Journal of Aeronautical Engineering

Journal of Aeronautical Engineering

Vibration analyses of trapezoidal sandwich panel under supersonic flow

Document Type : Original Article

Authors
1 Department of Mechanical Engineering, Khatmol Anbia Air Defense, Tehran, Iran
2 Department of Aerospace Engineering, MalekAshtar University of Technology, Tehran, Iran
3 bahonar university , kerman, iran
Abstract
In this article, vibration and supersonic flutter analyses are studied for trapezoidal sandwich panels. Functionally graded trapezoidal panel as well as reinforced sandwich panel by graphene nano platelets are considered. It is assumed that the graphene platelet (GPL) nanofillers are distributed in the matrix either uniformly or non-uniformly in the direction of thickness. UD, FG-X, FG-V, FG-O and FG-A are the distribution patterns of GPLs. Based on the Kant higher-order theories, the dynamic equations of sandwich panels reinforced with graphene nanoplates  are obtained using extended Hamilton’s principle. Dynamic pressure is estimated according to the quasi-stable theory of supersonic piston. Then, using a transformation of coordinates, the governing equations and boundary conditions are converted from the original coordinates into new computational ones. Finally, the differential squares method (DQM) to obtain the natural frequencies, the shape of the modes, and the critical aerodynamic pressure is used. The effect of different porosity distribution, porosity coefficients, distribution of graphene nanoplates, weight fraction, geometry of graphene nanofillers and geometric dimensions on natural frequencies and system instability behavior are studied.
Keywords

 [1]. Jafari, N., Azhari, M., Stability analysis of arbitrarily shaped moderately thick viscoelastic plates using Laplace–Carson transformation and a simple hp cloud method, Mechanics of Time-Dependent Materials, Vol. 21, No. 3, pp.365-381, 2017.
[2]. Jaberzadeh, E., Azhari, M., Boroomand, B., Thermal buckling of functionally graded skew and trapezoidal plates with different boundary conditions using the element-free Galerkin method, European Journal of Mechanics-A/Solids, Vol. 42, pp.18-26, 2013.
[3]. Najarzadeh, L., Movahedian, B., Azhari, M., Stability analysis of the thin plates with arbitrary shapes subjected to non-uniform stress fields using boundary element and radial integration methods, Engineering Analysis with Boundary Elements, Vol. 87, pp.111-121, 2018.
[4]. Zhao, Z., Feng, C., Wang, Y., Yang, J., Bending and vibration analysis of functionally graded trapezoidal nanocomposite plates reinforced with graphene nanoplatelets (GPLs), Composite Structures. Vol. 180, pp. 799-808, 2017.
[5]. Torabi, K., Afshari, H., Vibration analysis of a cantilevered trapezoidal moderately thick plate with variable thickness, Engineering Solid Mechanics, Vol. 5, No. 1, pp.71-92, 2017.
[6]. Zamani, M., Fallah, A., Aghdam, M., Free vibration analysis of moderately thick trapezoidal symmetrically laminated plates with various combinations of boundary conditions, European Journal of Mechanics-A/Solids, Vol. 36, pp. 204-21, 2012.
[7]. Shokrollahi, S., Shafaghat, S., A global Ritz formulation for the free vibration analysis of hybrid metal-composite thick trapezoidal plates, Scientia Iranica, Vol. 23, No. 1, pp. 249-59, 2016.
[8]. Mania, R., Buckling analysis of trapezoidal composite sandwich plate subjected to in-plane compression, Composite Structures, Vol. 69, No. 4, pp. 482-490, 2005.
[9]. Hildebrand, F., Reissner, E., Thomas, G., Notes on the foundations of the theory of small displacements of orthotropic shells, 1949.
[10]. Kant, T., Owen, D., Zienkiewicz, O., A refined higher-order C plate bending element, Computers & structures, Vol. 15, No. 2, pp.177-183,1982.
[11]. Pandya, B., Kant, T., A consistent refined theory for flexure of a symmetric laminate, Mechanics research communications, Vol. 14, No. 2, pp. 107-113, 1987.
[12]. Pandya, B., Kant, T., Higher-order shear deformable theories for flexure of sandwich plates—finite element evaluations, international Journal of Solids and Structures, Vol. 24, No. 12, pp. 1267-1286, 1988.
[13]. Pandya, B., Kant, T., Flexural analysis of laminated composites using refined higher-order C° plate bending elements, Computer Methods in Applied Mechanics and Engineering, Vol. 66, No. 2, pp. 173-198, 1988.
[14]. Pandya, B., Kant, T., A refined higher-order generally orthotropic C0 plate bending element, Computers & structures,  Vol. 28, No. 2, pp. 119-133, 1988.
[15]. Pandya, B., Kant, T., Finite element analysis of laminated composite plates using a higher-order displacement model, Composites Science and Technology, Vol. 32, No. 2, pp. 137-155, 1988.
[16]. Kant, T., Manjunatha, B., An unsymmetric FRC laminate C° finite element model with 12 degrees of freedom per node, Engineering Computations: Int J for Computer-Aided Engineering, Vol. 5, No. 4, pp. 300-308, 1993.
[17]. Kant, T., Manjunatha, B., On accurate estimation of transverse stresses in multilayer laminates, Computers & structures, Vol. 50, No. 3, pp. 351-365, 1994.
[18]. Manjunatha, B., Kant, T., A comparison of 9 and 16 node quadrilateral elements based on higher-order laminate theories for estimation of transverse stresses, Journal of reinforced plastics and composites, Vol. 11, No. 9, pp. 968-1002, 1992.
[19]. Kant, T., Free vibration of symmetrically laminated plates using a higher‐order theory with finite element technique, International journal for numerical methods in engineering, Vol. 28, No. 8, pp. 1875-89, 1989.
[20]. Kant, T., Gupta, A., A finite element model for a higher-order shear-deformable beam theory, Journal of sound and vibration, Vol. 125, No. 2, pp. 193-202, 1988.
[21]. Kant, T., Marur, S., Rao, G., Analytical solution to the dynamic analysis of laminated beams using higher order refined theory, Composite Structures, Vol. 40, No. 1, pp. 1-9, 1997.
[22]. Marur, S., Kant, T., Free vibration analysis of fiber reinforced composite beams using higher order theories and finite element modelling, Journal of sound and vibration, Vol. 194, No. 3, pp. 337-351, 1996.
[23]. Reddy, J.N., A simple higher-order theory for laminated composite plates, Journal of applied mechanics, Vol. 51, No. 4, pp. 745-75, 1984.
[24]. Reddy, J., Phan, N., Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory, Journal of sound and vibration, Vol. 98, No. 2, pp.157-170, 1985.
[25]. Noor, A.K., Burton, W.S., Assessment of shear deformation theories for multilayered, composite plates, 1989.
[26]. Punera, D., Kant, T., Free vibration of functionally graded open cylindrical shells based on several refined higher order displacement models, Thin-Walled Structures, Vol. 119, pp. 707-726, 2017.
[27]. Punera, D., Kant, T., Elastostatics of laminated and functionally graded sandwich cylindrical shells with two refined higher order models, Composite Structures, Vol. 182, pp. 505-52, 2017.
[28]. پورموید، علیرضا، ملک­زاده فرد، کرامت، شهروی، مرتضی، " تحلـیل فلاتر پانل ساندویچی استوانه­ای تحت اثـر نیروی تعقیب­کننده با استفاده از روش تربیع تفاضلی تعمیم­یافته"، نشریه علمی پژوهشی مهندسی هوانوردی، دوره 20، شماره 1، صفحات 61-49، 1397.
[29]. Kitipornchai, S., Chen, D., Yang, J., Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets, Materials & Design, Vol. 116, pp.656-665, 2017.
[30]. کرانیان، سید­عیسی، اسماعیل­زاده خادم، سیامک، کوکبی،  مهرداد، " تحلیل ارتعاشات اجباری صفحه نانو کامپوزیت ویسکوالاستیک تقویت‌شده با نانو لوله­های کربنی"، سومین همایش ملی تکنولوژ­ی­های نوین در شیمی، پتروشیمی و نانو ایران، دانشگاه شهید بهشتی تهران، 22 و 23 خرداد، 1392.
[31]. Reddy, J.N., Energy and variational methods in applied mechanics: with an introduction to the finite element method, Wiley New York, 1984.
[32]. Afshari, H., Torabi, K., A Parametric Study on Flutter Analysis of Cantilevered Trapezoidal FG Sandwich Plates, AUT Journal of Mechanical Engineering , Vol. 1, pp. 191-210, 2017.
[33]. Romero, G., Alvarez, L., Alanı́s, E., Nallim, L., Grossi, R., Study of a vibrating plate: comparison between experimental (ESPI) and analytical results, Optics and lasers in engineering, Vol. 40, pp. 81-90, 2003.
[34]. Allahverdizadeh, A., Naei, M., Bahrami, M.N., Nonlinear free and forced vibration analysis of thin circular functionally graded plates, Journal of sound and vibration, Vol. 310, No. 4-5, pp. 966-984, 2008.
[35]. Kiani, Y., Mirzaei, M., Enhancement of non-linear thermal stability of temperature dependent laminated beams with graphene reinforcements, Composite Structures, Vol. 186, pp. 114-122, 2018.
[36]. Zhao, X., Lee, Y.Y., Liew, K.M., Free vibration analysis of functionally graded plates using the element-free kp-Ritz method, Journal of Sound and Vibration, Vol. 319, pp. 918–939, 2009. 
Volume 22, Issue 2
December 2020
Pages 1-22

  • Receive Date 27 February 2021