Free vibration analysis of conical shells via the element-free kp-Ritz method

In this paper, we consider the free vibration analysis of thin conical shells under different boundary conditions. The analysis is carried out using the element-free kp-Ritz method. The present study is based on the classical thin-shell theory. The kernel particle (kp) functions are employed in hybridized form with harmonic functions to approximate the two-dimensional displacement field. In order to examine the numerical stability of the present approach, convergence studies are performed based on the influences of the support size and the number of nodes. To verify the accuracy of this method, comparisons of the present results are made with results available in the open literature. This study also examines in detail the effects of semi-vertex angles and boundary conditions on the frequency characteristics of the conical shells.

[1]  S. M. Dickinson,et al.  On the use of simply supported plate functions in the Rayleigh-Ritz method applied to the flexural vibration of rectangular plates , 1978 .

[2]  K. M. Liew,et al.  Vibration Characteristics of Conical Shell Panels With Three-Dimensional Flexibility , 2000 .

[3]  K. M. Liew,et al.  Effects of initial twist and thickness variation on the vibration behaviour of shallow conical shells , 1995 .

[4]  W. Ritz.  Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik. , 1909 .

[5]  Yoshihiro Narita,et al.  Buckling studies for simply supported symmetrically laminated rectangular plates , 1990 .

[6]  Liyong Tong,et al.  Free vibration of orthotropic conical shells , 1993 .

[7]  K. M. Liew,et al.  Vibration of pretwisted cantilever shallow conical shells , 1994 .

[8]  A. Leissa,et al.  Vibration of shells , 1973 .

[9]  K. M. Liew,et al.  Application of two-dimensional orthogonal plate function to flexural vibration of skew plates , 1990 .

[10]  E. J. Wisniewski,et al.  Vibrations of Conical Shells , 1959 .

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

[12]  K. M. Liew,et al.  THE ELEMENT-FREE kp-RITZ METHOD FOR VIBRATION OF LAMINATED ROTATING CYLINDRICAL PANELS , 2002 .

[13]  Y. K. Cheung,et al.  Free vibration analysis of singly curved shell by spline finite strip method , 1989 .

[14]  Liyong Tong,et al.  Free vibration of composite laminated conical shells , 1993 .

[15]  Wing Kam Liu,et al.  Reproducing kernel particle methods , 1995 .

[16]  K. M. Liew,et al.  Free vibration analysis of rectangular plates using orthogonal plate function , 1990 .

[17]  J. Reddy.  An introduction to the finite element method , 1989 .

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

[19]  Jack R. Vinson,et al.  Free vibration analysis of laminated composite truncated circular conical shells , 1989 .

[20]  D. Zhou,et al.  The Free Vibrations of Tapered Rectangular Plates Using a New Set of Beam Functions with the Rayleigh–Ritz Method , 1999 .

[21]  Charles W. Bert,et al.  Free Vibrational Analysis of Sandwich Conical Shells with Free Edges , 1970 .

[22]  K. M. Liew,et al.  Vibration of shallow conical shells with shear flexibility: A first-order theory , 1996 .

[23]  S. M. Dickinson,et al.  On the use of orthogonal polynomials in the Rayleigh-Ritz method for the study of the flexural vibration and buckling of isotropic and orthotropic rectangular plates , 1986 .

[24]  K. M. Liew,et al.  Vibration of cantilevered laminated composite shallow conical shells , 1998 .

[25]  Gen Yamada,et al.  Free vibration of a conical shell with variable thickness , 1982 .

[26]  K. M. Liew,et al.  Vibratory behaviour of shallow conical shells by a global Ritz formulation , 1995 .

[27]  N. Ganesan,et al.  VIBRATION ANALYSIS OF LAMINATED CONICAL SHELLS WITH VARIABLE THICKNESS , 1991 .

[28]  Gen Yamada,et al.  Natural frequencies of truncated conical shells , 1984 .

[29]  Charles W. Bert,et al.  DIFFERENTIAL QUADRATURE AND RAYLEIGH–RITZ METHODS TO DETERMINE THE FUNDAMENTAL FREQUENCIES OF SIMPLY SUPPORTED RECTANGULAR PLATES WITH LINEARLY VARYING THICKNESS , 1996 .

[30]  N. Ganesan,et al.  Vibration analysis of thick composite clamped conical shells of varying thickness , 1992 .

[31]  Li Hua,et al.  Influence of boundary conditions on the frequency characteristics of a rotating truncated circular conical shell , 1999 .

[32]  Hyman Garnet,et al.  Axisymmetric Free Vibrations of Conical Shells , 1964 .

[33]  L. Rayleigh,et al.  The theory of sound , 1894 .