Vibration analysis of FG annular sector in moderately thick plates with two piezoelectric layers

doi:10.1007/s10483-019-2468-8

摘要/Abstract

摘要： Free vibration of functionally graded (FG) annular sector plates embedded with two piezoelectric layers is studied with a generalized differential quadrature (GDQ) method. Based on the first-order shear deformation (FSD) plate theory and Hamilton's principle with parameters satisfying Maxwell's electrostatics equation in the piezoelectric layers, governing equations of motion are developed. Both open and closed circuit (shortly connected) boundary conditions on the piezoelectric surfaces, which are respective conditions for sensors and actuators, are accounted for. It is observed that the open circuit condition gives higher natural frequencies than a shortly connected condition. For the simulation of the potential electric function in piezoelectric layers, a sinusoidal function in the transverse direction is considered. It is assumed that properties of the FG material (FGM) change continuously through the thickness according to a power distribution law. The fast rate convergence and accuracy of the GDQ method with a small number of grid points are demonstrated through some numerical examples. With various combinations of free, clamped, and simply supported boundary conditions, the effects of the thicknesses of piezoelectric layers and host plate, power law index of FGMs, and plate geometrical parameters (e.g., angle and radii of annular sector) on the in-plane and out-of-plane natural frequencies for different FG and piezoelectric materials are also studied. Results can be used to predict the behaviors of FG and piezoelectric materials in mechanical systems.

关键词: Newtonian fluid, non-Newtonian fluid, turbulent flows, numerical simulation, free vibration, annular sector, first-order shear deformation (FSD), piezoelectric, functionally graded material (FGM)

Abstract: Free vibration of functionally graded (FG) annular sector plates embedded with two piezoelectric layers is studied with a generalized differential quadrature (GDQ) method. Based on the first-order shear deformation (FSD) plate theory and Hamilton's principle with parameters satisfying Maxwell's electrostatics equation in the piezoelectric layers, governing equations of motion are developed. Both open and closed circuit (shortly connected) boundary conditions on the piezoelectric surfaces, which are respective conditions for sensors and actuators, are accounted for. It is observed that the open circuit condition gives higher natural frequencies than a shortly connected condition. For the simulation of the potential electric function in piezoelectric layers, a sinusoidal function in the transverse direction is considered. It is assumed that properties of the FG material (FGM) change continuously through the thickness according to a power distribution law. The fast rate convergence and accuracy of the GDQ method with a small number of grid points are demonstrated through some numerical examples. With various combinations of free, clamped, and simply supported boundary conditions, the effects of the thicknesses of piezoelectric layers and host plate, power law index of FGMs, and plate geometrical parameters (e.g., angle and radii of annular sector) on the in-plane and out-of-plane natural frequencies for different FG and piezoelectric materials are also studied. Results can be used to predict the behaviors of FG and piezoelectric materials in mechanical systems.

Key words: Newtonian fluid, non-Newtonian fluid, turbulent flows, numerical simulation, functionally graded material (FGM), annular sector, piezoelectric, free vibration, first-order shear deformation (FSD)

中图分类号:

70-XX
70Jxx

S. AZARIPOUR, M. BAGHANI. Vibration analysis of FG annular sector in moderately thick plates with two piezoelectric layers[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(6): 783-804.

参考文献

[1] TUTUNCU, N. and OZTURK, M. Exact solutions for stresses in functionally graded pressure vessels. Composites Part B:Engineering, 32, 683-686(2001)
[2] JALALI, M. H., ZARGAR, O., and BAGHANI, M. Size-dependent vibration analysis of FG microbeams in thermal environment based on modified couple stress theory. Iranian Journal of Science and Technology, Transactions of Mechanical Engineering (2018) https://doi.org/10.1007/s40997-018-0193-6
[3] BAKHTIARI-NEJAD, F., SHAMSHIRSAZ, M., MOHAMMADZADEH, M., and SAMIE, S. Free vibration analysis of FG skew plates based on second order shear deformation theory. ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, American Society of Mechanical Engineers, New York (2014)
[4] HASSANZADEH-AGHDAM, M. K., EDALATPANAH, S. A., and AZARIPOUR, S. Interphase region effect on the biaxial yielding envelope of SiC fiber-reinforced Ti matrix composites. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science, 0954406218777532(2018)
[5] ZARGAR, O., MASOUMI, A., and MOGHADDAM, A. O. Investigation and optimization for the dynamical behaviour of the vehicle structure. International Journal of Automotive and Mechanical Engineering, 14, 4196-4210(2017)
[6] LIU, F. L. and LIEW, K. Free vibration analysis of Mindlin sector plates:numerical solutions by differential quadrature method. Computer Methods in Applied Mechanics and Engineering, 177, 77-92(1999)
[7] WANG, X. and WANG, Y. Free vibration analyses of thin sector plates by the new version of differential quadrature method. Computer Methods in Applied Mechanics and Engineering, 193, 3957-3971(2004)
[8] NIE, G. and ZHONG, Z. Vibration analysis of functionally graded annular sectorial plates with simply supported radial edges. Composite Structures, 84, 167-176(2008)
[9] KELESHTERI, M., ASADI, H., and WANG, Q. Postbuckling analysis of smart FG-CNTRC annular sector plates with surface-bonded piezoelectric layers using generalized differential quadrature method. Computer Methods in Applied Mechanics and Engineering, 325, 689-710(2017)
[10] KIANI, Y. and ESLAMI, M. An exact solution for thermal buckling of annular FGM plates on an elastic medium. Composites Part B:Engineering, 45, 101-110(2013)
[11] HOSSEINI, R., ZARGAR, O., and HAMEDI, M. Improving power density of piezoelectric vibration-based energy scavengers. Journal of Solid Mechanics, 10, 98-109(2018)
[12] JALALI, M. H., SHAHRIARI, B., ZARGAR, O., BAGHANI, M., and BANIASSADI, M. Free vibration analysis of rotating functionally graded annular disc of variable thickness using generalized differential quadrature method. Scientia Iranica, 25, 728-740(2018)
[13] HAGHSHENAS, A. and ARANI, A. G. Nonlocal vibration of a piezoelectric polymeric nanoplate carrying nanoparticle via Mindlin plate theory. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science, 228, 907-920(2014)
[14] ARANI, A. G., HAGHSHENAS, A., AMIR, S., MOZDIANFARD, M. R., and LATIFI, M. Electrothermo-mechanical response of thick-walled piezoelectric cylinder reinforced by boron-nitride nanotubes. Strength of Materials, 45, 102-115(2013)
[15] WANG, Y., XU, R. Q., and DING, H. J. Free axisymmetric vibration of FGM circular plates. Applied Mathematics and Mechanics (English Edition), 30, 1077-1082(2009) https://doi.org/10.1007/s10483-009-0901-x
[16] CHEN, W., LYU, C., and BIAN, Z. Free vibration analysis of generally laminated beams via state-space-based differential quadrature. Composite Structures, 63, 417-425(2004)
[17] WANG, X. and LI, S. R. Free vibration analysis of functionally graded material beams based on Levinson beam theory. Applied Mathematics and Mechanics (English Edition), 37, 861-878(2016) https://doi.org/10.1007/s10483-016-2094-9
[18] SOHN, J. W., KIM, H. S., and CHOI, S. B. Active vibration control of smart hull structures using piezoelectric actuators. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science, 220, 1329-1337(2006)
[19] CHENG, G. M., GUO, K., ZENG, P., and SUN, Y. M. Development of a two-degree-of-freedom piezoelectric motor using single plate vibrator. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science, 226, 1036-1052(2011)
[20] LI, F. M. and SONG, Z. G. Vibration analysis and active control of nearly periodic two-span beams with piezoelectric actuator/sensor pairs. Applied Mathematics and Mechanics (English Edition), 36, 279-292(2015) https://doi.org/10.1007/s10483-015-1912-6
[21] JAVANBAKHT, M., SHAKERI, M., and SADEGHI, S. N. Dynamic analysis of functionally graded shell with piezoelectric layers based on elasticity. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science, 223, 2039-2047(2009)
[22] AREFI, M., KARROUBI, R., and IRANI-RAHAGHI, M. Free vibration analysis of functionally graded laminated sandwich cylindrical shells integrated with piezoelectric layer. Applied Mathematics and Mechanics (English Edition), 37, 821-834(2016) https://doi.org/10.1007/s10483-016-2098-9
[23] MOHAMMADIMEHR, M. and ROSTAMI, R. Bending and vibration analyses of a rotating sandwich cylindrical shell considering nanocomposite core and piezoelectric layers subjected to thermal and magnetic fields. Applied Mathematics and Mechanics (English Edition), 39, 1-22(2018) https://doi.org/10.1007/s10483-018-2301-6
[24] WANG, Q., QUEK, S., SUN, C., and LIU, X. Analysis of piezoelectric coupled circular plate. Smart Materials and Structures, 10, 229-239(2001)
[25] KELESHTERI, M., ASADI, H., and WANG, Q. Large amplitude vibration of FG-CNT reinforced composite annular plates with integrated piezoelectric layers on elastic foundation. Thin-Walled Structures, 120, 203-214(2017)
[26] WU, N., WANG, Q., and QUEK, S. Free vibration analysis of piezoelectric coupled circular plate with open circuit. Journal of Sound and Vibration, 329, 1126-1136(2010)
[27] DUAN, W., QUEK, S. T., and WANG, Q. Free vibration analysis of piezoelectric coupled thin and thick annular plate. Journal of Sound and Vibration, 281, 119-139(2005)
[28] EBRAHIMI, F. and RASTGOO, A. An analytical study on the free vibration of smart circular thin FGM plate based on classical plate theory. Thin-Walled Structures, 46, 1402-1408(2008)
[29] EBRAHIMI, F. and RASTGOO, A. Free vibration analysis of smart annular FGM plates integrated with piezoelectric layers. Smart Materials and Structures, 17, 015044(2008)
[30] HASHEMI, S. H., ES'HAGHI, M., and KARIMI, M. Closed-form vibration analysis of thick annular functionally graded plates with integrated piezoelectric layers. International Journal of Mechanical Sciences, 52, 410-428(2010)
[31] PRAVEEN, G. and REDDY, J. Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates. International Journal of Solids and Structures, 35, 4457-4476(1998)
[32] REDDY, J. N. A simple higher-order theory for laminated composite plates. Journal of Applied Mechanics, 51, 745-752(1984)
[33] MOHAMMADZADEH-KELESHTERI, M., ASADI, H., and AGHDAM, M. Geometrical nonlinear free vibration responses of FG-CNT reinforced composite annular sector plates integrated with piezoelectric layers. Composite Structures, 171, 100-112(2017)
[34] LIU, X., WANG, Q., and QUEK, S. Analytical solution for free vibration of piezoelectric coupled moderately thick circular plates. International Journal of Solids and Structures, 39, 2129-2151(2002)
[35] KELESHTERI, M., ASADI, H., and WANG, Q. On the snap-through instability of post-buckled FG-CNTRC rectangular plates with integrated piezoelectric layers. Computer Methods in Applied Mechanics and Engineering, 331, 53-71(2018)
[36] MOHAMMADZADEH-KELESHTERI, M., SAMIE-ANARESTANI, S., and ASSADI, A. Large deformation analysis of single-crystalline nanoplates with cubic anisotropy. Acta Mechanica, 228, 3345-3368(2017)
[37] MOHAMMADSALEHI, M., ZARGAR, O., and BAGHANI, M. Study of non-uniform viscoelastic nanoplates vibration based on nonlocal first-order shear deformation theory. Meccanica, 52, 1063-1077(2017)
[38] SHU, C. and DU, H. Implementation of clamped and simply supported boundary conditions in the GDQ free vibration analysis of beams and plates. International Journal of Solids and Structures, 34, 819-835(1997)
[39] TORNABENE, F. and VIOLA, E. Vibration analysis of spherical structural elements using the GDQ method. Computers and Mathematics with Applications, 53, 1538-1560(2007)
[40] ZHAO, X., LEE, Y., and LIEW, K. M. Free vibration analysis of functionally graded plates using the element-free kp-Ritz method. Journal of Sound and Vibration, 319, 918-939(2009)
[41] HOSSEINI-HASHEMI, S., ES'HAGHI, M., and TAHER, H. R. D. An exact analytical solution for freely vibrating piezoelectric coupled circular/annular thick plates using Reddy plate theory. Composite Structures, 92, 1333-1351(2010)
[42] FARSANGI, M. A., SAIDI, A., and BATRA, R. Analytical solution for free vibrations of moderately thick hybrid piezoelectric laminated plates. Journal of Sound and Vibration, 332, 5981-5998(2013)
[43] HASANI, S., SOLEYMANI, A. P., PANJEPOUR, M., and GHAEI, A. A tension analysis during oxidation of pure aluminum powder particles:non-isothermal condition. Oxidation of Metals, 82, 209-224(2014)
[44] LIEW, K. and LIU, F. L. Differential quadrature method for vibration analysis of shear deformable annular sector plates. Journal of Sound and Vibration, 230, 335-356(2000)
[45] FARSANGI, M. A. and SAIDI, A. Levy type solution for free vibration analysis of functionally graded rectangular plates with piezoelectric layers. Smart Materials and Structures, 21, 094017(2012)