Influence of Rotation on Vibration Behavior of a Functionally Graded Moderately Thick Cylindrical Nanoshell Considering Initial Hoop Tension
محورهای موضوعی : EngineeringH Safarpour 1 , M.M Barooti 2 , M Ghadiri 3
1 - Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin, Iran
2 - Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin, Iran
3 - Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin, Iran
کلید واژه: Functionally graded material, Modified couple stress theory, Critical speed, GDQM, Initial hoop tension, Moderately thick cylindrical nanoshell,
چکیده مقاله :
In this research, the effect of rotation on the free vibration is investigated for the size-dependent cylindrical functionally graded (FG) nanoshell by means of the modified couple stress theory (MCST). MCST is applied to make the design and the analysis of nano actuators and nano sensors more reliable. Here the equations of motion and boundary conditions are derived using minimum potential energy principle and first-order shear deformation theory (FSDT). The formulation consists of the Coriolis, centrifugal and initial hoop tension effects due to the rotation. The accuracy of the presented model is verified with literatures. The novelty of this study is the consideration of the rotation effects along with the satisfaction of various boundary conditions. Generalized differential quadrature method (GDQM) is employed to discretize the equations of motion. Then the investigation has been made into the influence of some factors such as the material length scale parameter, angular velocity, length to radius ratio, FG power index and boundary conditions on the critical speed and natural frequency of the rotating cylindrical FG nanoshell.
[1] Ghadiri M., Safarpour H., 2016, Free vibration analysis of embedded magneto-electro-thermo-elastic cylindrical nanoshell based on the modified couple stress theory, Applied Physics A 122: 833.
[2] Bryan G. H., 1890, On the beats in the vibrations of a revolving cylinder or bell, Proceedings of the Cambridge Philosophical Society.
[3] DiTaranto R., Lessen M., 1964, Coriolis acceleration effect on the vibration of a rotating thin-walled circular cylinder, Journal of Applied Mechanics 31: 700-701.
[4] Srinivasan A., Lauterbach G. F., 1971, Traveling waves in rotating cylindrical shells, Journal of Engineering for Industry 93: 1229-1232.
[5] Zohar A., Aboudi J., 1973, The free vibrations of a thin circular finite rotating cylinder, International Journal of Mechanical Sciences 15: 269-278.
[6] Padovan J., 1973, Natural frequencies of rotating prestressed cylinders, Journal of Sound and Vibration 31: 469-482.
[7] Padovan J., 1975, Traveling waves vibrations and buckling of rotating anisotropic shells of revolution by finite elements, International Journal of Solids and Structures 11: 1367-1380.
[8] Padovan J., 1975, Numerical analysis of asymmetric frequency and buckling eigenvalues of prestressed rotating anisotropic shells of revolution, Computers & Structures 5: 145-154.
[9] Endo M., Hatamura K., Sakata M., Taniguchi O., 1984, Flexural vibration of a thin rotating ring, Journal of Sound and Vibration 92: 261-272.
[10] Saito T., Endo M., 1986, Vibration of finite length, rotating cylindrical shells, Journal of Sound and Vibration 107: 17-28.
[11] Huang S., Soedel W., 1988, Effects of coriolis acceleration on the forced vibration of rotating cylindrical shells, Journal of Applied Mechanics 55: 231-233.
[12] Huang S., Hsu B., 1990, Resonant phenomena of a rotating cylindrical shell subjected to a harmonic moving load, Journal of Sound and Vibration 136: 215-228.
[13] Yang Z., Nakajima M., Shen Y., Fukuda T., 2011, Nano-gyroscope assembly using carbon nanotube based on nanorobotic manipulation, Micro-Nano Mechatronics and Human Science (MHS), International Symposium.
[14] Malekzadeh P., Heydarpour Y., 2012, Free vibration analysis of rotating functionally graded cylindrical shells in thermal environment, Composite Structures 94: 2971-2981.
[15] Firouz-Abadi R., Torkaman-Asadi M., Rahmanian M., 2013, Whirling frequencies of thin spinning cylindrical shells surrounded by an elastic foundation, Acta Mechanica 224: 881-892.
[16] Hosseini-Hashemi S., Ilkhani M., Fadaee M., 2013, Accurate natural frequencies and critical speeds of a rotating functionally graded moderately thick cylindrical shell, International Journal of Mechanical Sciences 76: 9-20.
[17] Toupin R. A., 1962, Elastic materials with couple-stresses, Archive for Rational Mechanics and Analysis 11: 385-414.
[18] Koiter W., 1964, Couple stresses in the theory of elasticity, Proceedings van de Koninklijke Nederlandse Akademie van Wetenschappen.
[19] Mindlin R. D., 1964, Micro-structure in linear elasticity, Archive for Rational Mechanics and Analysis 16: 51-78.
[20] Asghari M., Kahrobaiyan M., Rahaeifard M., Ahmadian M., 2011, Investigation of the size effects in Timoshenko beams based on the couple stress theory, Archive of Applied Mechanics 81: 863-874.
[21] Yang F., Chong A., Lam D., Tong P., 2002, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures 39: 2731-2743.
[22] Park S., Gao X., 2006, Bernoulli–Euler beam model based on a modified couple stress theory, Journal of Micromechanics and Microengineering 16: 2355.
[23] Reddy J., 2011, Microstructure-dependent couple stress theories of functionally graded beams, Journal of the Mechanics and Physics of Solids 59: 2382-2399.
[24] Shaat M., Mahmoud F., Gao X.-L., Faheem A. F., 2014, Size-dependent bending analysis of Kirchhoff nano-plates based on a modified couple-stress theory including surface effects, International Journal of Mechanical Sciences 79: 31-37.
[25] Ghadiri M., Safarpour H., 2017, Free vibration analysis of size-dependent functionally graded porous cylindrical microshells in thermal environment, Journal of Thermal Stresses 40: 55-71.
[26] Miandoab E. M., Pishkenari H. N., Yousefi-Koma A., Hoorzad H., 2014, Polysilicon nano-beam model based on modified couple stress and Eringen’s nonlocal elasticity theories, Physica E: Low-dimensional Systems and Nanostructures 63: 223-228.
[27] Love A. E. H., 2013, A Treatise on the Mathematical Theory of Elasticity , Cambridge University Press.
[28] Donnell L. H., 1934, A new theory for the buckling of thin cylinders under axial compression and bending, Transactions of the American Society of Mechanical Engineers 56: 795-806.
[29] Sanders Jr J. L., 1959, An Improved First-Approximation Theory for Thin Shells, Nasa TR R-24.
[30] Leissa A. W., 1973, Vibration of Shells, Scientific and Technical Information Office, Nasa Report No. SP-288.
[31] Reissner E., 1945, The effect of transverse shear deformation on the bending of elastic plates, Journal of Applied Mechanics 12: 68-77.
[32] Mindlin R. D., 1951, Influence of rotary inertia and shear on flexural motions of isotropic elastic plates, Journal of Applied Mechanics 18: 31-38.
[33] Arani A. G., Zarei M. S., Amir S., Maraghi Z. K., 2013, Nonlinear nonlocal vibration of embedded DWCNT conveying fluid using shell model, Physica B: Condensed Matter 410: 188-196.
[34] Arani A. G., Kolahchi R., Maraghi Z. K., 2013, Nonlinear vibration and instability of embedded double-walled boron nitride nanotubes based on nonlocal cylindrical shell theory, Applied Mathematical Modelling 37: 7685-7707.
[35] Hosseini-Hashemi S., Ilkhani M., 2016, Exact solution for free vibrations of spinning nanotube based on nonlocal first order shear deformation shell theory, Composite Structures 157: 1-11.
[36] Tu Q., Yang Q., Wang H., Li S., 2016, Rotating carbon nanotube membrane filter for water desalination, Scientific Reports 6: 26183.
[37] Wattanasakulpong N., Ungbhakorn V., 2014, Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities, Aerospace Science and Technology 32: 111-120.
[38] Safarpour H., Hosseini M., Ghadiri M., 2017, Influence of three-parameter viscoelastic medium on vibration behavior of a cylindrical nonhomogeneous microshell in thermal environment: An exact solution, Journal of Thermal Stresses 40: 1353-1367.
[39] Barber J. R., 2010, Intermediate Mechanics of Materials , Springer Science & Business Media.
[40] Tauchert T. R., 1974, Energy Principles in Structural Mechanics, McGraw-Hill Companies.
[41] Bellman R., Casti J., 1971, Differential quadrature and long-term integration, Journal of Mathematical Analysis and Applications 34: 235-238.
[42] Bellman R., Kashef B., Casti J., 1972, Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations, Journal of Computational Physics 10: 40-52.
[43] Shu C., 2012, Differential Quadrature and its Application in Engineering, Springer Science & Business Media.
[44] Shu C., Richards B. E., 1992, Application of generalized differential quadrature to solve two‐dimensional incompressible Navier‐Stokes equations, International Journal for Numerical Methods in Fluids 15: 791-798.
[45] Ghadiri M., Shafiei N., Akbarshahi A., 2016, Influence of thermal and surface effects on vibration behavior of nonlocal rotating Timoshenko nanobeam, Applied Physics A 122: 1-19.
[46] Beni Y. T., Mehralian F., Razavi H., 2015, Free vibration analysis of size-dependent shear deformable functionally graded cylindrical shell on the basis of modified couple stress theory, Composite Structures 120: 65-78.
[47] Alibeigloo A., Shaban M., 2013, Free vibration analysis of carbon nanotubes by using three-dimensional theory of elasticity, Acta Mechanica 224: 1415-1427.
[48] Tadi Beni Y., Mehralian F., Zeighampour H., 2016, The modified couple stress functionally graded cylindrical thin shell formulation, Mechanics of Advanced Materials and Structures 23: 791-801.
