Nonlinear free vibration of piezoelectric cylindrical nanoshells

doi:10.1007/s10483-019-2476-6

Abstract

Abstract:

The nonlinear vibration characteristics of the piezoelectric circular cylindrical nanoshells resting on an elastic foundation are analyzed. The small scale effect and thermo-electro-mechanical loading are taken into account. Based on the nonlocal elasticity theory and Donnell's nonlinear shell theory, the nonlinear governing equations and the corresponding boundary conditions are derived by employing Hamilton's principle. Then, the Galerkin method is used to transform the governing equations into a set of ordinary differential equations, and subsequently, the multiple-scale method is used to obtain an approximate analytical solution. Finally, an extensive parametric study is conducted to examine the effects of the nonlocal parameter, the external electric potential, the temperature rise, and the Winkler-Pasternak foundation parameters on the nonlinear vibration characteristics of circular cylindrical piezoelectric nanoshells.

Key words: jets, environmental hydraulics, similarity solutions., nonlocal elasticity theory, piezoelectric cylindrical nanoshell, multiple-scale method, Donnell's nonlinear shell theory, nonlinear vibration, size effect

2010 MSC Number:

74H45

Yanqing WANG, Yunfei LIU, J. W. ZU. Nonlinear free vibration of piezoelectric cylindrical nanoshells. Applied Mathematics and Mechanics (English Edition), 2019, 40(5): 601-620.

TrendMD

References

[1] GAO, Z., ZHU, X., FANG, Y., and ZHANG, H. Active monitoring and vibration control of smart structure aircraft based on FBG sensors and PZT actuators. Aerospace Science and Technology, 63, 101-109(2017)
[2] SCHINDEL, D. W., HUTCHINS, D. A., and GRANDIA, W. A. Capacitive and piezoelectric air-coupled transducers for resonant ultrasonic inspection. Ultrasonics, 34, 621-627(1996)
[3] LU, F., LEE, H. P., and LIM, S. P. Modeling and analysis of micro piezoelectric power generators for micro-electromechanical-systems applications. Smart Materials and Structures, 13, 57-63(2003)
[4] YANG, M. and QIAO, P. Modeling and experimental detection of damage in various materials using the pulse-echo method and piezoelectric sensors/actuators. Smart Materials and Structures, 14, 1083-1100(2005)
[5] GUPTA, V., SHARMA, M., and THAKUR, N. Optimization criteria for optimal placement of piezoelectric sensors and actuators on a smart structure:a technical review. Journal of Intelligent Material Systems and Structures, 21, 1227-1243(2010)
[6] AKSEL, E. and JONES, J. L. Advances in lead-free piezoelectric materials for sensors and actuators. Sensors, 10, 1935-1954(2010)
[7] PAN, Z. W., DAI, Z. R., and WANG, Z. L. Nanobelts of semiconducting oxides. Science, 291, 1947-1949(2001)
[8] WU, C., KAHN, M., and MOY, W. Piezoelectric ceramics with functional gradients:a new application in material design. Journal of the American Ceramic Society, 79, 809-812(1996)
[9] PARK, K. I., XU, S., LIU, Y., HWANG, G. T., KANG, S. J. L., WANG, Z. L., and LEE, K. J. Piezoelectric BaTiO₃ thin film nanogenerator on plastic substrates. Nano Letters, 10, 4939-4943(2010)
[10] XU, S. and WANG, Z. L. One-dimensional ZnO nanostructures:solution growth and functional properties. Nano Research, 4, 1013-1098(2011)
[11] ZHU, C. S., FANG, X. Q., LIU, J. X., and LI, H. Y. Surface energy effect on nonlinear free vibration behavior of orthotropic piezoelectric cylindrical nano-shells. European Journal of MechanicsA/Solids, 66, 423-432(2017)
[12] FANG, X. Q., ZHU, C. S., LIU, J. X., and LIU, X. L. Surface energy effect on free vibration of nano-sized piezoelectric double-shell structures. Physica B:Condensed Matter, 529, 41-56(2018)
[13] GAO, P. X., SONG, J., LIU, J., and WANG, Z. L. Nanowire piezoelectric nanogenerators on plastic substrates as flexible power sources for nanodevices. Advanced Materials, 19, 67-72(2007)
[14] SEOL, M. L., IM, H., MOON, D. I., WOO, J. H., KIM, D., CHOI, S. J., and CHOI, Y. K. Design strategy for a piezoelectric nanogenerator with a well-ordered nanoshell array. ACS Nano, 7, 10773-10779(2013)
[15] WANG, X. and SHI, J. Piezoelectric nanogenerators for self-powered nanodevices. Piezoelectric Nanomaterials for Biomedical Applications, Springer, New York, 135-172(2012)
[16] ZHAO, M. H., WANG, Z. L., and MAO, S. X. Piezoelectric characterization of individual zinc oxide nanobelt probed by piezoresponse force microscope. Nano Letters, 4, 587-590(2004)
[17] CHEN, C. Q., SHI, Y., ZHANG, Y. S., ZHU, J., and YAN, Y. J. Size dependence of Young's modulus in ZnO nanowires. Physical Review Letters, 96, 75505(2006)
[18] ERINGEN, A. C. Nonlocal Continuum Field Theories, Springer, New York (2002)
[19] ERINGEN, A. C. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of Applied Physics, 54, 4703-4710(1983)
[20] ERINGEN, A. C. Nonlocal polar elastic continua. International Journal of Engineering Science, 10, 1-16(1972)
[21] KE, L. L. and WANG, Y. S. Thermoelectric-mechanical vibration of piezoelectric nanobeams based on the nonlocal theory. Smart Materials and Structures, 21, 025018(2012)
[22] WANG, K. F. and WANG, B. L. The electromechanical coupling behavior of piezoelectric nanowires:surface and small-scale effects. Europhysics Letters, 97, 66005(2012)
[23] ANSARI, R., OSKOUIE, M. F., GHOLAMI, R., and SADEGHI, F. Thermo-electro-mechanical vibration of postbuckled piezoelectric Timoshenko nanobeams based on the nonlocal elasticity theory. Composites Part B:Engineering, 89, 316-327(2016)
[24] KE, L. L., WANG, Y. S., and REDDY, J. N. Thermo-electro-mechanical vibration of sizedependent piezoelectric cylindrical nanoshells under various boundary conditions. Composite Structures, 116, 626-636(2014)
[25] JANDAGHIAN, A. A. and RAHMANI, O. Size-dependent free vibration analysis of functionally graded piezoelectric plate subjected to thermo-electro-mechanical loading. Journal of Intelligent Material Systems and Structures, 28, 3039-3053(2017)
[26] RAZAVI, H., BABADI, A. F., and BENI, Y. T. Free vibration analysis of functionally graded piezoelectric cylindrical nanoshell based on consistent couple stress theory. Composite Structures, 160, 1299-1309(2017)
[27] KHEIBARI, F. and BENI, Y. T. Size dependent electro-mechanical vibration of single-walled piezoelectric nanotubes using thin shell model. Materials and Design, 114, 572-583(2017)
[28] KE, L. L., WANG, Y. S., and WANG, Z. D. Nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory. Composite Structures, 94, 2038-2047(2012)
[29] ASEMI, S. R., FARAJPOUR, A., and MOHAMMADI, M. Nonlinear vibration analysis of piezoelectric nanoelectromechanical resonators based on nonlocal elasticity theory. Composite Structures, 116, 703-712(2014)
[30] ANSARI, R. and GHOLAMI, R. Size-dependent nonlinear vibrations of first-order shear deformable magneto-electro-thermo elastic nanoplates based on the nonlocal elasticity theory. International Journal of Applied Mechanics, 8, 1650053(2016)
[31] LIU, C., KE, L. L., WANG, Y. S., and YANG, J. Nonlinear vibration of nonlocal piezoelectric nanoplates. International Journal of Structural Stability and Dynamics, 15, 1540013(2015)
[32] WANG, Y. Q. Electro-mechanical vibration analysis of functionally graded piezoelectric porous plates in the translation state. Acta Astronautica, 143, 263-271(2018)
[33] WANG, Y. Q. and ZU, J. W. Nonlinear steady-state responses of longitudinally traveling functionally graded material plates in contact with liquid. Composite Structures, 164, 130-144(2017)
[34] WANG, Y. Q. and ZU, J. W. Nonlinear dynamics of a translational FGM plate with strong mode interaction. International Journal of Structural Stability and Dynamics, 18, 1850031(2018)
[35] DING, H., CHEN, L. Q., and YANG, S. P. Convergence of Galerkin truncation for dynamic response of finite beams on nonlinear foundations under a moving load. Journal of Sound and Vibration, 331, 2426-2442(2012)
[36] DING, H., YANG, Y., CHEN, L. Q., and YANG, S. P. Vibration of vehicle-pavement coupled system based on a Timoshenko beam on a nonlinear foundation. Journal of Sound and Vibration, 333, 6623-6636(2014)
[37] WANG, Y. Q., HUANG, X. B., and LI, J. Hydroelastic dynamic analysis of axially moving plates in continuous hot-dip galvanizing process. International Journal of Mechanical Sciences, 110, 201-216(2016)
[38] SOEDEL, W. Vibrations of Shells and Plates, CRC Presss, Boca Raton (2004)
[39] AMABILI, M. Nonlinear Vibrations and Stability of Shells and Plates, Cambridge University Press, Cambridge (2008)
[40] WANG, Q. On buckling of column structures with a pair of piezoelectric layers. Engineering Structures, 24, 199-205(2002)
[41] LI, H. Y., LIN, Q. R., LIU, Z. X., and WANG, C. Free vibration of piezoelastic laminated cylindrical shells under hydrostatic pressure. International Journal of Solids and Structures, 38, 7571-7585(2001)
[42] ZHANG, D. P., LEI, Y. J., and SHEN, Z. B. Thermo-electro-mechanical vibration analysis of piezoelectric nanoplates resting on viscoelastic foundation with various boundary conditions. International Journal of Mechanical Sciences, 131, 1001-1015(2017)
[43] ZHAO, M. H., QIAN, C. F., LEE, S. W. R., TONG, P., SUEMASU, H., and ZHANG, T. Y. Electro-elastic analysis of piezoelectric laminated plates. Advanced Composite Materials, 16, 63-81(2007)
[44] WANG, Y. Q., YE, C., and ZU, J. W. Identifying temperature effect on vibrations of functionally graded cylindrical shells with porosities. Applied Mathematics and Mechanics (English Edition), 39(11), 1587-1604(2018) https://doi.org/10.1007/s10483-018-2388-6
[45] NAYFEH, A. H. and MOOK, D. T. Nonlinear Oscillations, John Wiley & Sons, New York (2008)
[46] WANG, Y. Q. and ZU, J. W. Instability of viscoelastic plates with longitudinally variable speed and immersed in ideal liquid. International Journal of Applied Mechanics, 9, 1750005(2017)
[47] GONÇALVES, P. B. and RAMOS, N. R. S. S. Numerical method for vibration analysis of cylindrical shells. Journal of Engineering Mechanics, 123, 544-550(1997)
[48] DYM, C. L. Some new results for the vibrations of circular cylinders. Journal of Sound and Vibration, 29, 189-205(1973)
[49] SHEN, H. S. and XIANG, Y. Nonlinear vibration of nanotube-reinforced composite cylindrical shells in thermal environments. Computer Methods in Applied Mechanics and Engineering, 213, 196-205(2012)
[50] RAJU, K. K. and RAO, G. V. Large amplitude asymmetric vibrations of some thin shells of revolution. Journal of Sound and Vibration, 44, 327-333(1976)
[51] RAFIEE, M., MOHAMMADI, M., ARAGH, B. S., and YAGHOOBI, H. Nonlinear free and forced thermo-electro-aero-elastic vibration and dynamic response of piezoelectric functionally graded laminated composite shells, part Ⅱ:numerical results. Composite Structures, 103, 188-196(2013)