Vibration characteristics of FGM circular cylindrical shells using wave propagation approach

In this paper, the wave propagation approach is employed to study the vibration characteristics of functionally graded material circular cylindrical shells. Axial modal dependence is approximated by exponential functions. This is a very simple and easily applicable technique. This avoids a large amount of algebraic manipulations. A theoretical analysis of shell natural frequencies are conducted for various boundary conditions. Validity and accuracy of the present method are confirmed by comparing the present results with those available in the literature. A good agreement is observed between the two sets of the results.

[1]  E. Reissner A New Derivation of the Equations for the Deformation of Elastic Shells , 1941 .

[2]  K. Y. Lam,et al.  Vibration of cylindrical shells with ring support , 1997 .

[3]  K. Y. Lam,et al.  VIBRATION ANALYSIS OF THIN CYLINDRICAL SHELLS USING WAVE PROPAGATION APPROACH , 2001 .

[4]  Arcangelo Messina,et al.  VIBRATION STUDIES OF CROSS-PLY LAMINATED SHEAR DEFORMABLE CIRCULAR CYLINDERS ON THE BASIS OF ORTHOGONAL POLYNOMIALS , 1998 .

[5]  H. Chung,et al.  Free vibration analysis of circular cylindrical shells , 1981 .

[6]  R N Arnold,et al.  Flexural vibrations of the walls of thin cylindrical shells having freely supported ends , 1949, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[7]  新楽 和夫 J.C.Slater: Quantum Theory of Atomic Structure, Vol.1, Mc Graw-Hill Book Co., New York 1960, 502頁, 16×23cm, $11. , 1961 .

[8]  M. R. Isvandzibaei,et al.  Vibration of functionally graded cylindrical shells based on higher order shear deformation plate theory with ring support , 2007 .

[9]  Arcangelo Messina,et al.  Ritz-type dynamic analysis of cross-ply laminated circular cylinders subjected to different boundary conditions , 1999 .

[10]  J. N. Reddy,et al.  Vibration of functionally graded cylindrical shells , 1999 .

[11]  R. Blevins,et al.  Formulas for natural frequency and mode shape , 1984 .

[12]  M. Naeem,et al.  Frequency analysis of functionally graded material cylindrical shells with various volume fraction laws , 2007 .

[13]  Chang Shu,et al.  Analysis of Cylindrical Shells Using Generalized Differential Quadrature , 1997 .

[14]  Š. Markuš,et al.  The mechanics of vibrations of cylindrical shells , 1988 .

[15]  Somsak Swaddiwudhipong,et al.  Ritz Method for Vibration Analysis of Cylindrical Shells with Ring Stiffeners , 1997 .

[16]  A. Love A treatise on the mathematical theory of elasticity , 1892 .

[17]  Xiaoming Zhang,et al.  Coupled vibration analysis of fluid-filled cylindrical shells using the wave propagation approach , 2001 .

[18]  S. Timoshenko,et al.  THEORY OF PLATES AND SHELLS , 1959 .

[19]  E. Reissner,et al.  On the foundations of the theory of elastic shells , 1966 .

[20]  Wilhelm Flügge,et al.  Statik und Dynamik der Schalen , 1962 .

[21]  J. N. Reddy,et al.  Vibration characteristics of functionally graded cylindrical shells under various boundary conditions , 2000, Applied Acoustics.