On the Aeroelastic Stability of a Two-Directional FG GNP-Enriched Conical Shell
محورهای موضوعی : Structural Mechanics
Alireza Shahidi
1
(Isfahan University of Technology,Department of Mechanical Engineering)
Arashk Darakhsh
2
(Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran)
کلید واژه: Two-directional functionally graded, Flutter analysis, Graphene nanoplatelets (GNPs), Aeroelastic stability,
چکیده مقاله :
In this article, the supersonic flutter analysis of a truncated conical shell made of polymer enriched with graphene nanoplatelets (GNPs) exposed to supersonic fluid flow is discussed. It is assumed that the mass fraction of the GNPs is functionally graded (FG) along thickness and length directions according to different dispersion patterns. Modeling of the shell is done using the first-order shear deformation theory (FSDT), the mechanical properties are computed according to the Halpin-Tsai model alongside the rule of the mixture, and the aerodynamic pressure is computed utilizing the piston theory. Utilizing Hamilton’s principle, the boundary conditions and the governing equations are achieved. Harmonic trigonometric functions are used to provide an analytical solution in the circumferential direction and an approximate solution is presented in the meridional direction using the differential quadrature method (DQM). The efficacy of various parameters on the aeroelastic stability are discussed such as the percentage and dispersion pattern of the GNPs and gradient indices. It is observed that to achieve higher aeroelastic stability in the GNP-enriched truncated conical shells, it is better to dispense the GNPs near the small radius and the inner surface of the shell.
In this article, the supersonic flutter analysis of a truncated conical shell made of polymer enriched with graphene nanoplatelets (GNPs) exposed to supersonic fluid flow is discussed. It is assumed that the mass fraction of the GNPs is functionally graded (FG) along thickness and length directions according to different dispersion patterns. Modeling of the shell is done using the first-order shear deformation theory (FSDT), the mechanical properties are computed according to the Halpin-Tsai model alongside the rule of the mixture, and the aerodynamic pressure is computed utilizing the piston theory. Utilizing Hamilton’s principle, the boundary conditions and the governing equations are achieved. Harmonic trigonometric functions are used to provide an analytical solution in the circumferential direction and an approximate solution is presented in the meridional direction using the differential quadrature method (DQM). The efficacy of various parameters on the aeroelastic stability are discussed such as the percentage and dispersion pattern of the GNPs and gradient indices. It is observed that to achieve higher aeroelastic stability in the GNP-enriched truncated conical shells, it is better to dispense the GNPs near the small radius and the inner surface of the shell.
[1] Civalek O., 2006, An efficient method for free vibration analysis of rotating truncated conical shells, International Journal of Pressure Vessels and Piping 83:1-12.
[2] Li FM, Kishimoto K, Huang WH., 2009, The calculations of natural frequencies and forced vibration responses of conical shell using the Rayleigh-Ritz method, Mechanics Research Communications 36:595-602.
[3] Jooybar N, Malekzadeh P, Fiouz A, Vaghefi M., 2016, Thermal effect on free vibration of functionally graded truncated conical shell panels, Thin-Walled Structures103:45-61.
[4] Yousefi AH, Memarzadeh P, Afshari H, Hosseini SJ., 2021, Dynamic characteristics of truncated conical panels made of FRPs reinforced with agglomerated CNTs, Structures 33: 4701-4717.
[5] Yousefi AH, Memarzadeh P, Afshari H, Hosseini SJ., 2023, Optimization of CNT/polymer/fiber laminated truncated conical panels for maximum fundamental frequency and minimum cost, Mechanics Based Design of Structures and Machines 51:3922-3944.
[6] Miserentino R., 1971, Vibration and flutter tests of a pressurized thin-walled truncated conical shell, National Aeronautics and Space Administration.
[7] Bismarck-Nasr MN, Costa Savio HR., 1979, Finite-element solution of the supersonic flutter of conical shells, AIAA Journal 17:1148-1150.
[8] Sunder P, Ramakrishnan C, Sengupta S., 1983, Optimum cone angles in aeroelastic flutter, Computers & Structures 17:25-29.
[9] Sunder P, Ramakrishnan C, Sengupta S., 1983, Finite element analysis of 3‐ply laminated conical shell for flutter, International Journal for Numerical Methods in Engineering 19:1183-1192.
[10] Sabri F, Lakis AA., 2010, Hybrid finite element method applied to supersonic flutter of an empty or partially liquid-filled truncated conical shell, Journal of sound and vibration 329:302-316.
[11] Davar A, Shokrollahi H., 2013, Flutter of functionally graded open conical shell panels subjected to supersonic air flow, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 227:1036-1052.
[12] Mehri M, Asadi H, Wang Q., 2016, On dynamic instability of a pressurized functionally graded carbon nanotube reinforced truncated conical shell subjected to yawed supersonic airflow, Composite Structures 153:938-951.
[13] Bakhtiari M, Lakis AA, Kerboua Y., 2020, Nonlinear supersonic flutter of truncated conical shells, Journal of Mechanical Science and Technology 34:1375-1388.
[14] Mahmoudkhani S, Haddadpour H, Navazi H., 2010, Supersonic flutter prediction of functionally graded conical shells, Composite Structures 92:377-386.
[15] Rahmanian M, Javadi M., 2020, 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 155:106910.
[16] Amirabadi H, Farhatnia F, Civalek Ӧ., 2021, Frequency response of rotating two-directional functionally graded GPL-reinforced conical shells on elastic foundation, Journal of the Brazilian Society of Mechanical Sciences and Engineering 43:1-24.
[17] Nasution MK, Syah R, Ramdan D, Afshari H, Amirabadi H, Selim MM, Afrasyab Khan, Rahman ML, Sani Sarjadi M, Su CH, 2022, Modeling and computational simulation for Supersonic flutter prediction of polymer/GNP/fiber laminated composite joined conical-conical shells, Arabian Journal of Chemistry 15:103460.
[18] Houshangi A, Jafari AA, Haghighi SE, Nezami M., 2022, Supersonic flutter characteristics of truncated sandwich conical shells with MR core, Thin-Walled Structures 173:108888.
[19] Amirabadi H, Afshari H, Afjaei MA, Sarafraz M., 2022, Effect of variable thickness on the aeroelastic stability boundaries of truncated conical shells, Waves in Random and Complex Media 1-24.
[20] Afshari H, Ariaseresht Y, Rahimian Koloor SS, Amirabadi H, Bidgoli MO. 2022, Supersonic flutter behavior of a polymeric truncated conical shell reinforced with agglomerated CNTs, Waves in Random and Complex Media: 1-25.
[21] Song M, Kitipornchai S, Yang J., 2017, Free and forced vibrations of functionally graded polymer composite plates reinforced with graphene nanoplatelets, Composite Structures 159:579-588.
[22] Afshari H, Adab N. 2022, Size-dependent buckling and vibration analyses of GNP reinforced microplates based on the quasi-3D sinusoidal shear deformation theory, Mechanics Based Design of Structures and Machines 50:184-205.
[23] Affdl JH, Kardos J. 1976, The Halpin‐Tsai equations: a review, Polymer Engineering & Science 16:344-352.
[24] Mindlin RD. 1951, Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates, Journal of Applied Mechanics 18:31-38.
[25] Mirzaei M, Kiani Y., 2015, Thermal buckling of temperature dependent FG-CNT reinforced composite conical shells, Aerospace Science and Technology 47:42-53.
[26] Krumhaar H., 1963, The accuracy of linear piston theory when applied to cylindrical shells, AIAA Journal 1:1448-1449.
[27] Ghorbanpour Arani A, Kiani F, Afshari H., 2019, Aeroelastic Analysis of Laminated FG-CNTRC Cylindrical Panels Under Yawed Supersonic Flow, International Journal of Applied Mechanics 11:1950052.
[28] Bismarck-Nasr MN, Costa Savio HR., 1979, Finite element solution of the supersonic flutter of conical shells, AIAA Journal 17:1148-1150.
[29] Afshari H. 2020, Effect of graphene nanoplatelet reinforcements on the dynamics of rotating truncated conical shells, Journal of the Brazilian Society of Mechanical Sciences and Engineering 42:1-22.
[30] Bert CW, Malik M., 1996, Differential quadrature method in computational mechanics: a review, Applied Mechanics Reviews 49:1-28.
[31] Torabi K, Afshari H., 2017, Optimization for flutter boundaries of cantilevered trapezoidal thick plates, Journal of the Brazilian Society of Mechanical Sciences and Engineering 39:1545-1461.
[32] Yasmin A, Daniel IM. 2004, Mechanical and thermal properties of graphite platelet/epoxy composites, Polymer 45:8211-8219.
[33] Liu F, Ming P, Li J., 2007, Ab initio calculation of ideal strength and phonon instability of graphene under tension, Physical Review B 76:064120.
[34] Rafiee MA, Rafiee J, Wang Z, Song H, Yu Z-Z, Koratkar N., 2009, Enhanced mechanical properties of nanocomposites at low graphene content, ACS nano 3:3884-3890.
[35] Liew KM, NG TY, Zhao X, 2005, Free vibration analysis of conical shells via the element-free kp-Ritz method, Journal of Sound and Vibration 281(3-5): 627-645.
[36] Platus DH, 1965, Conical shell vibrations, National Aeronautics and Space Administration (NASA).
[37] Afshari H. 2022, Free vibration analysis of GNP-reinforced truncated conical shells with different boundary conditions. Australian Journal of Mechanical Engineering 20(5): 1363-1378.
[38] Afshari H, Amirabadi H., 2022, Vibration characteristics of rotating truncated conical shells reinforced with agglomerated carbon nanotubes, Journal of Vibration and Control 28:1894-1914.
[39] Yousefi AH, Memarzadeh P, Afshari H, Hosseini SJ., 202, Agglomeration effects on free vibration characteristics of three-phase CNT/polymer/fiber laminated truncated conical shells, Thin-Walled Structures 157:107077.
