Moradi-Dastjerdi, R., Foroutan, M., Pour Asghar, A. (2009). Free and Forced Vibration Analysis of Functionally Graded Material Cylinders by a Mesh-Free Method. Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 2(1), 69-77.
R. Moradi-Dastjerdi; M. Foroutan; A. A. Pour Asghar. "Free and Forced Vibration Analysis of Functionally Graded Material Cylinders by a Mesh-Free Method". Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 2, 1, 2009, 69-77.
Moradi-Dastjerdi, R., Foroutan, M., Pour Asghar, A. (2009). 'Free and Forced Vibration Analysis of Functionally Graded Material Cylinders by a Mesh-Free Method', Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 2(1), pp. 69-77.
Moradi-Dastjerdi, R., Foroutan, M., Pour Asghar, A. Free and Forced Vibration Analysis of Functionally Graded Material Cylinders by a Mesh-Free Method. Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 2009; 2(1): 69-77.
Free and Forced Vibration Analysis of Functionally Graded Material Cylinders by a Mesh-Free Method
In this paper, free and forced vibration analysis of functionally graded material cylinders was carried out by mesh-free and finite element method. In this analysis, MLS shape functions are used for approximation of displacement field in the weak form of motion equation and essential boundary conditions are imposed by transformation method. Resulted set of differential equations are solved using central difference approximation. Mechanical properties of cylinders were assumed to be variable in the radial direction as a function of volume fraction. Effects of geometrical dimensions of the cylinders, exponent of material volume fraction and the effect of loading type were investigated by the proposed model and FEM. Results obtained by this analysis were compared with the analytical solutions and the results of finite element analysis, and a very good agreement was seen between them.
تحلیل ارتعاشات آزاد و اجباری استوانه‌هایی ازجنس مواد هدفمند به روش بدون المان
Authors [Persian]
رسول مرادی دستجردی, مهرداد فروتن, امین‌الله پوراصغر
Abstract [Persian]
در این تحقیق تحلیل ارتعاشات آزاد و اجباری در استوانه‌هایی از جنس مواد هدفمند به روش‌های بدون المان و المان محدود بررسی شده است. روش بدون المان استفاده شده مبتنی بر فرم ضعیف معادله حرکت است. در این روش بدون المان از توابع شکل حداقل مربعات متحرک برای تقریب میدان تغییر مکان و از روش تبدیل برای اعمال شرایط مرزی اساسی استفاده شده است. برای حل مسئله وابسته به زمان نیز روش تقاضل محدود مرکزی به‌کار رفته است. تغییرات خواص مواد در راستای شعاعی و طبق رابطه کسر حجمی در نظر گرفته شده است. در این مقاله اثر ضخامت استوانه، توان کسر حجمی توزیع مواد و همچنین اثر نوع بارگذاری بر مولفه‌های ارتعاشی این استوانه‌ها بررسی شد. نتایج حاصل از دو روش بدون المان و المان محدود با یکدیگر و با کارهای قبلی منتشر شده مقایسه و مطابقت بسیار خوبی مشاهده شد.
Keywords [Persian]
مواد هدفمند، روش بدون المان، حداقل مربعات متحرک، ارتعاشات، تابع تبدیل
References
[1] Koizumi M. , The concept of FGM. Ceram., Trans. Function Graded Material, 34, 1993, pp. 3–10.
[2] Kashtalyan M., Three-dimensional elasticity solution for bending of functionally graded rectangular plates, Eur. J. Mech. A–Solid, 23, 2004, pp. 853–864.
[3] Loy C.T., Lam K.Y., Reddy J.N., Vibration of functionally graded cylindrical shells, Int. J. Mech. Sci., 41, 1999, pp. 309–324.
[4] Pradhan S.C., Loy C.T., Reddy J.N., Vibration characteristics of functionally graded cylindrical shells under various boundary conditions, Appl. Acoust., 61, 2000, pp. 111–129.
[5] Kadoli R., Ganesan K., Buckling and free vibration analysis of functionally graded cylindrical shells subjected to a temperature-speciefied boundary condition, J. Sound. Vib., 289, 2006, pp. 450–480.
[6] Haddadpour H., Mahmoudkhani S., Navazi H.M., Free vibration analysis of functionally graded cylindrical shells including thermal effects, Thin-Walled Structures., 45, 2007, pp. 591-599.
[7] Ansari R., Darvizeh M., Prediction of dynamic behaviour of FGM shells under arbitrary boundary conditions, Compos. Struct., 85, 2008, pp. 284–292.
[8] Shakeri M., Akhlaghi M., Hoseini S.M., Vibration and radial wave propagation velocity in functionally graded thick hollow cylinder, Compos. Struct., 76, 2006, pp. 174-181.
[9] Hosseini S.M., Akhlaghi M, Shakeri M., Dynamic response and radial wave propagation velocity in thick hollow cylinder made of functionally graded materials. Int. J. Comput. Aid. Eng. Software, 24, 2007, pp. 288-303.
[10] Asgari M., Akhlaghi M., Hosseini S. M., Dynamic analysis of two-dimensional functionally graded thick hollow cylinder with finite length under impact loading, Acta. Mech., 208, 2009, pp. 163-180.
[11] Zhang G.M., Batra R.C., Wave propagation in functionally graded materials by modified smoothed particle hydrodynamics (MSPH) method, J. Comput. Phys., 222, 2007, pp. 374-390.
[12] Lancaster P., Salkauskas K., Surface Generated by Moving Least Squares Methods, Math. Comput., 37, 1981, pp. 141-158.
[13] Li S., Liu W.K., Meshfree and particle methods and their applications, Appl. Mech. Rev., 55, 2002, pp. 1-34.
[14] Belytschko Liu W. K., Belytschko T., Nonlinear Finite Elements for Continua and Structures, John Wiley & Sons, 2000, p. 318
[15] Zhou D., Cheung Y.K., Lo S.H., Au FTK., 3D vibration analysis of solid and hollow circular cylinders via Chebyshev–Ritz method. Comput. Methods Appl. Mech. Engrg., 192, 2003, pp. 1575-1589.
[16] Hutchinson J.R., Comments on, Accurate vibration frequencies of circular cylinders from three-dimensional analysis, J. Acoust. Soc. Am., 100, 1996, pp. 1894 –1895.
[17] Leissa A.W., So J., Accurate vibration frequencies of circular cylinders from three dimensional analysis, J. Acoust. Soc. Am., 98, 1995, pp. 2136–2141.
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