ارتعاشات آزاد پوسته های استوانه ای از جنس مواد هدفمند بر روی بستر الاستیک تحت نیروی محوری، فشار جانبی و شرایط مرزی مختلف

نوع مقاله : مقاله پژوهشی

نویسندگان

1 مهندسی هوافضا، پژوهشگاه هوافضا، وزارت علوم، تحقیقات و فناوری، تهران، ایران

2 پژوهشکده سامان ههای حمل و نقل فضایی، پژوهشگاه فضایی ایران، تهران، ایران

3 دانشکده مهندسی هوافضا، دانشگاه صنعتی امیرکبیر، تهران، ایران

چکیده

در این مقاله ارتعاشات آزاد پوسته‌های استوانه‌ای از جنس مواد هدفمند تحت نیروی محوری و فشار جانبی، احاطه شده با بستر الاستیک به ازای شرایط مرزی مختلف با استفاده از روش حل گسترش موج بررسی شده است. خواص مواد هدفمند مطابق قانون توانی در جهت ضخامت تغییر می‌کند. بستر الاستیک از نوع بستر دو پارامتری پسترناک می‌باشد. معادلات حاکم بر پوسته استوانه‌ای بر روی بستر الاستیک تحت نیروهای مکانیکی مبتنی بر نظریه مرتبه اول برشی سندرز-کویتر با استفاده از اصل همیلتون استخراج شده‌اند. با فرض میدان تغییر مکان به صورت گسترش موج معادلات حاکم حل شده‌اند. بسامدهای طبیعی پوسته استوانه‌ای تحت شرایط مرزی مختلف، به دست آمده و با نتایج مراجع مقایسه شده‌اند. مشخص می‌شود که استفاده از میدان تغییر مکان به فرم گسترش موج به صورت یک روش مؤثر و قابل اطمینان عمل نموده و به ازای شرایط مرزی مختلف نتایج قابل قبولی ارائه می‌دهد. البته نشان داده می‌شود که به ازای شرایط مرزی مختلف و ابعاد هندسی پوسته، دقت روش گسترش موج نیز متفاوت است. همچنین با تکیه بر نظریه توسعه داده شده، اثرات شرایط مرزی مختلف، نیروی محوری، فشار جانبی و پارامترهای بستر الاستیک بر رفتار ارتعاشی پوسته استوانه‌ای از جنس مواد هدفمند مورد بررسی قرار گرفت.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Free Vibration of, Functionally Graded Materials Cylindrical Shells on Elastic Foundation under Axial force, Lateral Pressure and Different Boundary Conditions

نویسندگان [English]

  • A. Hadi 1
  • S. Shakhesi 2
  • H. Ovesy 3
  • J. Fazilati 1
1 Aerospace Research Institute, Ministry of Science, Research and Technology, Tehran, Iran
2 Space Transportation Research Institute, Iranian Space Research Center, Tehran, Iran
3 Aerospace Engineering Department, Amirkabir University of Technology, Tehran, Iran
چکیده [English]

Free vibration characteristics of functionally graded materials cylindrical shells surrounded by elastic medium under axial force, lateral pressure and different boundary conditions using wave propagation method are investigated in this paper. The material properties of functionally graded materials are assumed to be graded in the thickness direction according to the power law. The elastic medium is assumed as two-parameter Pasternak elastic foundation. Governing equations based on the first order shear deformation theory of Sanders-Koiter for the cylindrical shell resting on elastic foundation under mechanical loads are derived by using Hamilton’s principle. By assuming displacement field in wave propagation form, governing equations are solved. Natural frequencies of cylindrical shell under various boundary conditions are obtained and compared with the results in the literature. It is seen that using displacement field in wave propagation form, acts as an effective and reliable method and gives the acceptable results for various boundary conditions. Although it is shown that for different boundary conditions and geometry dimensions, accuracy of the wave propagation approach is different. In addition, based on the developed theory the effects of different boundary conditions, axial force, lateral pressure and elastic foundation parameters on vibration behavior of functionally graded cylindrical shell are investigated.

کلیدواژه‌ها [English]

  • free vibration
  • Functionally graded materials
  • Cylin‌drical shells
  • axial force and lateral pressure
  • Elastic foundation

مراجع

[1] A.W. Leissa, Vibration of Shells, The Acoustical Society of America, 1973.
[2] K. Forsberg, Influence of boundary conditions on modal characteristics of cylindrical shells, Journal of American institute of aeronautics and astronautics, 2 (1964) 182-189.
[3] F. Shadmehri, S. Hoa, M. Hojjati, The Effect of Displacement Field on Bending, Buckling, and Vibration of Cross-Ply Circular Cylindrical Shells, Mechanics of Advanced Materials and Structures, 21(21) (2014) 14-22.
[4] C.B. Sharma, Vibration characteristics of thin circular cylinders, Journal of sound and vibration, 63 (1979) 581-592.
[5] W. Soedel, A new frequency formula for closed circular cylindrical shells for a large variety of boundary conditions, Journal of sound and vibration, 70 (1980) 309-317.
[6] K.Y. Lam, C.T. Loy, Effects of boundary conditions on frequencies of a multi-layered cylindrical shell, Journal of sound and vibration, 188(3) (1995) 363-384.
[7] A. Messina, K.P. Soldatos, Ritz-type dynamic analysis of cross-ply laminated circular cylinders subjected to different boundary conditions, Journal of Sound and Vibration, 227(4) (1999) 749-768.
[8] R. Ansari, M. Darvizeh, M. Hemmatnezhad, Vibration Analysis of FGM Cylindrical Shells Under Various Boundary Conditions, Iranian Aerospace Society, 5(3) (2008) 129-138.
[9] D.N. Paliwal, R.K. Pandey, T. Nath, Free vibration of circular cylindrical shell on Winkler and Pasternak foundation, Journal of pressure vessel and piping, 69 (1996) 79-89.
[10] D.N. Paliwal, R.K. Pandey, The free vibration of a cylindrical shell on an elastic foundation, Journal of vibration and acoustics, 120 (1998) 63-71.
[11] G.G. Sheng, X. Wang, Thermal vibration, buckling and dynamic stability of functionally graded cylindrical shells embedded in an elastic medium, Journal of Reinforced Plastics and Composites, 27(2) (2008) 117–134.
[12] A.G. Shah, T. Mahmood, M.N. Naeem, Z. Iqbal, S.H. Arshad, Vibrations of functionally graded cylindrical shells based on elastic foundations, Acta Mechanica, 211 (2010) 293-307.
[13] M. Mohammadimehr, M. Moradi, A. Loghman Influence of the elastic foundation on the free vibration and buckling of thin-walled piezoelectric-based FGM cylindrical shells under combined loadings, Journal of Solid Mechanics, 6(4) (2014) 347-365.
[14] X.M. Zhang, G.R. Liu, K.Y. Lam, Vibration analysis of thin cylindrical shells using the wave propagation approach, Journal of sound and vibration, 239(3) (2001) 397-403.
[15] X.M. Zhang, G.R. Liu, K.Y. Lam, Coupled vibration analysis of fluid-filled cylindrical shells using the wave propagation approach, Applied Acoustics, 62 (2001) 229-243.
[16] L. Xuebin, Study on free vibration analysis of circular cylindrical shells using wave propagation, Journal of Sound and Vibration, 311 (2008) 667–682.
[17] S. Wang, D.J. Dawe, Buckling of composite shell structures using the spline finite strip method, Composites: Part B, 30 (1999) 351–364.
[18] J.N. Reddy, Mechanics of laminated composite plates and shells: theory and analysis, second ed., CRC Press, Boca Raton, FL, 2004.
[19] C.W. Lim, Y.F. Ma, S. Kitipornchai, C.M. Wang, R.K.K. Yuen, Buckling of Vertical Cylindrical Shells Under Combined End Pressure and Body Force, Journal of Engineering Mechanics, 129 (2003) 876-884.
[20] H. Huang, Q. Han, N. Feng, X. Fan, Buckling of functionally graded cylindrical shells under combined loads, Mechanics of Advanced Materials and Structures, 18(5) (2011) 337-346.
[21] P.B. Goncalves, R.S.S. Ramos, Numerical Method for Vibration Analysis of Cylindrical Shells, Journal of Engineering Mechanics, (1997) 544-550.
[22] L.F.F. Gasser, Free Vibrations of thin cylindrical shells containing liquid, Federal Univ. of Rio de Janeiro, 1987.
[23] C.T. Loy, K.Y. Lam, Vibration of cylindrical shells with ring support, International Journal of Mechanical Sciences, 39(4) (1997) 455-471.
[24] M.M. Najafizadeh, M.R. Isvandzibaei, Vibration of functionally graded cylindrical shells based on higher order shear deformation plate theory with ring support, Acta Mechanica, 191 (2007) 75-91.
[25] M.N. Naeem, C.B. Sharma, Prediction of natural frequencies for thin circular cylindrical shell, Journal of mechanical engineering science, 214 (2000) 1313-1328.
[26] A.G. Shah, Vibration characteristics of fluid-filled functionally graded cylindrical shells on elastic foundations, The Islamia University of Bahawalpur, Pakistan, 2011.
[27] J.M. Santiago, H.L. Wisniewski, Convergence of finite element frequency prediction for a thin walled cylinder, Computers and Structures, 32(3/4) (1989) 745–759.
[28] R.N. Arnold, G.B. Warburton, The flexural vibrations of thin cylinders, in: Proceedings of the institution of mechanical engineers A, 1953, pp. 62-80.
[29] C.T. Loy, K.Y. Lam, C. Shu, Analysis of cylindrical shells using generalized differential quadrature method, Shock and vibration, 4 (1997) 193-198.
[30] P.A.T. Gill, Vibrations of clamped-free circular cylindrical shells, Journal of Sound and Vibration, 25 (1972) 501-502.
[31] C.T. Loy, K.Y. Lam, J.N. Reddy, Vibration of functionally graded cylindrical shells, International Journal of Mechanical Sciences, 41 (1999) 309-324.
نشریه مهندسی مکانیک امیرکبیر
دوره 50، شماره 5
آذر و دی 1397
صفحه 1097-1112

فایل ها

اشتراک گذاری

ارجاع به این مقاله

آمار