نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی دکتری، دانشکده مهندسی صنایع و مکانیک ، دانشگاه ازاد اسلامی ، واحد قزوین، قزوین

2 استادیار، دانشکده مهندسی صنایع و مکانیک، دانشگاه آزاد اسلامی، واحد قزوین ، قزوین

3 استادیار، دانشکده مهندسی مکانیک دانشگاه آزاد اسلامی، واحد تاکستان، تاکستان

10.22068/jstc.2019.104648.1520

چکیده

به دلیل کاربرد گسترده پوسته‌های مخروطی ساندویچی در صنایع پیشرفته، بررسی رفتار مکانیکی این سازه‌ها امری ضروری است. در این تحقیق، برای اولین بار، با در نظر گرفتن انعطاف‌پذیری هسته در تئوری مرتبه بالای پوسته‌های ساندویچی، رفتار ارتعاشی پوسته مخروطی ناقص ساندویچی که شامل هسته هدفمند متخلخل و رویه‌های همگن است، در توزیع دماهای مختلف بررسی شده است. خواص مواد رویه ها و هسته وابسته به دما در نظر گرفته شده و تغییرات خواص مواد هدفمند به کمک قانون توانی که با در نظر گرفتن دو مدل توزیع تخلخل اصلاح شده، نشان داده می‌شود. با استفاده از اصل همیلتون و در نظر گرفتن تنش‌های درون صفحه‌ای در هسته و رویه‌ها و کرنش غیرخطی ون کارمن هم برای تنش مکانیکی و هم تنش حرارتی، معادلات حرکت سازه بدست آمده‌اند. برای حل معادلات در شرایط تکیه‌گاهی ساده از روش گلرکین استفاده شده است. برای بررسی اثر تغییر دما در سازه، توزیع دما به صورت یکنواخت، خطی و غیرخطی در نظر گرفته شده است. نتایج تحلیل حاضر به منظور صحت سنجی، در حالات خاص با مقالات دیگر و همچنین با نتایج بدست آمده از نرم افزار آباکوس مقایسه شده و همچنین تغییرات فرکانس ویژه بی‌بعد نسبت به تغییرات هندسی سازه، تغییرات دما، خواص مواد و تخلخل بررسی شده است.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Vibration analysis of truncated conical sandwich shell with porous FG core in different thermal loading

نویسندگان [English]

  • Mohsen Rahmani 1
  • Younes Mohammadi 2
  • Farshad Kakavand 3

1 Faculty of Industrial and Mechanical Engineering,Qazvin Branch,Islamic Azad University,Qazvin,Iran.

2 Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran.

3 Department of Mechanical Engineering, ,Takestan Branch, Islamic Azad University, Takestan, Iran.

چکیده [English]

Due to wide application of conical sandwich shells in the advanced industries, it is nessesary to investigate the mechanical behavior of theses structures. In this paper, for the first time, by considering the flexibility of the core in the high order sandwich shells theory, the the vibration behavior of the truncated conical sandwich shells which include a porous FG core and two homogeneous face sheets are investigated in various thermal conditions. Temperature dependent materials are used in the core and the facesheets. The power law rule which modified by considering the two types of porosity volume fractions are applied to model the gradually variation of FGMs. By applying Hamilton's energy principle, considering the in-plane stresses in the core and the faces, and nonlinear von-karman strains for both mechanical and thermal stresses, the governing equations of motion are obtained. A Galerkin procedure are used to solve the equations in a simply supported boundary condition. Uniform, linear and nonlinear temperature distributions are used to model the effect of the temperature changing in the sandwich shell. To verify the results of these work, they are compared with FEM results obtained by Abaqus software and for special cases with the results in literature. Eigen frequencies variations are surveyed versus the temperature changing, geometrical effects, porosities, and some others in the numerical examples.

کلیدواژه‌ها [English]

  • Conical sandwich shell
  • Functionally Graded Core
  • High Order Theory
  • Porosity
  • Temperature distribution
[1]Vinson, J.R, “Sandwich structures,” Applied Mechanics Reviews, Vol. 54, No. 3, pp. 201-214, 2001.‏
[2]Etemadi, E., Khatibi, A.A., Takaffoli, M., “3D finite element simulation of sandwich panels with a functionally graded core subjected to low velocity impact,” Composite Structures, Vol. 89, No. 1, pp. 28-34, 2009.‏
[3]Vafakhah, Z., Neya, B.N., “An exact three dimensional solution for bending of thick rectangular FGM plate,” Composites Part B: Engineering, Vol. 156, pp. 72-87, 2019.‏
[4]Hadi, A., Shakhesi, S., Ovesy, H.R., Fazilati, J., “Thermal Stability of FGM Cylindrical Shells on Pasternak Elastic Foundation under Axial Load” In Persian, Journal of Science and Technology of Composite, Vol. 5, No. 2, pp. 200-207, 2018.
[5]Ghaheri, A. and Nosier, A., “Nonlinear forced vibrations of thin circular functionally graded plates,” In Persian, Journal of Science and Technology of Composite, Vol. 1, No. 2, pp. 1-10, 2015.
[6]Alibeigloo, A., “Three dimensional coupled thermoelasticity solution of sandwich plate with FGM core under thermal shock,” Composite Structures, Vol. 177, pp. 96-103, 2017.‏
[7]Ghasemi, A.R., Meskini, M.,. “Investigations on dynamic analysis and free vibration of FGMs rotating circular cylindrical shells,” SN Applied Sciences, Vol. 1, No. 4, pp. 301, 2019.
[8]Ebrahimi, F., Jafari, A., “A fourvariable refined shear deformation beam theory for thermomechanical vibration analysis of temperature dependent FGM beams with porosities,”  Mechanics of Advanced Materials and Structures, Vol. 25, No. 3, pp. 212-224, 2018.
[9]Cong, P.H., Chien, T.M., Khoa, N.D., Duc, N.D., “Nonlinear thermomechanical buckling and post-buckling response of porous FGM plates using Reddy's HSDT,” Aerospace Science and Technology, Vol. 77, pp. 419-428, 2018.
[10]Barati, M.R., Shahverdi, H., “Aero-hygro-thermal stability analysis of higher-order refined supersonic FGM panels with even and uneven porosity distributions,” Journal of Fluids and Structures, Vol. 73, pp. 125-136, 2017.‏
[11]Jinseok, K.,  Kamil, Ż.K, Reddy, J.N., “Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates,” Composite Structures, Vol. 209, pp. 879-888,‏ 2019.
[12]Jafari, A., Yousefzadeh, S., Mohammadzadeh, A., “Hydroelastic vibration analysis of functionally graded circular plate in contact with bounded fluid by Ritz method,” In Persian, Journal of Science and Technology of Composite, Vol. 5, No. 4, pp. 529-538, 2018.
[13]Shaban, M.,  Alibeigloo, A., “Three-dimensional elasticity solution for sandwich panels with corrugated cores by using energy method,” Thin-Walled Structures, Vol. 119, pp. 404-411, 2017.
[14]yousefzadeh, S., Najafi, M., Akbari, A., “Dynamic response of FG rectangular plate in contact with stationary fluid under moving load,” In Persian, Journal of Science and Technology of Composite, Vol. 6, No. 2, pp. 213-224, 2019.
[15]Mohandes, M., Ghasemi, A.R “A new approach to reinforce the fiber of nanocomposite reinforced by CNTs to analyze free vibration of hybrid laminated cylindrical shell using beam modal function method,”  European Journal of Mechanics-A/Solids, Vol. 73, pp. 224-234, 2019. ‏
[16]Ghasemi, A.R., Mohandes, M., Dimitri, R., Tornabene, F., “Agglomeration effects on the vibrations of CNTs/fiber/polymer /metal hybrid laminates cylindrical shell,” Composites Part B: Engineering.‏ Vol. 167, pp.700-716, 2019.
[17]Mohandes, M., Ghasemi, A.R., Irani, R.M., Torabi, K., Taheri, B.F. “Development of beam modal function for free vibration analysis of FML circular cylindrical shells,” Journal of Vibration and Control, Vol. 24, No. 14, pp.3026-3035, 2018.‏
[18]Malekzadeh, K., Rezaei, M.H, “Free Vibration and Static Bending Analysis of Curved Sandwich Panel with Magneto-Rheological Fluid Layer in Sheets using Improved High Order Sandwich Panel Theory,” In Persian, Journal of Science and Technology of Composite, Vol. 1, No. 2, pp. 49-62, 2015.
[19]MalekZadeh, K., Payganeh, G., Kardan, M., “Dynamic Response of Sandwich Panels with Flexible Cores and Elastic Foundation Subjected to Low-Velocity Impact,” In Persian, Amirkabir Journal of Mechanical Engineering, Vol. 45, No. 2, pp. 27-42, 2013.
[20]Khorshidi, K., Fallah, A., Siahpush, A., “Free vibrations analaysis of functionally graded composite rectangular na-noplate based on nonlocal exponential shear deformation theory in thermal environment,” In Persian, Journal of Science and Technology of Composite, Vol. 4, No.1, pp. 109-120, 2017.
[21]Moosaie, A., Panahi, K.H., "Exact solution of steady nonlinear heat conduction in exponentially graded cylindrical and spherical shells with temperature-dependent properties." In Persian, Journal of Science and Technology of Composite, Vol. 3, No.3, pp. 301-306, 2016.
[22]Dehkordi, M.B., Khalili, S.M.R., “Frequency analysis of sandwich plate with active SMA hybrid composite face sheets and temperature dependent flexible core,” Composite Structures, Vol. 1, pp. 408-4019, 2015.
[23]Mohammadimehr, M.,  Mostafavifar, M., “Free vibration analysis of sandwich plate with a transversely flexible core and FG-CNTs reinforced nanocomposite face sheets subjected to magnetic field and temperature-dependent material properties using SGT,” Composites Part B: Engineering, Vol. 94, pp. 253-270, 2016.
[24]Chen, Y.,  Jin, G.,  Zhang, C.,  Ye, T.,  Xue, Y., “Thermal vibration of FGM beams with general boundary conditions using a higher-order shear deformation theory,” Composites Part B: Engineering, Vol. 153, pp. 376-386, 2018.
[25]Fazzolari, F.,  Fiorenzo, A., “Natural frequencies and critical temperatures of functionally graded sandwich plates subjected to uniform and non-uniform temperature distributions,” Composite Structures, Vol. 121, pp. 197-210, 2015.
[26]Talebitooti, M., “Thermal effect on free vibration of ring-stiffened rotating functionally graded conical shell with clamped ends,” Mechanics of Advanced Materials and Structures, Vol. 25, No. 2, pp. 155-165, 2018.
[27]Malekzadeh, P., Fiouzb, A.R., Sobhrouyan, M., “Three-dimensional free vibration of functionally graded truncated conical shells subjected to thermal environment”, International Journal of Pressure Vessels and Piping, Vol. 89, oo. 210-221, 2012.
[28]Sofiyev, A.H., Kuruoglu, N., “On a problem of the vibration of functionally graded conical shells with mixed boundary conditions”, Composites Part B: Engineering, Vol. 70, pp. 122-130, 2015.
[29]Zarei, M., Rahimi, G.H., “Free vibration analysis of grid stiffened composite conical shells,” In Persian, Journal of Science and Technology of Composite, Vol. 4, No, 1, pp. 1-8, 2017.
[30]Aghaei, N., TalebiTooti, M., “Free vibration analysis of nanotube-reinforced composite conical shell in high temperature environment,” In Persian, Amirkabir Journal of Mechanical Engineering, 2018.
[31]Sofiyev, A.H., “Application of the first order shear deformation theory to the solution of free vibration problem for laminated conical shells,” Composite Structures, Vol. 188, pp. 340-346, 2018.
[32]Lam, K.Y.,  Li, H., Ng, T.Y., Chua, C.F. “Generalized differential quadrature method for the free vibration of truncated conical panels,” Journal of Sound and Vibration, Vol. 251, No. 2, pp. 329-348, 2002.
[33]Sheng, G.G., Wang, X., “Nonlinear response of fluid-conveying functionally graded cylindrical shells subjected to mechanical and thermal loading conditions,” Composite Structures, Vol. 168, pp. 675-684, 2017. ‏
[34]Khalili, S.M., Mohammadi, Y., “Free vibration analysis of sandwich plates with functionally graded face sheets and temperature dependent material properties: A new approach,” European Journal of Mechanics-A/Solids, Vol. 35, pp. 61-74, 2012.
[35]Shen, H.S., “Functionally Graded Materials Nonlinear Analysis of Plates and Shells,” New York: CRC Press, pp. 1-100, 2009.
[36]Boutahar, L., Benamar, R., “A homogenization procedure for geometrically non-linear free vibration analysis of functionally graded annular plates with porosities, resting on elastic foundations,” Ain Shams Engineering Journal, Vol. 7, No. 1, pp. 313-33, 2016.
[37]Talebitooti, M., “Thermal effect on free vibration of ring-stiffened rotating functionally graded conical shell with clamped ends,” Mechanics of Advanced Materials and Structures, Vol. 25, No. 2, pp. 155-65, 2018.
[38]Li, FM., Kishimoto, K.,  Huang, W.H., “The calculations of natural frequencies and forced vibration responses of conical shell using the Rayleigh–Ritz method,” Mechanics Research Communications, Vol. 36, No. 5, pp. 595-602, 2009.
[39]Lam, K.Y., Hua, L., “Influence of boundary conditions on the frequency characteristics of a rotating truncated circular conical shell,” Journal of Sound and Vibration, Vol. 223, No. 2, pp. 171-195, 1999.‏