Frequencies Values of Orthotropic Composite Circular and Annular Plates

Yıl 2017, Cilt: 9 Sayı: 2, 55 - 65, 30.04.2017

Kadir Mercan Bekir Akgöz Çiğdem Demir Ömer Civalek

https://doi.org/10.24107/ijeas.309060

Cited By: 5

Öz

Free vibration analysis of orthotropic
composite annular plate is investigated. First-order shear deformation theory
(FSDT) is used for equation of motion. Two different kernels such as
Regularized Shannon delta (RSD) kernel and Lagrange delta sequence (LDS) kernel are used. The method of
discrete singular convolution (DSC) is used for numerical simulation of
governing equations to obtain the frequency values. It is shown that the
convergence and accuracy of the DSC method is very good for vibration problem
of orthotropic annular plate. 

Anahtar Kelimeler

Frequency, annular plate, discrete singular convolution, composite laminated

Kaynakça

• Leissa AW., Vibration of plates, Acoustical Society of America, USA,1993.
• Reddy JN. Mechanics of laminated composite plates and shells: theory and analysis. (2nd ed.) New York: CRC Press, 2003.
• Qatu M. Vibration of Laminated Shells and Plates, Academic Press, U.K., 2004.
• Soedel W. Vibrations of shells and plates, Third Edition, CRC Press, 2004.
• Hui-Shen Shen, Functionally Graded Materials: Nonlinear Analysis of Plates and Shells, CRC Press, USA,2009.
• Elishakoff I., Demetris Pentaras D, Gentilini C, Mechanics of Functionally Graded Material Structures, World Scientific, USA, 2016.
• Ugural A. C. Stresses in Beams, Plates, and Shells, Third Edition, CRC Press, 2010.
• Ye j. Laminated Composite Plates and Shells: 3D Modelling, Springer, 2003.
• Jin G, Ye T, Su Z. Structural Vibration: A Uniform Accurate Solution for Laminated Beams, Plates and shells with general boundary conditions, Springer, 2015.
• Civalek O. Finite Element analyses of plates and shells, Elazığ: Fırat University, (in Turkish), 1998.
• Nie GJ and Zhong Z. Semi-analytical solution for three-dimensional vibration of functionally graded circular plates. Comput Methods Appl Mech Eng 2007; 196: 4901-4910.
• Nie GJ and Zhong Z. Dynamic analysis of multidirectional functionally graded annular plates. Appl Math Model 2010; 34: 608-616.
• Civalek O, Gürses M. Free vibration analysis of rotating cylindrical shells using discrete singular convolution technique. Int J Pres Ves Pip 2009; 86(10):677-683.
• Zhou D, Lo SH and Cheung YK. 3-D vibration analysis of annular sector plates using the Chebyshev-Ritz method. J Sound Vib 2009;320: 421–437.
• Civalek O. Vibration analysis of laminated composite conical shells by the method of discrete singular convolution based on the shear deformation theory. Compos Part B Eng 2013;45(1):1001-1009.
• Civalek O. Free vibration analysis of composite conical shells using the discrete singular convolution algorithm. Steel Compos Struct 2006; 6(4):353-366.
• Civalek O. The determination of frequencies of laminated conical shells via the discrete singular convolution method. J Mech Mater Struct 2006;1(1):163-182.
• Zhao X, Liew KM, Free vibration analysis of functionally graded conical shell panels by a meshless method, Compos Struct 2011; 93:649-664.
• Liew KM, Feng ZC. Vibration characteristics of conical shell panels with three-dimensional flexibility. J Appl Mech 2000; 67(2):314–320.
• Liew KM, Ng TY, Zhao X. Free vibration analysis of conical shells via the element-free kp-Ritz method. J Sound Vib 2005;281:627-645.
• Demir Ç, Mercan K, Civalek O. Determination of critical buckling loads of isotropic, FGM and laminated truncated conical panel. Compos Part B: Eng 2016; 94:1-10.
• Tornabene F, Fantuzzi N, Viola E, Ferreira AJM. Radial basis function method applied to doubly-curved laminated composite shells and panels with a General Higher-order Equivalent Single Layer formulation. Compos Part B: Eng 2013;55:642–659.
• Liu B, Ferreira AJM, Xing YP, Neves AMA. Analysis of functionally graded sandwich and laminated shells using a layerwise theory and a differential quadrature finite element method. Compos Struct 2016;136:546-553.
• Ferreira AJM, Jorge RMN, Roque CMC. Free vibration analysis of symmetric laminated composite plates by FSDT and radial basis functions. Comput Method Appl Mech Eng 2005;194:4265–4278.
• Ferreira AJM, Roque CMC, Neves AMA, Jorge RMN, Soares CMM, Reddy JN. Buckling analysis of isotropic and laminated plates by radial basis functions according to a higher-order shear deformation theory. Thin-Wall Struct 2011;49(7):804-811.
• Fantuzzi N, Tornabene F, Bacciocchi M, Dimitri R. Free vibration analysis of arbitrarily shaped Functionally Graded Carbon Nanotube-reinforced plates, Compos Part B: Eng doi.org/10.1016/j.compositesb.2016.09.021.
• Jin G, Ma X, Shi S, Ye T, Liu Z. A modified Fourier series solution for vibration analysis of truncated conical shells with general boundary conditions. Appl Acoustics 2014; 85: 82-96.
• Xie X, Jin G, Ye T, Liu Z. Free vibration analysis of functionally graded conical shells and annular plates using the Haar wavelet method. Appl Acoustics 2014; 85: 130-142.
• Su Z, Jin G, Shi S, Ye T, Jia Z. A unified solution for vibration analysis of functionally graded cylindrical, conical shells and annular plates with general boundary conditions. Int J Mech Sci 2014; 80: 62-80.
• Jooybar N, Malekzadeh P, Fious A, Vaghefi M. Thermal effect on free vibration of functionally graded truncated conical shell panels. Thin Wall Struct 2016; 103:45-61.
• Malekzadeh P, Heydarpour Y. Free vibration analysis of rotating functionally graded cylindrical shells in thermal environment. Compos Struct 2012;94:2971–81.
• Su Z, Jin G, Ye T. Three-dimensional vibration analysis of thick functionally graded conical, cylindrical shell and annular plate structures with arbitrary elastic restraints. Compos Struct 2014;118:432-447.
• Akgöz, B., Civalek O. Nonlinear vibration analysis of laminated plates resting on nonlinear two-parameters elastic foundations. Steel and Composite Structures 11 (5), 2011,403-421
• Saidi AR, Baferani AH, Jomehzadeh E. Benchmark solution for free vibration of functionally graded moderately thick annular sector plates. Acta Mech 2011;219:309-335.
• Civalek, O., Ersoy, H. Free vibration and bending analysis of circular Mindlin plates using singular convolution method. International Journal for Numerical Methods in Biomedical Engineering, 25(8) 2009,907-922.
• Lin CC, Teng CS. Free vibration of polar orthotropic laminated circular and annular plates. J Sound Vib 1988;209:797-810.
• Civalek, O. Dairesel Plakların Nöro-Fuzzy Tekniği ile Analizi. Dokuz Eylül Üniversitesi Mühendislik Fakültesi 1 (2),1999, 13-31
• Wang Q, Shi D, Liang Q, Ahad F. An improved Fourier series solution for the dynamic analysis of laminated composite annular, circular, and sector plate with general boundary conditions. J Comp Mater 2016;50: 4199-4233.
• Civalek, O., Çatal, HH. Linear static and vibration analysis of circular and annular plates by the harmonic differential quadrature (HDQ) method. Osmangazi Üniversitesi, Mühendislik ve Mimarlık Fakültesi Dergisi 16 (1), 2003, 43-71.
• Jin G, Ma X, Shi S, Ye T, Liu Z. A modified Fourier series solution for vibration analysis of truncated conical shells with general boundary conditions. Appl Acoustics 2014; 85: 82-96.
• Civalek, O., Çatal, HH. Plakların Diferansiyel Quadrature Metodu ile Stabilite ve Titreşim Analizi, Teknik Dergi 14 (1)2003, 2835-2852.
• Su Z, Jin G, Shi S, Ye T, Jia X. A unified solution for vibration analysis Int J Mech Sci 80(2014)62-80.
• Tong L. Free vibration of laminated conical shells including transverse shear deformation. Int J Solids Struct 1994;31:443–456.
• Wei GW. Solving quantum eigenvalue problems by discrete singular convolution. J Phys B 2000; 20: 343-352.
• Wei GW. A new algorithm for solving some mechanical problems. Comput Meth Appl Mech Eng 2001;190:2017-2030.
• Wei GW. Vibration analysis by discrete singular convolution. J Sound Vib 2001;244: 535-553.
• Wei GW. Discrete singular convolution for beam analysis. Eng Struct 2001;23:1045-1053.
• DK Hoffman, GW Wei, DS Zhang, DJ Kouri, Shannon–Gabor wavelet distributed approximating functional, Chemical Physics Letters 287 (1998), 119-124.
• Z Shao, GW Wei, S Zhao, DSC time-domain solution of Maxwell’s equations, Journal of computational physics 189 (2003), 427-453.
• Wei GW. Zhao YB, Xiang Y. A novel approach for the analysis of high-frequency vibrations. J Sound Vib 2002;257: 207-246.
• Wei GW, Zhao YB, Xiang Y. Discrete singular convolution and its application to the analysis of plates with internal supports. Part 1: Theory and algorithm. Int J Num Meth Eng 2002;55:913-946.
• Ng CHW, Zhao YB, Wei GW. Comparison of discrete singular convolution and generalized differential quadrature for the vibration analysis of rectangular plates. Comput Methods Appl Mech Eng 2004;193: 2483-2506.
• Hou Y, Wei GW, Xiang Y. DSC-Ritz method for the free vibration analysis of Mindlin plates. Int J Num Meth Eng 2005;62: 262-288.
• Civalek O. Numerical analysis of free vibrations of laminated composite conical and cylindrical shells: discrete singular convolution (DSC) approach. J Comput Appl Math 2007;205: 251- 271.
• Civalek O, Korkmaz A, Demir Ç. Discrete singular convolution approach for buckling analysis of rectangular Kirchhoff plates subjected to compressive loads on two opposite edges. Adv Eng Softw 2010;41:557-560.
• Civalek O. Analysis of thick rectangular plates with symmetric cross-ply laminates based on first-order shear deformation theory. J Compos Mater 2008;42:2853–2867.
• Xin L, Hu Z. Free vibration of layered magneto-electro-elastic beams by SSDSC approach. Compos Struct 2015;125:96-103.
• Xin L, Hu Z. Free vibration of simply supported and multilayered magnetoelectro-elastic plates. Compos Struct 2015;121:344-350.
• Baltacıoğlu AK, Civalek Ö, Akgöz B, Demir F. Large deflection analysis of laminated composite plates resting on nonlinear elastic foundations by the method of discrete singular convolution. Int J Pres Ves Pip 2011;88:290-300.
• Civalek Ö, Akgöz B. Vibration analysis of micro-scaled sector shaped graphene surrounded by an elastic matrix. Comp Mater Sci 2013;77:295-303.
• Gürses M, Civalek Ö, Korkmaz A, Ersoy H. Free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first-order shear deformation theory. Int J Numer Methods Eng 2009;79:290-313.
• Baltacıoglu AK, Akgöz B, Civalek Ö. Nonlinear static response of laminated composite plates by discrete singular convolution method. Compos Struct 2010;93:153-161.
• Gürses M, Akgöz B, Civalek Ö. Mathematical modeling of vibration problem of nano-sized annular sector plates using the nonlocal continuum theory via eight-node discrete singular convolution transformation. Appl Math Comput 2012;219:3226–3240.
• Mercan K, Civalek Ö. DSC method for buckling analysis of boron nitride nanotube (BNNT) surrounded by an elastic matrix. Compos Struct 2016;143:300-309.
• Xin L, Hu Z. Free vibration analysis of laminated cylindrical panels using discrete singular convolution. Compos Struct 2016;149:362-368.
• Civalek O, Mercan K, Demir C. Vibration analysis of FG cylindrical shells with power-law index using discrete singular convolution technique. Curved and Layer Struct 2016;3: 82-90.
• Civalek O, Ulker M. HDQ-FD integrated methodology for nonlinear static and dynamic response of doubly curved shallow shells. Struct Eng Mech 2005;19: 535-550.
• SY Yang, YC Zhou, GW Wei, Comparison of the discrete singular convolution algorithm and the Fourier pseudospectral method for solving partial differential equations. Computer Physics Communications 143 (2002), 113-135.
• Civalek, O. Nonlinear dynamic response of laminated plates resting on nonlinear elastic foundations by the discrete singular convolution-differential quadrature coupled approaches. Composites Part B: Engineering 50, 171-179.
• Mercan, K., Civalek, Ö., Buckling Analysis of Silicon Carbide Nanotubes (SiCNTs). Int J Eng Appl Sci, 8(2), 101-108, 2016.
• Mercan, K., Demir, Ç., Akgöz, B., Civalek, Ö., Coordinate Transformation for Sector and Annular Sector Shaped Graphene Sheets on Silicone Matrix. Int J Eng Appl Sci, 7(2), 56-73, 2015.
• Wang X, Xu S. Free vibration analysis of beams and rectangular plates with free edges by the discrete singular convolution. J Sound Vib 2010;329:1780-1792.
• Wang X, Wang Y, Xu S. DSC analysis of a simply supported anisotropic rectangular plate. Compos Struct 2012;94:2576-2584.
• Duan G, Wang X, Jin C. Free vibration analysis of circular thin plates with stepped thickness by the DSC element method. Thin Wall Struct 2014;85:25-33.