Free Vibration Analysis of Composite Grid Stiffened Cylindrical Shells Using A Generalized Higher Order Theory

Document Type : Research Paper


University Complex of Materials and Manufacturing Technology, Malek Ashtar University of Technology, Tehran, Iran



The present study analyzes the free vibration of multi-layered composite cylindrical shells and perforated composite cylindrical shells via a modified version of Reddy’s third-order shear deformation theory (TSDT) under simple support conditions. An advantage of the proposed theory over other high-order theories is the inclusion of the shell section trapezoidal form coefficient term in the displacement field and strain equations to improve the accuracy of results. The non-uniform stiffness and mass distributions across reinforcement ribs and the empty or filled bays between the ribs in perforated shells were addressed via a proper distribution function. For integrated perforated cylindrical shells, the results were validated by comparison to other studies and the numerical results obtained via ABAQUS. The proposed theory was in good consistency with numerical results and the results of previous studies. It should be noted that the proposed theory was more accurate than TSDT. 


[1] Hideo T., 1991, Static analyses of elastic plates with voids, International Journal of Solids and Structures 28: 179-196.
[2] Hideo T., 1991, Dynamic analyses of elastic plates with voids, International Journal of Solids and Structures 28: 879-895.
[3] De-Chih L., Chih-Shiung W., Lin-Tsang L., 2011, The natural frequency of elastic plates with void by ritz-method, Studies in Mathematical Sciences 2: 36-50.
[4] Huybrechts S., Tsai S.W., 1996, Analysis and behavior of grid structures, Composites Science and Technology 56: 1001-1015.
[5] Huybrechts S.M., 2002, Manufacturing theory for advanced grid stiffened structures, Composites Part A: Applied Science and Manufacturing 33: 155-161.
[6] Han D., Tsai S.W., 2003, Interlocked composite grids design and manufacturing, Journal of Composite Materials 37: 287-316.
[7] Jiang J., Olson M., 1994, Vibration analysis of orthogonally stiffened cylindrical shells using super finite elements, Journal of Sound and Vibration 173: 73-83.
[8] Hemmatnezhad M., Rahimi G., Ansari R., 2014, On the free vibrations of grid-stiffened composite cylindrical shells, Acta Mechanica 225: 609-623.
[9] Luan Y., Ohlrich M., Jacobsen F., 2011, Improvements of the smearing technique for cross-stiffened thin rectangular plates, Journal of Sound and Vibration 330: 4274-4286.
[10] Edalata P., Khedmati M.R., Soares C.G., 2013, Free vibration and dynamic response analysis of stiffened parabolic shells using equivalent orthotropic shell parameters, Latin American Journal of Solids and Structures 10: 747-766.
[11] Eskandari Jam J., Nouradbadi M., Taghavian S., 2011, Designing a non-isotropic perforated conical structure, International Conference of Composites, Iran University of Science and Technology.
[12] Nourabadi M., Taghavian S., 2010, Designing a non-isotropic conical perforated structure, The 2nd International Conference of Composites, Iran University of Science and Technology.
[13] Sayyad K., 2011, Analyzing the inter-layer shear effect on the local buckling of a perforated polymer composite cylinder under compressive axia loading, The 10th Conference of Iran Aerospace Association.
[14] Liew K., Lim C., 1996, A higher-order theory for vibration of doubly curved shallow shells, Journal of Applied Mechanics 63: 587-593.
[15] Garg A.K., Khare R.K., Kant T., 2006, Higher-order closed-form solutions for free vibration of laminated composite and sandwich shells, Journal of Sandwich Structures and Materials 8: 205-235.
[16] Reddy J.N.,2004, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press.
[17] Reddy J., Liu C., 1985, A higher-order shear deformation theory of laminated elastic shells, International Journal of Engineering Science 23: 319-330.
[18] Bert C.W., 1967, Structural theory for laminated anisotropic elastic shells, Journal of Composite Materials 1: 414-423.
[19] Leissa A., Chang J.-D., 1996, Elastic deformation of thick, laminated composite shells, Composite Structures 35: 153-170.
[20] Davar A., 2010, Analyzing FML and FGM Cylindrical Shells Under Transverse Impact Loading, Doctorial Dissertation, K. N. Toosi University of Technology.
[21] Leissa A.W., 1973, Vibration of Shells, Nasa SP-288, US Governmet Printing Office, Washington D.C., Reprinted by the Acoustical Society of America.
[22] Amabili M., 2003, A comparison of shell theories for large-amplitude vibrations of circular cylindrical shells: Lagrangian approach, Sound and Vibration 264: 1091-1125.
[23] Kahandani R., 2014, Analyzing the Free Vibration of Perforated Composite Shells with Two Curvatures by an Extended High-Order Theory, Master’s thesis, Malek-Ashtar University of Technology.
[24] Ye J., Soldatos K., 1994, Three-dimensional vibration of laminated cylinders and cylindrical panels with symmetric or antisymmetric cross-ply lay-up, Composites Engineering 4: 429-444.
[25] Qatu M.S.,2004, Vibration of Laminated Shells and Plates, Elsevier.
[26] Reddy J.N., 2002, Energy Principles and Variational Methods in Applied Mechanics, John Wiley & Sons.
[27] Li G., Cheng J., 2007, A generalized analytical modeling of grid stiffened composite structures, Journal of Composite Materials 41: 2939-2969.
[28] Meirovitch L., 2001, Fundamentals of Vibrations, McGraw-Hill.
[29] Armenàkas A.E., Gazis D.C., Herrmann G., 1969, Free Vibrations of Circular Cylindrical Shells, DTIC Document.
[30] Hasheminejad S.M., Mirzaei Y., 2009, Free vibration analysis of an eccentric hollow cylinder using exact 3D elsticity theory, Journal of Sound and Vibration 326: 687-702.
[31] Loy C.T., Lam K.Y., 1999, Vibration of thick cylindrical shells on the basis of three dimensional theory of elasticity, Journal of Sound and Vibration 37: 226-719.
[32] Xie X., Jin G., Yan Y., Shi S.X., Liu Z., 2014, Free vibration analysis of composite laminated cylinderical shells using the Haar wavelet method, Composite Structures 109: 169-177.
[33] Li X., Zhang W., Yang X-D., Song L.-K., 2019, A unified approach of free vibration analysis for stiffened cylindrical shell with general boundary conditions, Mathematical Problems in Engineering 2019: 1-14.

Articles in Press, Corrected Proof
Available Online from 28 April 2021