Thermoelastic strongly nonlinear vibration of rotating functionally graded ring plate
Yu Da Hu 1, 2  
,   Hai Jun Bao 1, 2,   Hao Ran Xu 1, 2
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School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao, China
Hebei Key Laboratory of Mechanical Reliability for Heavy Equipment and Large Structures, Yanshan University, Qinhuangdao, China
Yu Da Hu   

1. School of Civil Engineering and Mechanics; 2. Hebei Key Laboratory of Mechanical Reliability for Heavy Equipment and Large Structures, Yanshan University, China
Submission date: 2020-06-28
Final revision date: 2020-10-08
Acceptance date: 2020-12-02
Online publication date: 2020-12-08
Publication date: 2021-01-15
Journal of Theoretical and Applied Mechanics 2021;59(1):157–171
For a metal ceramic functionally graded (FGM) ring plate, considering variations in physical properties with temperature and a power-law distribution of material components along the thickness direction, thermoelastic coupled nonlinear vibration equation in thermal environment is derived by means of Kirchhoff’s thin plate theory and the Hamiltonian principle. The transverse nonlinear vibration differential equation of the inner and outside-clamped ring plate under static load is obtained by using the Galerkin method; moreover, perturbation solution of static deflection is carried out. An improved L-P method is employed to solve the strongly nonlinear vibration equation. The vibration response and nonlinear natural frequency expression are developed. Through numerical examples, natural frequency characteristic curves of the rotating FGM ring plate are plotted. The Runge Kutta method is applied to obtain vibration response, phase and power spectrum diagrams. The influence of different parameters on natural vibration characteristics is analyzed. The results show that analytical solutions are consistent with numerical solutions, and the natural frequency decreases with an increase in the metal content and surface temperature, but grows with an increase in the rotational speed.
Chen Y.R., Chen L.W., 2007, Vibration and stability of rotating polar orthotropic sandwich annular plates with a viscoelastic core layer, Composite Structures, 78, 1, 45-57.
Chonan S., Mikami T., Ishikawa H., 1986, The vibrations and critical speeds of rotating sawblades, Transactions of the Japan Society of Mechanical Engineers, 52, 478, 1805-1812.
Dai T., Dai H.L., 2016, Thermo-elastic analysis of a functionally graded rotating hollow circular disk with variable thickness and angular speed, Applied Mathematical Modelling, 40, 7-18, 7689-7707.
Hashemi S.H., Farhadi S., Carra S., 2009, Free vibration analysis of rotating thick plates, Journal of Sound and Vibration, 323, 1-2, 366-384.
Hu Y.D., Piao J.M., Li W.Q., 2017, Magneto-elastic dynamics and bifurcation of rotating annular plate, Chinese Physics B, 26, 9, 094302.
Hu Y.D., Zhang Z.Z., 2012, The bifurcation analysis on the circular functionally graded plate with combination resonances, Nonlinear Dynamics, 67, 3, 1779-1790.
Lamb H., Southwell R.V., 1921, The vibration of spinning disk, Proceedings of the Royal Society, 99, 272-280.
Li L.F., Wang X.Z., Zhou Y.H., 2011, Dynamic characteristics of traveling waves for a rotating laminated circular plate with viscoelastic core layer, Journal of Sound and Vibration, 330, 12, 2836-2847.
Ma L.S., Wang T.J., 2003, Nonlinear bending and post-buckling of a functionally graded circular plate under mechanical and thermal loadings, International Journal of Solids and Structures, 40, 13-14, 3311-3330.
Ma L.S., Wang T.J., 2004, Relationships between axisymmetric bending and buckling solutions of FGM circular plates based on third-order plate theory and classical plate theory, International Journal of Solids and Structures, 41, 1, 85-101.
Malekzadeh P., Golbahar Haghighi M. R., Atashi M. M., 2011, Free vibration analysis of elastically supported functionally graded annular plates subjected to thermal environment, Acta Mechanica, 46, 7, 893-913.
Norouzi H., Younesian D., 2015, Forced vibration analysis of spinning disks subjected to transverse loads, International Journal of Structural Stability and Dynamics, 15, 3, 1-18.
Nosier A., Fallah F., 2009, Non-linear analysis of functionally graded circular plates under asymmetric transverse loading, International Journal of Non-Linear Mechanics, 44, 8, 928-942.
Reddy J.N., Chin C.D., 1998, Thermomechanical analysis of functionally graded cylinders and plates, Journal of Thermal Stress, 21, 6, 593-629.
Shakouri M., 2019, Free vibration analysis of functionally graded rotating conical shells in thermal environment, Composites Part B: Engineering, 163, 15, 574-584.
Shen H.S., 2007, Thermal postbulking behavior of shear deformable FGMplates with temperaturedependent properties, International Journal of Mechanical Sciences, 49, 4, 466-478.
Southwell R.V., 1992, On the free transverse vibrations of a uniform circular disc clamped at its centre and on the effects of rotation, Proceedings of the Royal Society A, 101, 709, 133-153.
Yousefitabar M., Matapouri M.K., 2017, Thermally induced buckling of thin annular FGM plates, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39, 3, 969-980.
Żur K.K., 2018, Free vibration analysis of elastically supported functionally graded annular plates via quasi-Green’s function method, Composites Part B: Engineering, 144, 1, 37-55.