Free Vibration and Transient Response of Heterogeneous Piezoelectric Sandwich Annular Plate Using Third-Order Shear Deformation Assumption

Document Type : Research Paper


1 Department of Mechanical Engineering, Lahijan Branch, Islamic Azad University, Lahijan, Iran

2 Department of Mechanical Engineering, University of Guilan, Rasht, Iran--- Department of Civil Engineering, Zhejiang University, Hangzhou 310058, People’s Republic of China, China



Based on the third-order shear deformation theory (TSDT), this paper numerically investigates the natural frequencies and time response of three-layered annular plate with functionally graded materials (FGMs) sheet core and piezoelectric face sheets, under initial external electric voltage. The impressive material specifications of FGM core are assumed to vary continuously across the plate thickness utilizing a power law distribution. The equilibrium equations are obtained employing Hamilton’s method and then solved applying differential quadrature method (DQM) in conjunction with Newmark-β. Numerical studies are carried out to express the influences of the external electric voltage, aspect ratio, and material gradient on the variations of the natural frequencies and time response curves of FGM piezoelectric sandwich annular plate. It is precisely shown that these parameters have considerable effects on the free vibration and transient response.


[1] Liu X., Wang Q., Quek S.T., 2002, Analytical solution for free vibration of piezoelectric coupled moderately thick circular plates, International Journal of Solids and Structures 39: 2129-2151.
[2] Dash P., Singh B.N., 2009, Nonlinear free vibration of piezoelectric laminated composite plate, Finite Elements in Analysis and Design 45: 686-694.
[3] Phung-Van P., De Lorenzis L., Thai C.H., 2015, Analysis of laminated composite plates integrated with piezoelectric sensors and actuators using higher-order shear deformation theory and isogeometric finite elements, Computational Materials Science 96: 495-505.
[4] Kuang J-H., Hsu C-M., Lin A-D., 2016, Determination of piezoelectric parameters from the measured natural frequencies of a piezoelectric circular plate, Integrated Ferroelectrics 168: 36-52.
[5] Shu H., Liu W., Li S., 2016, Research on flexural wave band gap of a thin circular plate of piezoelectric radial phononic crystals, Journal of Vibration and Control 22: 1777-1789.
[6] Khorshidvand A.R., Joubaneh E.F., Jabbari M., 2014, Buckling analysis of a porous circular plate with piezoelectric sensor–actuator layers under uniform radial compression, Acta Mechanica 225: 179-193.
[7] Farzaneh Joubaneh E., Mojahedin A., Khorshidvand A., 2015, Thermal buckling analysis of porous circular plate with piezoelectric sensor-actuator layers under uniform thermal load, Journal of Sandwich Structures and Materials 17: 3-25.
[8] Duc N.D., Cong P.H., Quang V.D., 2016, Nonlinear dynamic and vibration analysis of piezoelectric eccentrically stiffened FGM plates in thermal environment, International Journal of Mechanical Sciences 115-116: 711-722.
[9] Hayashi M., Koyama D., Matsukawa M., 2016, Piezoelectric particle counter using the resonance vibration modes of a circular plate, Journal of the Acoustical Society of America 140: 3035-3035.
[10] Arefi M., 2015, Nonlinear electromechanical stability of a functionally graded circular plate integrated with functionally graded piezoelectric layers, Latin American Journal of Solids and Structures 12: 1653-1665.
[11] Fesharaki J.J., Madani S.G., Golabi S., 2017, Investigating the effect of stiffness/thickness ratio on the optimal location of piezoelectric actuators through PSO algorithm, Journal of Solid Mechanics 9: 832-848.
[12] Karami Khorramabadi M., 2009, Free vibration of functionally graded beams with piezoelectric layers subjected to axial load, Journal of Solid Mechanics 1: 22-28.
[13] Mohammadimehr M., Mohandes M., 2015, The effect of modified couple stress theory on buckling and vibration analysis of functionally graded double-layer boron nitride piezoelectric plate based on CPT, Journal of Solid Mechanics 7: 281-298.
[14] Hosseini M., Bahreman M., Jamalpoor A., 2017, Thermomechanical vibration analysis of FGM viscoelastic multi-nanoplate system incorporating the surface effects via nonlocal elasticity theory, Microsystem Technologies 23: 3041-3058.
[15] Bhangale R.K., Ganesan N., 2005, Free vibration studies of simply supported non-homogeneous functionally graded magneto-electro-elastic finite cylindrical shells, Journal of Sound and Vibration 288: 412-422.
[16] Yang T., Zheng W., Huang Q., 2016, Sound radiation of functionally graded materials plates in thermal environment, Composite Structures 144: 165-176.
[17] Su Z., Jin G., Ye T., 2018, Electro-mechanical vibration characteristics of functionally graded piezoelectric plates with general boundary conditions, International Journal of Mechanical Sciences 138-139: 42-53.
[18] Kiani Y., 2016, Free vibration of functionally graded carbon nanotube reinforced composite plates integrated with piezoelectric layers, Computers & Mathematics with Applications 72: 2433-2449.
[19] Barati M.R., Zenkour A.M., 2018, Electro-thermoelastic vibration of plates made of porous functionally graded piezoelectric materials under various boundary conditions, Journal of Vibration and Control 24: 1910-1926.
[20] Seibert H.F., 2006, Applications for PMI foams in aerospace sandwich structures, Reinforced Plastics 50: 44-48.
[21] Natarajan S., Haboussi M., Manickam G., 2014, Application of higher-order structural theory to bending and free vibration analysis of sandwich plates with CNT reinforced composite facesheets, Composite Structures 113: 197-207.
[22] Santos Silva J., Dias Rodrigues J., Moreira R.A.S., 2010, Application of cork compounds in sandwich structures for vibration damping, Journal of Sandwich Structures and Materials 12: 495-515.
[23] Vinson J.R., 2001, Sandwich structures, Applied Mechanics Reviews 54: 201.
[24] El Meiche N., Tounsi A., Ziane N., 2011, A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate, International Journal of Mechanical Sciences 53: 237-247.
[25] Hadji L., Atmane H.A., Tounsi A., 2011, Free vibration of functionally graded sandwich plates using four-variable refined plate theory, Applied Mathematics and Mechanics 32: 925-942.
[26] Dinh Duc N., Hong Cong P., 2018, Nonlinear thermo-mechanical dynamic analysis and vibration of higher order shear deformable piezoelectric functionally graded material sandwich plates resting on elastic foundations,Journal of Sandwich Structures and Materials 20: 191-218.
[27] Alibeigloo A., 2017, Three dimensional coupled thermoelasticity solution of sandwich plate with FGM core under thermal shock, Composite Structures 177: 96-103.
[28] Fatahi-Vajari A., Imam A., 2016, Lateral vibrations of single-layered graphene sheets using doublet mechanics, Journal of Solid Mechanics 8: 875-894.
[29] Fazzolari F.A., 2016, Stability analysis of FGM sandwich plates by using variable-kinematics Ritz models, Mechanics of Advanced Materials and Structures 23: 1104-1113.
[30] Arefi M., Mohammad-Rezaei Bidgoli E., Zenkour A.M., 2018, Free vibration analysis of a sandwich nano-plate including FG core and piezoelectric face-sheets by considering neutral surface, Mechanics of Advanced Materials and Structures 2018: 1-12.
[31] Hosseini M., Jamalpoor A., 2015, Analytical solution for thermomechanical vibration of double-viscoelastic nanoplate-systems made of functionally graded materials, Journal of Thermal Stresses 38: 1428-1456.
[32] Sahmani S., Bahrami M., Ansari R., 2014, Surface effects on the free vibration behavior of postbuckled circular higher-order shear deformable nanoplates including geometrical nonlinearity, Acta Astronautica 105: 417-427.
[33] Ansari R., Torabi J., Hasrati E., 2018, Axisymmetric nonlinear vibration analysis of sandwich annular plates with FG-CNTRC face sheets based on the higher-order shear deformation plate theory, Aerospace Science and Technology 77: 306-319.
[34] Ashoori A.R., Vanini S.A.S., Salari E., 2017, Size-dependent axisymmetric vibration of functionally graded circular plates in bifurcation/limit point instability, Applied Physics A 123: 226.
[35] Arefi M., Zamani M., Kiani M., 2018, Size-dependent free vibration analysis of three-layered exponentially graded nanoplate with piezomagnetic face-sheets resting on Pasternak’s foundation, Journal of Intelligent Materials Systems and Structures 29: 774-786.
[36] Mohammadimehr M., Emdadi M., Afshari H., 2017, Bending, buckling and vibration analyses of MSGT microcomposite circular-annular sandwich plate under hydro-thermo-magneto-mechanical loadings using DQM, International Journal of Smart and Nano Materials 2017: 1-28.
[37] Eshraghi I., Dag S., Soltani N.,2015, Consideration of spatial variation of the length scale parameter in static and dynamic analyses of functionally graded annular and circular micro-plates, Composites Part B: Engineering 78: 338-348.
[38] Liew K.M., Xiang Y., Kitipornchai S., 2018, Vibration of Mindlin Plates : Programming the P-Version Ritz Method, Elsevier.
[39] Ebrahimi F., Rastgoo A., 2008, Free vibration analysis of smart annular FGM plates integrated with piezoelectric layers, Smart Materials and Structures 17: 015044.