/j.tws.2014.01.030   DOI
13 Jafari, A.A., Khalili, S.M.R. and Tavakolian, M. (2014), "Nonlinear vibration of functionally graded cylindrical shells embedded with a piezoelectric layer", Thin-Wall. Struct., 79, 8-15. https://doi.org/10.1016/j.tws.2014.01.030   DOI
14 Kumar, A., Chakrabarti, A. and Bhargava, P. (2013), "Vibration of laminated composites and sandwich shells based on higher order zigzag theory", Eng. Struct., 56, 880-888. https://doi.org/10.1016/j.engstruct.2013.06.014   DOI
15 Frikha, A., Zghala, S. and Dammaka, F. (2018), "Dynamic analysis of functionally graded carbon nanotubes-reinforced plate and shell structures using a double directors finite shell element", Aerosp. Sci. Technol., 78, 438-451. https://doi.org/10.1016/j.ast.2018.04.048   DOI
16 Ghorbanpour Arani, A., Hashemian, M., Loghman, A. and Mohammadimehr, M. (2011), "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. Phys., 52(5), 815-824. https://doi.org/10.1134/S0021894411050178   DOI
17 Lam, K.Y. and Qian, W. (2000), "Free vibration of symmetric angle-ply thick laminated composite cylindrical shells", Compos.: Part B, Eng., 31, 345-354. https://doi.org/10.1016/S1359-8368(99)00075-X   DOI
18 Li, Y.S. and Pan, E. (2015), "Static bending and free vibration of a functionally graded piezoelectric micro plate based on the modified couple-stress theory", Int. J. Eng. Sci., 97, 40-59. https://doi.org/10.1016/j.ijengsci.2015.08.009   DOI
19 Li, Q., Iu, V.P. and Kou, K.P. (2008), "Three-dimensional vibration analysis of functionally graded material sandwich plates", J. Sound Vib., 311, 498-515. https://doi.org/10.1016/j.jsv.2007.09.018   DOI
20 Liew, K.M., He, X.Q. and Kitipornchai, S. (2004), "Finite element method for the feedback control of FGM shells in the frequency domain via piezoelectric sensors and actuators", Comput. Methods Appl. Mech. Eng., 193, 257-273. https://doi.org/10.1016/j.cma.2003.09.009   DOI
21 Liu, Y. and Chu, F. (2012), "Nonlinear vibrations of rotating thin circular cylindrical shell", Nonlinear Dyn., 67, 1467-1479. https://doi.org/10.1007/s11071-011-0082-7   DOI
22 Tornabene, F., Liverani, A. and Caligiana, G. (2011), "FGM and laminated doubly curved shells and panels of revolution with a free-form meridian: A 2-D GDQ solution for free vibrations", Int. J. Mech. Sci., 53, 446-470. https://doi.org/10.1016/j.ijmecsci.2011.03.007   DOI
23 Tornabene, F., Fantuzzi, N., Viola, E. and Batra, R.C. (2015a), "Stress and strain recovery for functionally graded free-form and doubly-curved sandwich shells using higher-order equivalent single layer theory", Compos. Struct., 119, 67-89. https://doi.org/10.1016/j.compstruct.2014.08.005   DOI
24 Tornabene, F., Fantuzzi, N., Bacciocchi, M. and Viola, E. (2015b), "Effect of agglomeration on the natural frequencies of functionally graded carbon nanotube-reinforced laminated composite doubly-curved shells", Compos. Part B Eng., 89(1), 187-218. https://doi.org/10.1016/j.compositesb.2015.11.016
25 Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2017), "Foam core composite sandwich plates and shells with variable stiffness: Effect of the curvilinear fiber path on the modal response", J. Sandw. Struct. Mater., 21(1), 320-365. https://doi.org/10.1177/1099636217693623
26 Trabelsi, S., Frikha, A., Zghal, S. and Dammak, F. (2019), "A modified FSDT-based four nodes finite shell element for thermal buckling analysis of functionally graded plates and cylindrical shells", Eng. Struct., 178, 444-459. https://doi.org/10.1016/j.engstruct.2018.10.047   DOI
27 Sun, S., Chu, S. and Cao, D. (2012), "Vibration characteristics of thin rotating cylindrical shells with various boundary conditions", J. Sound Vib., 331, 4170-4186. https://doi.org/10.1016/j.jsv.2012.04.018   DOI
28 Mohammadimehr, M., Rousta Navi, B. and Ghorbanpour Arani, A. (2015), "Surface stress effect on the nonlocal biaxial buckling and bending analysis of polymeric piezoelectric nanoplate reinforced by CNT using eshelby-mori-tanaka approach", J. Solid Mech., 7(2), 173-190.
29 Mohammadimehr, M., Rostami, R. and Arefi, M. (2016), "Electro-elastic analysis of a sandwich thick plate considering FG core and composite piezoelectric layers on Pasternak foundation using TSDT", Steel Compos. Struct., Int. J., 20(3), 513-544. http://dx.doi.org/10.12989/scs.2016.20.3.513   DOI
30 Mohammadimehr, M., Shahedi, S., Rousta Navi, B. (2017), "Nonlinear vibration analysis of FG-CNTRC sandwich Timoshenko beam based on modified couple stress theory subjected to longitudinal magnetic field using generalized differential quadrature method", Proceedings of the Institution of Mechanical Engineers, Part C: J. Mech. Eng. Sci., 231(20), 3866-3885.   DOI
31 Mohammadimehr, M., Okhravi, S.V. and Akhavan Alavi, S.M. (2018a), "Free vibration analysis of magneto-electro-elastic cylindrical composite panel reinforced by various distributions of CNTs with considering open and closed circuits boundary conditions based on FSDT", J. Vibr. Control, 24(8), 1551-1569. https://doi.org/10.1177/1077546316664022   DOI
32 Dehghan, M., Zamani Nejad, M. and Moosaie, A. (2016), "Thermo-electro-elastic analysis of functionally graded piezoelectric shells of revolution: Governing equations and solutions for some simple cases", Int. J. Eng. Sci., 104, 34-61. https://doi.org/10.1016/j.ijengsci.2016.04.007   DOI
33 Akhavan Alavi, S.M., Mohammadimehr, M. and Edjtahed, S.H. (2019), "Active control of micro Reddy beam integrated with functionally graded nanocomposite sensor and actuator based on linear quadratic regulator method", Eur. J. Mech., A/Solids, 74, 449-461. https://doi.org/10.1016/j.euromechsol.2018.12.008   DOI
34 Arefi, M. and Rahimi, G.H. (2012), "Comprehensive thermoelastic analysis of a functionally graded cylinder with different boundary conditions under internal pressure using first order shear deformation theory", Mechanika, 18(1), 5-13.
35 Dey, S., Sarkar, S., Das, A., Karmakar, A. and Adhikari, S. (2014), "Effect of twist and rotation on vibration of functionally graded conical shells", Int. J. Mech. Mater. Des., 11, 425-437. https://doi.org/10.1007/s10999-014-9266-x   DOI
36 Emdadi, M., Mohammadimehr, M. and Navi, B.R. (2019), "Free vibration of an annular sandwich plate with CNTRC facesheets and FG porous cores using Ritz method", Adv. Nano Res., Int. J., 7(2), 109-123. http://dx.doi.org/10.12989/anr.2019.7.2.109   DOI
37 Yazdani, R., Mohammadimehr, M. and Navi, B.R. (2019), "Free vibration of Cooper-Naghdi micro saturated porous sandwich cylindrical shells with reinforced CNT face sheets under magneto-hydro-thermo-mechanical loadings", Struct. Eng. Mech., Int. J., 70(3), 351-365. http://dx.doi.org/10.12989/sem.2019.70.3.351
38 Razavi, H., Faramarzi Babadi, A. and Tadi Beni, Y. (2016), "Free vibration analysis of functionally graded piezoelectr ic cylindr ical nanoshell based on consistent couple stress theory", Compos. Struct., 160, 1299-1309. https://doi.org/10.1016/j.compstruct.2016.10.056   DOI
39 Rostami, R., Irani Rahaghi, M. and Mohammadimehr, M. (2019), "Vibration control of the rotating sandwich cylindrical shell considering functionally graded core and functionally graded magneto-electro-elastic layers by using differential quadrature method", J. Sandw. Struct. Mater. https://doi.org/10.1177/1099636218824139
40 Rouzegar, J. and Abad, F. (2015), "Free vibration analysis of FG plate with piezoelectric layers using four-variable refined plate theory", Thin-Wall. Struct., 89, 76-83. https://doi.org/10.1016/j.tws.2014.12.010   DOI
41 Setoodeha, A.R., Shojaeea, M. and Malekzadeh, P. (2018), "Vibrational behavior of doubly curved smart sandwich shells with FG-CNTRC face sheets and FG porous core", Compos. Part B: Eng., 165, 798-822. https://doi.org/10.1016/j.compositesb.2019.01.022
42 Sheng, G.G. and Wang, X. (2009a), "Active control of functionally graded laminated cylindrical shells", Compos. Struct., 90, 448-457. https://doi.org/10.1016/j.compstruct.2009.04.017   DOI
43 Sheng, G.G. and Wang, X. (2009b), "Studies on dynamic behavior of functionally graded cylindrical shells with PZT layers under moving loads", J. Sound Vib., 323, 772-789. https://doi.org/10.1016/j.jsv.2009.01.017   DOI
44 Sheng, G.G. and Wang, X. (2017), "The non-linear vibrations of rotating functionally graded cylindrical shells", Nonlinear Dyn., 87(2), 1095-1109. https://doi.org/10.1007/s11071-016-3100-y   DOI
45 Shu, C. (1995), "An efficient approach for free vibration analysis of conical shells", Int. J. Mech. Sci., 38(9), 935-949. https://doi.org/10.1016/0020-7403(95)00096-8   DOI
46 Loghmani, A., Danesh, M., Keshmiri, M. and Savadi, M.M. (2015), "Theoretical and experimental study of active vibration control of a cylindrical shell using piezoelectric disks", J. Low Frequency Noise Vib. Active Control, 34(3), 269-288. https://doi.org/10.1260/0263-0923.34.3.269   DOI
47 Malekzadeh, P. and Heydarpour, Y. (2012), "Free vibration analysis of rotating functionally graded cylindrical shells in thermal environment", Compos. Struct., 94, 2971-2981. https://doi.org/10.1016/j.compstruct.2012.04.011   DOI
48 Mohammadimehr, M. and Shahedi, S. (2017), "High-order buckling and free vibration analysis of two types sandwich beam including AL or PVC-foam flexible core and CNTs reinforced nanocomposite face sheets using GDQM", Compos. Part B: Eng., 108, 91-107. https://doi.org/10.1016/j.compositesb.2016.09.040   DOI
49 Mohammadimehr, M. and Mehrabi, M. (2017), "Stability and free vibration analyses of double-bonded micro composite sandwich cylindrical shells conveying fluid flow", Appl. Math. Model., 47, 685-709. https://doi.org/10.1016/j.apm.2017.03.054   DOI
50 Mohammadimehr, M. and Alimirzaei, S. (2016), "Nonlinear static and vibration analysis of Euler-Bernoulli composite beam model reinforced by FG-SWCNT with initial geometrical imperfection using FEM", Struct. Eng. Mech., Int. J., 59(3), 431-454. http://dx.doi.org/10.12989/sem.2016.59.3.431   DOI
51 Mohammadimehr, M. and Rahmati, A.H. (2013), "Small scale effect on electro-thermo-mechanical vibration analysis of single-walled boron nitride nanorods under electric excitation", Turkish J. Eng. Environ. Sci., 37(1), 1-15.
52 Mohammadimehr, M., Moradi, M. and Loghman, A. (2014), "Influence of the Elastic Foundation on the Free Vibration and Buckling of Thin-Walled Piezoelectric-Based FGM Cylindrical Shells Under Combined Loadings", J. Solid Mech., 6(4), 347-365.
53 Assaee, H. and Hasani, H. (2015), "Forced vibration analysis of composite cylindrical shells using spline finite strip method Forced vibration analysis of composite cylindrical shells using spline finite strip method", Thin-Wall. Struct., 97, 207-214. https://doi.org/10.1016/j.tws.2015.09.014   DOI
54 Cao, X., Shi, L., Zhang, X. and Jiang, G. (2013), "Active control of acoustic radiation from laminated cylindrical shells integrated with a piezoelectric layer", Smart Mater. Struct., 22(6), 34-56. https://doi.org/10.1088/0964-1726/22/6/065003
55 Chen, W.Q., Bian, Z.G., Lv, C.F. and Ding, H.J. (2004), "3D free vibration analysis of a functionally graded piezoelectric hollow cylinder filled with compressible fluid", Int. J. Solids Struct., 41, 947-964. https://doi.org/10.1016/j.ijsolstr.2003.09.036   DOI
56 Das, A. and Karmakar, A. (2016), "Vibration Characteristics of Functionally Graded Pre-Twisted Turbo Machinery Blade with Rotational Effect", Adv. Sci. Lett., 22(1), 111-117. https://doi.org/10.1166/asl.2016.6769   DOI
57 Das, A. and Karmakar, A. (2018), "Free vibration characteristics of functionally graded pre-twisted conical shells under rotation", J. Inst. Eng. India Ser. C, 99(6), 681-692. https://doi.org/10.1007/s40032-017-0378-6   DOI