Nonlinear Flutter Analysis of Porous Functionally Graded Plate in Yawed Hypersonic Flow

Document Type : Research Article


Department of Aerospace Engineering, Shahid Sattari Aeronautical University of Science and Technology, Tehran, Iran


In this paper, an aerothermoelastic analysis of functionally graded plate containing porosities in yawed hypersonic flows is investigated. Due to some incorrect manufacturing processes, two different types of porosity, namely, even and uneven distributions are taken into account. The third-order piston theory is utilized to estimate the unsteady aerodynamic pressure induced by the hypersonic airflow. The material properties of a plate are assumed to vary across the thickness direction according to a simple power law. Based on classical plate theory, the motion equations are developed with geometric nonlinearity taking into consideration of von Karman strains. The formulations are established based on Hamilton’s principle while the generalized differential quadrature method is employed to solve the nonlinear aerothermoelastic equations. Due to lower computational efforts‎, the method of generalized differential quadrature is used to obtain accurate results. Moreover, the assumed mode method along with the Runge-Kutta integration algorithm is used as a solution method. The reliability and precision of the obtained results are validated by published literature. Then, the influence of porosity distribution, porosity coefficient, and yawed flow angle are discussed in detail. In general, this paper shows that even porosity distribution would have a more destabilizing effect compared with the ‎uneven porous model. And also, for both porosity distributions, the chaotic behavior appears in higher top surface temperature but even porosity distribution has a profound effect on chaotic motion.


Main Subjects

[1] H.-T. Thai, S.-E. Kim, A review of theories for the modeling and analysis of functionally graded plates and shells, Composite Structures, 128 (2015) 70-86.
[2] Z. Su, L. Wang, K. Sun, D. Wang, Vibration characteristic and flutter analysis of elastically restrained stiffened functionally graded plates in thermal environment, International Journal of Mechanical Sciences, 157 (2019) 872-884.
[3] M. Rahmanian, M. Javadi, A unified algorithm for fully-coupled aeroelastic stability analysis of conical shells in yawed supersonic flow to identify the effect of boundary conditions, Thin-Walled Structures, 155 (2020) 106910.
[4] W. Hayes, Hypersonic flow theory, Elsevier, 2012.
[5] E.H. Dowell, Aeroelasticity of plates and shells, Springer Science & Business Media, 1974.
[6] L.K. Abbas, C. Qian, P. Marzocca, G. Zafer, A. Mostafa, Active aerothermoelastic control of hypersonic double-wedge lifting surface, Chinese Journal of Aeronautics, 21(1) (2008) 8-18.
[7] T. Prakash, M. Ganapathi, Supersonic flutter characteristics of functionally graded flat panels including thermal effects, Composite structures, 72(1) (2006) 10-18.
[8] K.-J. Sohn, J.-H. Kim, Structural stability of functionally graded panels subjected to aero-thermal loads, Composite Structures, 82(3) (2008) 317-325.
[9] K.-J. Sohn, J.-H. Kim, Nonlinear thermal flutter of functionally graded panels under a supersonic flow, Composite Structures, 88(3) (2009) 380-387.
[10] G. Jiang, F. Li, Aerothermoelastic analysis of composite laminated trapezoidal panels in supersonic airflow, Composite Structures, 200 (2018) 313-327.
[11] V. Khalafi, J. Fazilati, Supersonic panel flutter of variable stiffness composite laminated skew panels subjected to yawed flow by using NURBS-based isogeometric approach, Journal of Fluids and Structures, 82 (2018) 198-214.
[12] Y. Chai, F. Li, Z. Song, C. Zhang, Influence of the boundary relaxation on the flutter and thermal buckling of composite laminated panels, Aerospace Science and Technology, 104 (2020) 106000.
[13] M. Rasool, M.K. Singha, Aeroelastic analysis of pre-stressed variable stiffness composite panels, Journal of Vibration and Control, 26(9-10) (2020) 724-734.
[14] P.K. Swain, N. Sharma, D.K. Maiti, B.N. Singh, Aeroelastic analysis of laminated composite plate with material uncertainty, Journal of Aerospace Engineering, 33(1) (2020) 04019111.
[15] X. Wang, Z. Yang, J. Zhou, W. Hu, Aeroelastic effect on aerothermoacoustic response of metallic panels in supersonic flow, Chinese Journal of Aeronautics, 29(6) (2016) 1635-1648.
[16] V.R. Kar, S.K. Panda, Nonlinear thermomechanical deformation behaviour of P-FGM shallow spherical shell panel, Chinese Journal of Aeronautics, 29(1) (2016) 173-183.
[17] P. Perlikowski, J. Warminski, S. Lenci, Recent advances in nonlinear dynamics and vibrations: special issue of meccanica, Meccanica,  (2020) 1-5.
[18] L.-C. Shiau, L.-T. Lu, Nonlinear flutter of two-dimensional simply supported symmetric composite laminated plates, Journal of aircraft, 29(1) (1992) 140-145.
[19] H.H. Ibrahim, M. Tawfik, M. Al-Ajmi, Non-linear panel flutter for temperature-dependent functionally graded material panels, computational mechanics, 41(2) (2008) 325-334.
[20] M. Kouchakzadeh, M. Rasekh, H. Haddadpour, Panel flutter analysis of general laminated composite plates, Composite Structures, 92(12) (2010) 2906-2915.
[21] H. Navazi, H. Haddadpour, Nonlinear aero-thermoelastic analysis of homogeneous and functionally graded plates in supersonic airflow using coupled models, Composite Structures, 93(10) (2011) 2554-2565.
[22] Z.-G. Song, F.-M. Li, Aerothermoelastic analysis of nonlinear composite laminated panel with aerodynamic heating in hypersonic flow, Composites Part B: Engineering, 56 (2014) 830-839.
[23] H. Shahverdi, V. Khalafi, Bifurcation analysis of FG curved panels under simultaneous aerodynamic and thermal loads in hypersonic flow, Composite Structures, 146 (2016) 84-94.
[24] Y. Chai, F. Li, Z. Song, Nonlinear vibrations, bifurcations and chaos of lattice sandwich composite panels on Winkler–Pasternak elastic foundations with thermal effects in supersonic airflow, Meccanica, 54(7) (2019) 919-944.
[25] W. Xia, X. Zhao, D. Li, S. Shen, Nonlinear flutter response of pre-heated functionally graded panels, International Journal of Computational Materials Science and Engineering, 7(01n02) (2018) 1850012.
[26] L. Ye, Z. Ye, Aeroelastic Stability and Nonlinear Flutter Analysis of Heated Panel with Temperature-Dependent Material Properties, Journal of Aerospace Engineering, 33(6) (2020) 04020068.
[27] M. Rahmanian, M. Javadi, Supersonic Aeroelasticity and Dynamic Instability of Functionally Graded Porous Cylindrical Shells Using a Unified Solution Formulation, International Journal of Structural Stability and Dynamics,  (2020) 2050132.
[28] M.-C. Trinh, D.-D. Nguyen, S.-E. Kim, Effects of porosity and thermomechanical loading on free vibration and nonlinear dynamic response of functionally graded sandwich shells with double curvature, Aerospace Science and Technology, 87 (2019) 119-132.
[29] M.R. Barati, H. Shahverdi, Aero-hygro-thermal stability analysis of higher-order refined supersonic FGM panels with even and uneven porosity distributions, Journal of Fluids and Structures, 73 (2017) 125-136.
[30] L. Hadji, M. Avcar, Free Vibration Analysis of FG Porous Sandwich Plates under‎ Various Boundary Conditions, Journal of Applied and Computational Mechanics,  (2020).
[31] N. Dinh Duc, V.D. Quang, P.D. Nguyen, T.M. Chien, Nonlinear dynamic response of functionally graded porous plates on elastic foundation subjected to thermal and mechanical loads, Journal of Applied and Computational Mechanics, 4(4) (2018) 245-259.
[32] K. Zhou, X. Huang, J. Tian, H. Hua, Vibration and flutter analysis of supersonic porous functionally graded material plates with temperature gradient and resting on elastic foundation, Composite Structures, 204 (2018) 63-79.
[33] R. Bahaadini, A.R. Saidi, K. Majidi-Mozafari, Aeroelastic flutter analysis of thick porous plates in supersonic flow, International Journal of Applied Mechanics, 11(10) (2019) 1950096.
[34] M. Rahmanian, T. Farsadi, H. Kurtaran, Nonlinear flutter of tapered and skewed cantilevered plates with curvilinear fiber paths, Journal of Sound and Vibration, 500 (2021) 116021.
[35] Y. Wang, C. Ye, J. Zu, Identifying the temperature effect on the vibrations of functionally graded cylindrical shells with porosities, Applied Mathematics and Mechanics, 39(11) (2018) 1587-1604.
[36] S.S. Rao, Vibration of continuous systems, Wiley Online Library, 2007.
[37] M. Amabili, Nonlinear vibrations and stability of shells and plates, Cambridge University Press, 2008.
[38] S.C. Dixon, M.L. Hudson, Flutter, vibration, and buckling of truncated orthotropic conical shells with generalized elastic edge restraint, National Aeronautics and Space Administration, 1970.
[39] M. Permoon, H. Haddadpour, M. Javadi, Nonlinear vibration of fractional viscoelastic plate: Primary, subharmonic, and superharmonic response, International Journal of Non-Linear Mechanics, 99 (2018) 154-164.
[40] M. Taskin, A. Arikoglu, O. Demir, Vibration and Damping Analysis of Sandwich Cylindrical Shells by the GDQM, AIAA Journal,  (2019) 3040-3051.
[41] F. Tornabene, N. Fantuzzi, F. Ubertini, E. Viola, Strong formulation finite element method based on differential quadrature: a survey, Applied Mechanics Reviews, 67(2) (2015).
[42] H. Shahverdi, V. Khalafi, S. Noori, Aerothermoelastic analysis of functionally graded plates using generalized differential quadrature method, Latin American Journal of Solids and Structures, 13(4) (2016) 796-818.