Calculation of Natural Frequencies of Bi-Layered Rotating Functionally Graded Cylindrical Shells
الموضوعات :
1 - Department of Mechanical Engineering, Golpayegan University of Technology, Golpayegan, Iran
الکلمات المفتاحية: Free vibration, Natural frequency, Functionally graded material (FGM), Bi-layered FGM cylindrical shell,
ملخص المقالة :
In this paper, an exact analytical solution for free vibration of rotating bi-layered cylindrical shell composed of two independent functionally graded layers was presented. The thicknesses of the shell layers were assumed to be equal and constant. The material properties of the constituents of bi-layered FGM cylindrical shell were graded in the thickness direction of the layers of the shell according to a volume fraction power-law distribution. In order to derive the equations of motion, the Sanders’ thin shell theory and Rayleigh-Ritz method were used. Also the results were extracted by considering Coriolis, centrifugal and initial hoop tension effects. Effects of rotating speed, geometrical parameters, and material distribution in the two functionally graded layers of the shell, circumferential and longitudinal wave number on the forward and backward natural frequencies were investigated. A comparison of the results was made with those available in the literature for the validity and accuracy of the present methodology.
[1] Loy C. T., Lam K. Y., Reddy J. N., 1999, Vibration of functionally graded cylindrical shells. International Journal of Mechanical Sciences 41: 309-324.
[2] Najafizadeh M. M., Isvandzibaei M. R., 2007, Vibration of functionally graded cylindrical shells based on higher order shear deformation plate theory with ring support, Acta Mechanica 191: 75-91.
[3] Arshad S. H., Naeem M. N., Sultana N., 2007, Frequency analysis of functionally graded material cylindrical shells with various volume fraction laws, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 221: 1483-1495.
[4] Shah A. G., Mahmood T., Naeem M. N., 2009, Vibrations of FGM thin cylindrical shells with exponential volume fraction law, Applied Mathematics and Mechanics 30: 607-615.
[5] Isvandzibaei M. R., Awasare P. J., 2009, Comparison of two kinds of functionally graded cylindrical shells with various volume fraction laws for vibration analysis, Journal of Solid Mechanics 1: 190-200.
[6] Rahimi G. H., Ansari R., Hemmatnezhad M., 2011, Vibration of functionally graded cylindrical shells with ring support, Scientia Iranica 18: 1313-1320.
[7] Moradi-Dastjerdi R., Foroutan M., 2014, Free vibration analysis of orthotropic FGM cylinders by a mesh-free method, Journal of Solid Mechanics 6: 70-81.
[8] Ebrahimi M. J., Najafizadeh M. M., 2014, Free vibration analysis of two-dimensional functionally graded cylindrical shells, Applied Mathematical Modelling 38: 308-324.
[9] Bahadori R., Najafizadeh M. M., 2015, Free vibration analysis of two-dimensional functionally graded axisymmetric cylindrical shell on Winkler–Pasternak elastic foundation by first-order shear deformation theory and using Navier-differential quadrature solution methods, Applied Mathematical Modelling 39: 4877-4894.
[10] Sofiyev A. H., Deniz A., Akçay I. H., Yusufoğlu E., 2006, The vibration and stability of a three-layered conical shell containing an FGM layer subjected to axial compressive load, Acta Mechanica 183: 129-144.
[11] Arshad S. H., Naeem M. N., Sultana N., Shah A. G., Iqbal Z., 2011, Vibration analysis of bi-layered FGM cylindrical shells, Archive of Applied Mechanics 81: 319-343.
[12] Arshad S. H., Naeem M. N., Sultana N., Iqbal Z., Shah A. G., 2010, Vibration of bilayered cylindrical shells with layers of different materials, Journal of Mechanical Science and Technology 24: 805-810.
[13] Shah A., Naeem M., Mahmood T., Arshad S., 2013, Vibration analysis of three-layered functionally graded cylindrical shells with isotropic middle layer resting on Winkler and Pasternak foundations,Pakistan Journal of Science 65: 256-262.
[14] Sepiani H., Rastgoo A., Ebrahimi F., Arani A. G., 2010, Vibration and buckling analysis of two-layered functionally graded cylindrical shell, considering the effects of transverse shear and rotary inertia, Materials & Design 31: 1063-1069.
[15] Li S.-R., Fu X.-H., Batra R. C., 2010, Free vibration of three-layer circular cylindrical shells with functionally graded middle layer, Mechanics Research Communications 37: 577-580.
[16] Ahmad M., Naeem M., 2009, Vibration characteristics of rotating FGM circular cylindrical shells using wave propagation method, European Journal of Scientific Research 36: 184-235.
[17] Civalek Ö., 2017, Discrete singular convolution method for the free vibration analysis of rotating shells with different material properties, Composite Structures 160: 267-279.
[18] Hosseini-Hashemi S., Ilkhani M. R., 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.
[19] Mehrparvar M., 2009, Vibration analysis of functionally graded spinning cylindrical shells using higher order shear deformation theory, Journal of Solid Mechanics 1: 159-170.
[20] Zhao X., Liew K., Ng T., 2002, Vibrations of rotating cross-ply laminated circular cylindrical shells with stringer and ring stiffeners, International Journal of Solids and Structures 39: 529-545.
[21] Sanders Jr J. L., 1959, An Improved First-Approximation Theory for Thin Shells, NASA TR R-24, U.S.
