نوع مقاله : مقاله پژوهشی

نویسنده

استادیار، مهندسی مکانیک، مجتمع آموزش عالی لارستان، لار.

چکیده

در این پژوهش ارتعاشات پوسته استوانه‌ای کامپوزیتی در حضور ترک طولی و محیطی نفوذ کامل مطالعه شده است. معادلات حاکم بر پایه تئوری تغییرشکل برشی مرتبه اول نوشته شده و با انتخاب مقادیر مناسب برای پارامترها می‌تواند به هر یک از تئوری‌های دانل، لاو و یا ساندرز تبدیل شود. برای حل، از روش مربعات تفاضلی تعمیم‌یافته چند دامنه‌ای استفاده شده است. در این روش، فضای حل به چندین زیردامنه تقسیم شده و گسسته‌سازی معادلات حاکمه و شرایط مرزی لبه‌های پوسته و شرایط سازگاری در مرز مشترک زیردامنه‌ها در هر دو راستای طولی و محیطی به کمک روش مربعات تفاضلی تعمیم‌یافته انجام شده است. در نهایت، با مونتاژ معادلات حاصله، یک دستگاه معادلات جبری تشکیل شده و با استفاده از حل مقدار ویژه فرکانس طبیعی پوسته تعیین شده است. این روند در محیط متلب کدنویسی شده است. پس از مقایسه نتایج این روش با نتایج ارائه شده در مقالات موجود و نیز نتایج نرم‌افزار آباکوس و اطمینان از صحت و دقت آن، از این روش برای بررسی اثر پارامترهای مختلف بر رفتار ارتعاشی پوسته‌های استوانه‌ای کامپوزیتی دارای تر‌ک استفاده شده است. از نتایج به دست آمده می‌توان برای صحت‌سنجی مطالعات آتی استفاده نمود.

کلیدواژه‌ها

عنوان مقاله [English]

Using a Multi Domain Generalized Differential Quadrature Method to Study the Effect of Crack on the Vibrational Behavior of Composite Cylindrical Shell

نویسنده [English]

  • Ali Talezadehlari

Department of Mechanical Engineering, University of Larestan, Lar, Iran

چکیده [English]

In this study, the vibration of a composite cylindrical shell in the presence of a longitudinal and circumferential crack was investigated. The governing equations were derived based on the first-order shear deformation theory and could be converted to Donnell’s, Love’s, and Sanders’ theories by selecting proper parameters. A multi-domain generalized differential quadrature method was used to solve the problem. In this technique, a physical domain was decomposed into several elements. Then, a generalized differential quadrature method was employed to discretize the governing equations, boundary conditions at shell edges, and the compatibility conditions at the interface boundaries of adjacent elements in both longitudinal and circumferential directions. Assembling these discretized equations led to a system of algebraic equations, which could be solved through an eigenvalue solution to calculate the natural frequency of the shell. This procedure was coded in Matlab environment. Numerical results obtained by the presented method were compared with Abaqus results and those available in the literature. After verifying the accuracy and precision of the proposed method, it was employed to study the effect of different parameters on the vibrational behavior of cracked composite shells. The obtained results can be used as a benchmark for further studies.

کلیدواژه‌ها [English]

  • Vibration
  • Composite Shell
  • Through-the-Thickness Crack
  • First-order Shear Deformation Theory (FSDT)
  • Multi Domain Generalized Differential Quadrature (GDQ)
[1]  Vinson, J. R., “The Behavior of Shells Composed of Isotropic and Composite Materials,”  1st ed., Springer Science & Business Media, pp. 221-22, 1993.
[2]  Haftchenari, H., Darvizeh, M., Darvizeh, A., Ansari, R. and  Sharma, C., “Dynamic Analysis of Composite Cylindrical Shells Using Differential Quadrature Method (Dqm),” Composite Structures, Vol. 78, No. 2, pp. 292-298, 2007.
[3]  Amabili, M. and  Reddy, J., “A New Non-Linear Higher-Order Shear Deformation Theory for Large-Amplitude Vibrations of Laminated Doubly Curved Shells,” International Journal of Non-Linear Mechanics, Vol. 45, No. 4, pp. 409-418, 2010.
[4] Qu, Y., Hua, H. and  Meng, G., “A Domain Decomposition Approach for Vibration Analysis of Isotropic and Composite Cylindrical Shells with Arbitrary Boundaries,” Composite Structures, Vol. 95, pp. 307-321, 2013.
[5] Talezadehlari, A. Ghorbani Menghari, H. and Rahimi, Gh., “Experimental and Numerical Investigation of the Effective Parameters on Vibrational Behavior of Unstiffened and Stiffened Composite Cylindrical Shells,” In Persian, Journal of Mechanical Engineering of Tabriz University, Vol. 50, No. 3, pp. 135-144, 2020.
[6]  Alijani, F. and  Amabili, M., “Non-Linear Vibrations of Shells: A Literature Review from 2003 to 2013,” International Journal of Non-Linear Mechanics, Vol. 58, pp. 233-257, 2014.
[7]  Wu, C.-P. and  Liu, Y.-C., “A Review of Semi-Analytical Numerical Methods for Laminated Composite and Multilayered Functionally Graded Elastic/Piezoelectric Plates and Shells,” Composite Structures, Vol. 147, pp. 1-15, 2016.
[8]  Nikpour, K., “Diagnosis of Axisymmetric Cracks in Orthotropic Cylindrical Shells by Vibration Measurement,” Composites science and technology, Vol. 39, No. 1, pp. 45-61, 1990.
[9] Tavaf, V. and Moradi, Sh. “Vibration Analysis of Cracked Cylindrical Shell with Finite Length,” In Persian, 20th Annual International Conference of the Iranian Association of Mechanical Engineers, Shiraz, Iran, 1391.
[10] Tavaf, V. Moradi, Sh. and Jamshidi Moghadam, P. “Vibration Analysis of Cracked Cylindrical Shell with Global Cracking,” In Persian, 2nd International Conference of Accustic and vibration, Tehran, Iran, 1391.
[11] Moradi, S. and  Tavaf, V., “Crack Detection in Circular Cylindrical Shells Using Differential Quadrature Method,” International Journal of Pressure Vessels and Piping, Vol. 111, pp. 209-216, 2013.
[12] Yin, T. and  Lam, H.-F., “Dynamic Analysis of Finite-Length Circular Cylindrical Shells with a Circumferential Surface Crack,” Journal of Engineering Mechanics, Vol. 139, No. 10, pp. 1419-1434, 2013.
[13] Sarker, L., Xiang, Y., Zhu, X. and  Zhang, Y., “Damage Detection of Circular Cylindrical Shells by Ritz Method and Wavelet Analysis,” Electronic Journal of Structural Engineering, Vol. 14, No. 1, pp. 62-74, 2015.
[14] Moazzez, K., Googarchin, H. S. and  Sharifi, S., “Natural Frequency Analysis of a Cylindrical Shell Containing a Variably Oriented Surface Crack Utilizing Line-Spring Model,” Thin-Walled Structures, Vol. 125, pp. 63-75, 2018.
[15] Googarchin, H. S. and  Moazzez, K., “Analytical Solution for Free Vibration of Cracked Orthotropic Cylindrical Shells,” International Journal of Mechanical Sciences, Vol. 153, pp. 254-270, 2019.
[16] Javidruzi, M., Vafai, A., Chen, J. and  Chilton, J., “Vibration, Buckling and Dynamic Stability of Cracked Cylindrical Shells,” Thin-walled structures, Vol. 42, No. 1, pp. 79-99, 2004.
[17] Dehghani Oskouei, S., Esmaeilpour Estekanchi, H. and Vafaei, A., “Free vibration of Cracked Cylindrical Shells,” In Persian, Sharif: Civil Engineering, Vol. 40, No. 1, pp. 27-33, 2008.
[18] Nasirmanesh, A. and  Mohammadi, S., “An Extended Finite Element Framework for Vibration Analysis of Cracked Fgm Shells,” Composite Structures, Vol. 180, pp. 298-315, 2017.
[19] Bellman, R. and  Casti, J., “Differential Quadrature and Long-Term Integration,” Journal of Mathematical Analysis and Applications, Vol. 34, No. 2, pp. 235-238, 1971.
[20] Bellman, R., Kashef, B. and  Casti, J., “Differential Quadrature: A Technique for the Rapid Solution of Nonlinear Partial Differential Equations,” Journal of computational physics, Vol. 10, No. 1, pp. 40-52, 1972.
[21] Bert, C. W., Jang, S. K. and  Striz, A. G., “Two New Approximate Methods for Analyzing Free Vibration of Structural Components,” AIAA journal, Vol. 26, No. 5, pp. 612-618, 1988.
[22] Shu, C., “Generalized Differential-Integral Quadrature and Application to the Simulation of Incompressible Viscous Flows Including Parallel Computation,” Ph.D. Thesis, University of Glasgow, United Kingdom, 1991.
[23] Zhang, L., Xiang, Y. and  Wei, G., “Local Adaptive Differential Quadrature for Free Vibration Analysis of Cylindrical Shells with Various Boundary Conditions,” International Journal of Mechanical Sciences, Vol. 48, No. 10, pp. 1126-1138, 2006.
[24] Redekop, D., “Three-Dimensional Free Vibration Analysis of Inhomogeneous Thick Orthotropic Shells of Revolution Using Differential Quadrature,” Journal of sound and vibration, Vol. 291, No. 3-5, pp. 1029-1040, 2006.
[25] Hosseini-Hashemi, S. and  Khorami, K., “Analysis of Free Vibrations of Moderately Thick Cylindrical Shells Made of Functionally Graded Materials Using Differential Quadrature Method, ” In Persian, Modares Mechanical Engineering, Vol. 11, No. 2, pp. 93-106, 2011.
[26] Golchi, M. and  Talebitooti, M., “Vibration Analysis of the Composite Sandwich Conical Shell with Various Boundary Conditions Using Finite Element and Differential Quadrature Methods (DQ), ” In Persian, Journal of Mechanical Engineering of Tabriz University, Vol. 48, No. 3, pp. 251-260, 2018.
[27] Sobhani, E., Masoodi, A. R. and  Ahmadi-Pari, A. R., “Vibration of FG-CNT and FG-GNP Sandwich Composite Coupled Conical-Cylindrical-Conical Shell,” Composite Structures, Vol. 273, pp. 114281, 2021.
[28] Malekzadeh, P., Farid, M. and  Zahedinejad, P., “A Three-Dimensional Layerwise-Differential Quadrature Free Vibration Analysis of Laminated Cylindrical Shells,” International Journal of Pressure Vessels and Piping, Vol. 85, No. 7, pp. 450-458, 2008.
[29] Daneshjou, K. and  Talebitooti, M., “Free Vibration Analysis of Rotating Stiffened Composite Cylindrical Shells by Using the Layerwise-Differential Quadrature (LW-DQ) Method,” Mechanics of Composite Materials, Vol. 50, No. 1, pp. 21-38, 2014.
[30] Alibeigloo, A., “Static and Vibration Analysis of Axi-Symmetric Angle-Ply Laminated Cylindrical Shell Using State Space Differential Quadrature Method,” International Journal of Pressure Vessels and Piping, Vol. 86, No. 11, pp. 738-747, 2009.
[31] Alibeigloo, A. and  Kani, A., “3D Free Vibration Analysis of Laminated Cylindrical Shell Integrated Piezoelectric Layers Using the Differential Quadrature Method,” Applied Mathematical Modelling, Vol. 34, No. 12, pp. 4123-4137, 2010.
[32] Tong, B., Li, Y., Zhu, X. and  Zhang, Y., “Three-Dimensional Vibration Analysis of Arbitrary Angle-Ply Laminated Cylindrical Shells Using Differential Quadrature Method,” Applied Acoustics, Vol. 146, pp. 390-397, 2019.
[33] Selahi, E., Setoodeh, A. R. and  Tahani, M., “Transient Analysis and Free Vibration of Functionally Graded Truncated Conical Shells Subjected to Moving Pressure, ” In Persian, Amirkabir Journal of Mechanical Engineering, Vol. 53, No. 2, pp. 897-912, 2021.
[34]Talezadehlari, A. and Rahimi, Gh., “Buckling Analysis of Perforated Composite Cylindrical Shell Using Generalized Differential Quadrature Method (GDQM),” In persian, Modares Mechanical Engineering, Vol. 17, No. 11, pp. 385-396, 2018.
[35] Talezadehlari, A., “Free Vibration Analysis of Perforated Composite Cylindrical Shell Using Generalized Differential Quadrature Method,” In Persian, Journal of Science and Technology of Composites, Vol. 7, No. 3, pp. 1120-1132, 2020.
[36] Talezadehlari, A., “Free Vibration Analysis of Perforated Composite Cylindrical Shell and Panel Using Multi-Domain Generalized Differential Quadrature (Gdq) Method,” Composite Structures, Vol. 287, pp. 115337, 2022.
[37] Quan, J. and  Chang, C., “New Insights in Solving Distributed System Equations by the Quadrature Method—I. Analysis,” Computers & Chemical Engineering, Vol. 13, No. 7, pp. 779-788, 1989.
[38] Quan, J. and  Chang, C.-T., “New Insights in Solving Distributed System Equations by the Quadrature Method—Ii. Numerical Experiments,” Computers & Chemical Engineering, Vol. 13, No. 9, pp. 1017-1024, 1989.
[39] Shu, C., Khoo, B. and  Yeo, K., “Numerical Solutions of Incompressible Navier-Stokes Equations by Generalized Differential Quadrature,” Finite elements in analysis and design, Vol. 18, No. 1-3, pp. 83-97, 1994.
[40] Sahu, S. and  Datta, P., “Research Advances in the Dynamic Stability Behavior of Plates and Shells: 1987–2005—Part I: Conservative Systems,” Applied mechanics reviews, Vol. 60, No. 2, pp. 65-75, 2007.
[41] Reddy, J. N., “Mechanics of Laminated Composite Plates and Shells: Theory and Analysis,” 2nd ed., CRC press, pp. 478-480, 2003.
[42] Hahn, H. T. and  Tsai, S. W., “Introduction to Composite Materials,” 1st ed., CRC Press, p. 19, 1980.