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Acta Mechanica
Published in: Acta Mechanica 6/2020

01-04-2020 | Original Paper

Dynamic analysis of a multilayered piezoelectric two-dimensional quasicrystal cylindrical shell filled with compressible fluid using the state-space approach

Authors: Yunzhi Huang, Yang Li, Liangliang Zhang, Han Zhang, Yang Gao

Published in: Acta Mechanica | Issue 6/2020

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Abstract

The state-space approach is developed to analyze the dynamic behaviors of a multilayered two-dimensional piezoelectric quasicrystal circular cylinder filled with the compressible fluid. With simple support at both ends, the hollow cylindrical shell has imperfect bonding between the layers. The analytical solution of a homogeneous cylindrical shell has been derived based on the state equations. The general solution for the corresponding multilayered case is also obtained by utilizing the propagator matrix method. The numerical results present the natural frequencies in free vibration with different length-to-radius and radius-to-thickness ratios. The critical load and dynamic behaviors of the model are exactly predicted in the axial buckling problem. For the impulse case, the influences of the density of the filled fluid and coefficients of interfacial imperfections on the dynamic responses are also discussed.
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Literature
1.
Shechtman, D.G., Blech, I.A., Gratias, D., Cahn, J.W.: Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 53, 1951–1953 (1984)
2.
Dubois, J.M.: Useful Quasicrystals. World Scientific, Singapore (2006)
3.
Wang, R.H., Hu, B.Z., Gui, J.N.: Quasicrystal Physics. Science Press, Beijing (2004) (in Chinese)
4.
Jaric, M.V., Nelson, D.R.: Introduction to quasicrystals. Phys. Today 43, 77–79 (1990)
5.
Zhou, Y.B., Li, X.F.: Elasto-hydrodynamics of quasicrystals with a crack under sudden impacts. Philos. Mag. Lett. 76, 419–436 (2018)
6.
Zhou, Y.B., Li, X.F.: Fracture analysis of an infinite 1D hexagonal piezoelectric quasicrystal plate with a penny-shaped dielectric crack. Eur. J. Mech. A-Solids 76, 224–234 (2019)MathSciNetMATH
7.
Rao, K.R.M., Rao, P.H., Chaitanya, B.S.K.: Piezoelectricity in quasicrystals: a group-theoretical study. Pramana J. Phys. 68, 481–487 (2007)
8.
Yang, L.Z., Gao, Y., Pan, E.: Electric-elastic field induced by a straight dislocation in one-dimensional quasicrystals. Acta Phys. Pol. A 126, 467–470 (2014)
9.
Li, X.Y., Li, P.D., Wu, T.H., Shi, M., Zhu, Z.: Three-dimensional fundamental solutions for one-dimensional hexagonal quasicrystal with piezoelectric effect. Phys. Lett. A 378, 826–834 (2014)MathSciNetMATH
10.
Guo, J.H., Pan, E.: Three-phase cylinder model of one-dimensional hexagonal piezoelectric quasicrystal composites. ASME J. Appl. Mech. 83, 08100701 (2016)
11.
Zhang, W., Liu, T., Xi, A., Wang, Y.N.: Resonant responses and chaotic dynamics of composite laminated circular cylindrical shell with membranes. J. Sound Vib. 423, 65–99 (2018)
12.
Mukhopadhyay, S.: Mixed convection boundary layer flow along a stretching cylinder in porous medium. J. Pet. Sci. Eng. 96–97, 73–78 (2012)
13.
Mahdi, D.D., Mahmood, F.G., Navid, N.: The full simulation of rapid refueling of a natural gas vehicle on-board cylinder. J. Nat. Gas Sci. Eng. 21, 1099–1106 (2014)
14.
Fan, T.Y., Mai, Y.M.: Elasticity theory, fracture mechanics, and some relevant thermal properties of quasi-crystalline materials. Appl. Mech. Rev. 57, 325–343 (2004)
15.
Shi, W.: Conservation laws of a decagonal quasicrystal in elastodynamics. Eur. J. Mech. A-Solids 24, 217–226 (2005)MathSciNetMATH
16.
Fan, T.Y.: Mathematical Theory of Elasticity of Quasicrystals and Its Applications. Science Press, Beijing (2010)MATH
17.
Agiasofitou, E., Lazar, M.: The elastodynamic model of wave-telegraph type for quasicrystals. Int. J. Solids Struct. 51, 923–929 (2014)
18.
Rochal, S., Lorman, V.: Minimal model of the phonon-phason dynamics in icosahedral quasicrystals and its application to the problem of internal friction in the i-AlPdMn alloy. Phys. Rev. B 66, 1442040 (2002)
19.
Fan, T.Y., Wang, X.F., Li, W., Zhu, A.Y.: Elasto-hydrodynamics of quasicrystals. Philos. Mag. 89, 501–512 (2009)
20.
Sladek, J., Sladek, V., Pan, E.: Bending analyses of 1D orthorhombic quasicrystal plates. Int. J. Solids Struct. 50, 3975–3983 (2013)
21.
Sladek, J., Sladek, V., Zhang, C., Wünsche, M.: Modelling of orthorhombic quasicrystal shallow shells. Eur. J. Mech. A-Solids 49, 518–530 (2015)MathSciNetMATH
22.
Li, Y.S., Feng, W.J., Zhang, C.: Buckling and vibration of the two-dimensional quasicrystal cylindrical shells under axial compression. Appl. Math. Model. 50, 68–91 (2017)MathSciNetMATH
23.
Hosseini, S.M., Sladek, J., Sladek, V.: Elastodynamic analysis of a hollow cylinder with decagonal quasicrystal properties: meshless implementation of local integral equations. Crystals 6, 1–16 (2016)
24.
Louzguine-Luzgin, D.V., Inoue, A.: Formation and properties of quasicrystals. Annu. Rev. Mater. Res. 38, 403–423 (2008)
25.
Yang, L.Z., Gao, Y., Pan, E., Waksmanski, N.: An exact closed-form solution for a multilayered one-dimensional orthorhombic quasicrystal plate. Acta Mech. 226, 3611–3621 (2015)MathSciNetMATH
26.
Waksmanski, N., Pan, E., Yang, L.Z., Gao, Y.: Free vibration of a multilayered one-dimensional quasi-crystal plate. J. Vib. Acoust. 136, 1–8 (2014)
27.
Waksmanski, N., Pan, E., Yang, L.Z., Gao, Y.: Harmonic response of multilayered one-dimensional quasicrystal plates subjected to patch loading. J. Sound Vib. 375, 237–253 (2016)
28.
Yang, L.Z., Li, Y., Gao, Y., Pan, E., Waksmanski, N.: Three-dimensional exact electric-elastic analysis of a multilayered two-dimensional decagonal quasicrystal plate subjected to patch loading. Compos. Struct. 171, 198–216 (2017)
29.
Li, Y., Yang, L., Gao, Y., Pan, E.: Cylindrical bending analysis of a layered two-dimensional piezoelectric quasicrystal nanoplate. J. Intell. Mater. Syst. Struct. 29, 2660–2676 (2018)
30.
Yang, L.Z., Li, Y., Gao, Y., Pan, E.: Three-dimensional exact thermo-elastic analysis of multilayered two-dimensional quasicrystal nanoplates. Appl. Math. Model. 63, 203–218 (2018)MathSciNetMATH
31.
Aboudi, J.: Damage in composites-modeling of imperfect bonding. Compos. Sci. Technol. 28, 103–128 (1987)
32.
Benveniste, Y.: The effective mechanical behaviour of composite materials with imperfect contact between the constituents. Mech. Mater. 4, 197–208 (1985)
33.
Ray, M.C., Reddy, J.N.: Active control of laminated cylindrical shells using piezoelectric fiber reinforced composites. Compos. Sci. Tech. 65, 1226–1236 (2005)
34.
Shakeri, M., Akhlaghi, M., Hoseini, S.M.: Vibration and radial wave propagation velocity in functionally graded thick hollow cylinder. Compos. Struct. 76, 174–181 (2006)
35.
Soldatos, K.P., Timarci, T.: A unified formulation of laminated composites, shear deformable, five-degrees-of-freedom cylindrical shell theories. Compos. Struct. 25, 165–171 (1993)
36.
Nath, J.K., Kapuria, S.: Improved smeared and zigzag third-order theories for piezoelectric angle-ply laminated cylindrical shells under electrothermomechanical loads. J. Mech. Mater. Struct. 4, 1157–1184 (2009)
37.
Zhu, J.Q., Chen, C.Q., Shen, Y.P., Wang, S.L.: Dynamic stability of functionally graded piezoelectric circular cylindrical shells. Mater. Lett. 59, 477–485 (2005)
38.
Zhu, J.Q., Chen, C.Q., Shen, Y.P.: Three dimensional analysis of the dynamic stability of piezoelectric circular cylindrical shells. Eur. J. Mech. A-Solids 22, 401–411 (2003)MATH
39.
Botta, F., Cerri, G.: Wave propagation in Reissner–Mindlin piezoelectric coupled cylinder with nonconstant electric field through the thickness. Int. J. Solid. Struct. 44, 6201–6219 (2007)MATH
40.
Haddadpour, H., Mahmoudkhani, S., Navazi, H.M.: Free vibration analysis of functionally graded cylindrical shells including thermal effects. Thin Wall. Struct. 45, 591–599 (2007)
41.
Chen, W.Q., Ding, H.J.: Natural frequencies of fluid-filled transversely isotropic cylindrical shells. Int. J. Mech. Sci. 41, 677–684 (1999)MATH
42.
Junger, M.C., Feit, D.: Sound Structures, and Their Interaction. Acoustical Society of America, Woodbury (1993)MATH
43.
Moore, I.D.: Buried pipes and culverts. Geotech. Geoenviron. Eng. Handb. 18, 541–567 (2001)
44.
Luo, P.L.: Combined Theory of Strength and Stability. Science Press, Beijing (2014). (in Chinese)
45.
Chen, W.Q., Bian, Z.G., Lv, C.F., Ding, H.J.: 3D free vibration analysis of a functionally graded piezoelectric hollow cylinder filled with compressible fluid. Int. J. Solids Struct. 41, 947–964 (2004)MATH
46.
Chen, W.Q., Bian, Z.G., Ding, H.J.: Three-dimensional vibration analysis of fluid-filled orthotropic FGM cylindrical shells. Int. J. Mech. Sci. 46, 159–171 (2004)MATH
47.
Zhao, J., Bian, Z.G., Chen, W.Q.: Steady-state response and free vibration of an embedded imperfect smart functionally graded hollow cylinder filled with compressible fluid. Struct. Eng. Mech. 34, 449–474 (2010)
48.
Gao, Y., Ricoeur, A.: Three-dimensional analysis of a spheroidal inclusion in a two-dimensional quasicrystal body. Philos. Mag. 92, 4334–4353 (2012)
49.
50.
Ding, H.J., Chen, W.Q.: Three Dimensional Problems of Piezoelasticity. Nova Science Publishers, New York (2001)
51.
Chen, W.Q., Cai, J.B., Ye, G.R.: Exact solutions of cross-ply laminates with bonding imperfections. AIAA J. 41, 2244–2250 (2003)
52.
Bian, Z.G., Chen, W.Q., Lim, C.W., Zhang, N.: Analytical solutions for single- and multi-span functionally graded plates in cylindrical bending. Int. J. Solids Struct. 42, 6433–6456 (2005)MATH
53.
Bian, Z.G., Lim, C.W., Chen, W.Q.: On functionally graded beams with integrated surface piezoelectric layers. Compos. Struct. 72, 339–351 (2006)
54.
Luo, P.L., Luo, H., Tong, F.: The influence of prebuckling deformations and stresses on the buckling of the spherical shell. Int. J. Offshore Polar 1, 284–292 (2013)
55.
Jafari, A.A., Khalili, S.M.R., Azarafza, R.: Transient dynamic response of composite circular cylindrical shells under radial impulse load and axial compressive loads. Thin Wall. Struct. 43, 1763–1786 (2005)
Metadata
Title
Dynamic analysis of a multilayered piezoelectric two-dimensional quasicrystal cylindrical shell filled with compressible fluid using the state-space approach
Authors
Yunzhi Huang
Yang Li
Liangliang Zhang
Han Zhang
Yang Gao
Publication date
01-04-2020
Publisher
Springer Vienna
Published in
Acta Mechanica / Issue 6/2020
Print ISSN: 0001-5970
Electronic ISSN: 1619-6937
DOI
https://doi.org/10.1007/s00707-020-02641-7

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