Vibration studies of rotating cylindrical shells with arbitrary edges using characteristic orthogonal polynomials in the Rayleigh–Ritz method

Abstract A general approach is presented for the vibration studies of rotating cylindrical shells having arbitrary edges. The present analysis is based on the Sanders' shell theory and the effects of centrifugal and Coriolis forces as well as initial hoop tension due to rotating are all taken into account. By taking the characteristic orthogonal polynomial series as the admissible functions, the Rayleigh–Ritz method is employed to derive the frequency equations of rotating cylinders with classical homogeneous boundary conditions. Further, utilizing artificial springs to simulate the elastic constraints imposed on the cylinders’ edges, one can derive the frequency equations of rotating cylindrical shells with more general boundary conditions by considering the strain energy of artificial springs during the Rayleigh–Ritz procedure. To validate the approach proposed in this paper, a series of comparison and convergence studies are performed and the investigations demonstrate high accuracy and low computational cost of the present approach. Finally, some further numerical results are given to illustrate the influence of the variations of spring stiffness on the frequencies of rotating cylinders.

[1]  Ö. Civalek,et al.  Free vibration analysis of rotating cylindrical shells using discrete singular convolution technique , 2009 .

[2]  Arthur W. Leissa,et al.  Free Vibrations of Thick Hollow Circular Cylinders From Three-Dimensional Analysis , 1997 .

[3]  R. Bhat.  Natural frequencies of rectangular plates using characteristic orthogonal polynomials in rayleigh-ritz method , 1986 .

[4]  K. Lam,et al.  On vibrations of thin rotating laminated composite cylindrical shells , 1994 .

[5]  K. Lam,et al.  Analysis of rotating laminated cylindrical shells by different thin shell theories , 1995 .

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

[7]  Fulei Chu,et al.  Vibration analysis of spinning cylindrical shells by finite element method , 2002 .

[8]  Shiming Chu,et al.  Vibration characteristics of thin rotating cylindrical shells with various boundary conditions , 2012 .

[9]  Rama B. Bhat,et al.  In-plane free vibration of circular annular disks , 2009 .

[10]  Y. K. Cheung,et al.  3D vibration analysis of solid and hollow circular cylinders via Chebyshev-Ritz method , 2003 .

[11]  K. Y. Lam,et al.  Free vibrations of a rotating multi-layered cylindrical shell , 1995 .

[12]  K. M. Liew,et al.  Harmonic reproducing kernel particle method for free vibration analysis of rotating cylindrical shells , 2002 .

[13]  Hua Li,et al.  Rotating Shell Dynamics , 2005 .

[14]  R. A. DiTaranto,et al.  Coriolis Acceleration Effect on the Vibration of a Rotating Thin-Walled Circular Cylinder , 1964 .

[15]  J. Padovan,et al.  Natural frequencies of rotating prestressed cylinders , 1973 .

[16]  Xumin Guo,et al.  Nonlinear dynamic response of rotating circular cylindrical shells with precession of vibrating shape—Part I: Numerical solution , 2010 .

[17]  Charles W. Bert,et al.  Critical speed analysis of laminated composite, hollow drive shafts , 1993 .

[18]  B. Kröplin,et al.  Vibrations Of High Speed Rotating Shells With Calculations For Cylindrical Shells , 1993 .

[19]  S. C. Huang,et al.  Resonant phenomena of a rotating cylindrical shell subjected to a harmonic moving load , 1990 .

[20]  Fulei Chu,et al.  Nonlinear vibrations of rotating thin circular cylindrical shell , 2012 .

[21]  K. Lam,et al.  Influence of boundary conditions for a thin laminated rotating cylindrical shell , 1998 .

[22]  T. Y. Ng,et al.  Vibration and critical speed of a rotating cylindrical shell subjected to axial loading , 1999 .

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

[24]  Masaru Sakata,et al.  Flexural vibration of a thin rotating ring , 1984 .

[25]  Arthur W. Leissa,et al.  Vibrations of cantilevered shallow cylindrical shells of rectangular planform , 1981 .

[26]  Ö. Civalek.  Linear vibration analysis of isotropic conical shells by discrete singular convolution (DSC) , 2007 .

[27]  Chang Shu,et al.  An efficient approach for free vibration analysis of conical shells , 1996 .

[28]  Y. Wang,et al.  Nonlinear dynamic response of rotating circular cylindrical shells with precession of vibrating shape—Part II: Approximate analytical solution , 2010 .

[29]  A. V. Srinivasan,et al.  Traveling Waves in Rotating Cylindrical Shells , 1971 .

[30]  Ö. Civalek.  A parametric study of the free vibration analysis of rotating laminated cylindrical shells using the method of discrete singular convolution , 2007 .

[31]  P. Malekzadeh,et al.  Free vibration analysis of rotating functionally graded cylindrical shells in thermal environment , 2012 .

[32]  Y. Xiang,et al.  Local adaptive differential quadrature for free vibration analysis of cylindrical shells with various boundary conditions , 2006 .

[33]  Jacob Aboudi,et al.  The free vibrations of a thin circular finite rotating cylinder , 1973 .

[34]  Omri Rand,et al.  Free vibrations of spinning composite cylindrical shells , 1991 .

[35]  T. Saito,et al.  Vibration of finite length, rotating cylindrical shells , 1986 .

[36]  Li Hua,et al.  Frequency characteristics of a thin rotating cylindrical shell using the generalized differential quadrature method , 1998 .