Electro-Thermo-Mechanical Vibration Analysis of a Foam-Core Smart Composite Cylindrical Shell Containing Fluid

Document Type: Research Paper


1 Faculty of Mechanical Engineering, University of Kashan--- Institute of Nanoscience & Nanotechnology, University of Kashan

2 Faculty of Mechanical Engineering, University of Kashan


In this study, free vibration of a foam-core orthotropic smart composite cylindrical shell (SCCS) filled with a non-viscous compressible fluid, subjected to combined electro-thermo-mechanical loads is investigated.  Piezoelectric polymeric cylindrical shell, is made from polyvinylidene fluoride (PVDF) and reinforced by armchair double walled boron nitride nanotubes (DWBNNTs). Characteristics of the equivalent composite are determined using micro-electro-mechanical models. The poly ethylene (PE) foam-core is modeled based on Winkler and Pasternak foundations. Employing the charge equation for coupling electrical and mechanical fields, the problem is turned into an eigenvalue one, for which analytical frequency equations are derived considering free electrical and simply supported mechanical boundary conditions at circular surfaces at either ends of the cylindrical shell. The influence of electric potential generated, filled-fluid, orientation angle of DWBNNTs, foam-core and a few other parameters on the resonance frequency of SCCS are investigated. Results show that SCCS and consequently the generated Φ improve sensor and actuator applications in several process industries, because it not only increases the vibration frequency, but also extends economic viability of the smart structure.


[1] Love A.E.H., 1888, On the small free vibrations and deformations of a thin elastic shell, Philosophical Transactions of the Royal Society A 179: 491–549.

[2] Arnold R.N., Warburton G.B., 1948, Flexural vibrations of the walls of thin cylindrical shells, Philosophical Transactions of the Royal Society 197: 238-256.

[3] Bert C.W., Baker J.L., Egle B.M., 1969, Free vibration of multilayer anisotropic cylindrical shells, Journal of Composite Material 3: 480-499.

[4] Blevins R.D., 1979, Formulas for Natural Frequency and Mode Shape, Van Nostrand Reinhold, New York.

[5] Soedel W.A., 1980, New frequency formula for closed circular cylindrical shells for a large variety of boundary conditions, Journal of Sound and Vibration 70: 309-317.

[6] Vanderpool M.E., Bert C.W., 1981, Vibration of materially monoclinic thick-wall circular cylindrical shell, American Institute of Aeronautics and Astronautics 19: 634-641 .

[7] Ludwig A., Krieg R., 1981, An analysis quasi-exact method for calculating eigen vibrations of thin circular shells, Journal of Sound and Vibration 74: 155-174.

[8] Chung H., Turul P., Mulcahy T.M., Jendrzejczyk J.A., 1981, Analysis of a cylindrical shell vibrating in a cylindrical fluid region, Nuclear Engineering Design 63: 109–120.

[9] Markus S., 1988, The Mechanics of Vibrations of Cylindrical Shells, Elsevier, New York.

[10] Xianga Y., Mab Y.F., Kitipornchaib S., Lim C.W., Lau C.W.H., 2002, Exact solutions for vibration of cylindrical shells with intermediate ring supports, International Journal of Mechanical Science 44: 1907–1924.

[11] Ye L., Lun G., Ong L.S., 2011, Buckling of a thin-walled cylindrical shell with foam core under axial compression, Thin-Walled Struct 49: 106–111.

[12] Junger M.C., Mass C., 1952, Vibration of elastic shells in a fluid medium and the associated radiation of sound, Journal of Applied Mechanics 74: 439–445.

[13] Jain R.K., 1974, Vibration of fluid-filled orthotropic cylindrical shells, Journal of Sound and Vibration 37: 379–388.

[14] Goncalves P.B., Batista R.C., 1987, Frequency response of cylindrical shells partially submerged or filled with liquid, Journal of Sound and Vibration 113: 59–70.

[15] Chen W.Q., Ding H.J., 1999, Natural frequencies of fluid-filled transversely isotropic cylindrical shells, International Journal of Mechanical Science 41: 677–684.

[16] Chung H., 1981, Free vibration analysis of circular cylindrical shells, Journal of Sound and Vibration 74: 331-359.

[17] Amabili M. 1999, Vibrations of circular tubes and shells filled and partially immersed in dense fluids, Journal of Sound and Vibration 221: 567–585.

[18] Amabili M., 1996, Free vibration of partially filled horizontal cylindrical shells, Journal of Sound and Vibration 191: 757–780.

[19] Pellicano F., Amabili M., 2003, Stability and vibration of empty and fluid-filled circular cylindrical shells under static and periodic axial loads, International Journal of Solids and Structures 40: 3229–3251.

[20] Chen W.Q., Bian Z.G., Ding H.J., 2004, Three-dimensional vibration analysis of fluid-filled orthotropic FGM cylindrical shells, International Journal of Mechanical Science 46: 159–171.

[21] Chen W.Q., Bian Z.G., Lv C.F., Ding H.J. 2004, 3D free vibration analysis of a functionally graded piezoelectric hollow cylinder filled with compressible fluid International, International Journal of Solids and Structures 41: 947–964.

[22] Tj H.G., Mikami T., Kanie S., Sato M., 2005, Free vibrations of fluid-filled cylindrical shells on elastic foundations, Thin-Wall Structures 43: 1746–1762.

[23] Daneshmand F., Ghavanloo E., 2010, Coupled free vibration analysis of a fluid-filled rectangular container with a sagged bottom membrane, Journal of Fluids and Structures 26: 236–252.

[24] Askari E., Daneshmand F., Amabili M., 2011, Coupled vibrations of a partially fluid-filled cylindrical container with an internal body including the effect of free surface waves, Journal of Fluids and Structures 27: 1049–1067.

[25] Gibson K., Ronald F.,1994, Principles of Composite Material Mechanics, McGraw Hill, New York.

[26] Bent A.A., Hagood N.W., Rodgers J.P., 1995, Anisotropic actuation with piezoelectric fiber composites, Journal of Material System Structures 6: 338–349.

[27] Messina A., Soldatos K.P., 1999, Vibration of completely free composite plates and cylindrical shell panels by a higher-order theory, International Journal of Mechanical Science 41: 891-918.

[28] Tan P., Tong L., 2001, Micro-electromechanics models for piezoelectric-fiber-reinforced composite materials, Composite Science Technology 61: 759–769.

[29] Kadoli R., Ganesan N., 2003, Free vibration and buckling analysis of composite cylindrical shells conveying hot fluid, Composite Structures 60: 19–32.

[30] Ray M.C., Reddy J.N., 2005, Active control of laminated cylindrical shells using piezoelectric fiber reinforced composites, Composite Science Technology 65: 1226–1236.

[31] Matsuna H., 2007, Vibration and buckling of cross-ply laminated composite circular cylindrical shells according to a global higher-order theory, International Journal of Mechanical Science 49: 1060-1075.

[32] Rahmani O., Khalili S.M.R., Malekzadeh K., 2010, Free vibration response of composite sandwich cylindrical shell with flexible core, Composite Structures 92: 1269–1281.

[33] Nguyen-Van H., Mai-Duy N., Karunasena W., Tran-Cong T., 2011, Buckling and vibration analysis of laminated composite plate/shell structures via a smoothed quadrilateral flat shell element with in-plane rotations, Computers and Structures 89: 612–625.

[34] Mosallaie Barzoki A.A., Ghorbanpour Arani A., Kolahchi R., Mozdianfard M.R., 2011, Electro-thermo-mechanical torsional buckling of a piezoelectric polymeric cylindrical shell reinforced by DWBNNTs with an elastic core, Applied Mathematical Modelling 27: 1278-1284.

[35] Ghorbanpour Arani A., Kolahchi R., Mosallaie Barzoki A.A., 2011, Effect of material inhomogeneity on electro-thermo-mechanical behaviors of functionally graded piezoelectric rotating cylinder, Applied Mathematical Modelling 35: 2771–2789.

[36] Ghorbanpour Arani A., Kolahchi R., Mosalaei Barzoki A.A., Loghman A., 2012, Electro-thermo-mechanical behaviors of FGPM Spheres Using Analytical Method and ANSYS Software, Applied Mathematical Modelling 36: 139–157.

[37] Reddy J.N., 2004, Mechanics of Laminated Composite Plates and Shells-Theory and Analysis, CRC Press, New York.

[38] Ghorbanpour Arani A., Mosallaie Barzoki A.A., Kolahchi R., Loghman A., 2011, Pasternak foundation effect on the axial and torsional waves propagation in embedded DWCNTs using nonlocal elasticity cylindrical shell theory, Journal of Mechanical Science and Technology 25: 1-8.

[39] Timoshenko SP., 1951, Theory of Elasticity, McGraw-Hill, New York.