A domain decomposition approach for vibration analysis of isotropic and composite cylindrical shells with arbitrary boundaries

Abstract An efficient domain decomposition method is proposed for solving the free, harmonic and transient vibrations of isotropic and composite cylindrical shells subjected to various combinations of classical and non-classical boundary conditions. Multi-segment partitioning strategy is adopted to accommodate the computing requirements of high-order vibration modes and responses. The continuity constraints on the segment interfaces are incorporated into the system potential functional by means of a modified variational principle and least-squares weighted residual method. An arbitrarily laminated version of Reissner–Naghdi’s shell theory is employed to formulate the theoretical model. Double mixed series, i.e., the Fourier series and orthogonal polynomials, are used as admissible displacement functions for each shell segment. The utility and robustness of the method for the application of various basis functions are evaluated with the following four sets of orthogonal polynomial series, i.e., the Chebyshev orthogonal polynomials of first and second kind, Legendre orthogonal polynomials of first kind and Hermite orthogonal polynomials. To test the convergence, efficiency and accuracy of the present method, free and forced vibrations (including the harmonic and transient vibrations) of isotropic and composite laminated cylindrical shells are examined under different combinations of free, shear-diaphragm, simply-supported, clamped and elastic supported boundaries. The theoretical results are compared with those previously published in literature, and the ones obtained by using the finite element program ANSYS. Very good agreement is observed.

[1]  S. Khalili,et al.  Transient dynamic response of initially stressed composite circular cylindrical shells under radial impulse load , 2009 .

[2]  Francesco Pellicano,et al.  Vibrations of circular cylindrical shells: Theory and experiments , 2007 .

[3]  J. Reddy,et al.  Dynamic response of cross‐ply laminated shallow shells according to a refined shear deformation theory , 1989 .

[4]  Li Xuebin,et al.  Study on free vibration analysis of circular cylindrical shells using wave propagation , 2008 .

[5]  G. B. Warburton,et al.  Harmonic Response of Cylindrical Shells , 1974 .

[6]  Dipankar Chakravorty,et al.  Applications of FEM on Free and Forced Vibration of Laminated Shells , 1998 .

[7]  X. Li,et al.  TRANSIENT DYNAMIC RESPONSE ANALYSIS OF ORTHOTROPIC CIRCULAR CYLINDRICAL SHELL UNDER EXTERNAL HYDROSTATIC PRESSURE , 2002 .

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

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

[10]  B. P. Patel,et al.  Comparative dynamic studies of thick laminated composite shells based on higher-order theories , 2002 .

[11]  Chang Shu,et al.  Free vibration analysis of laminated composite cylindrical shells by DQM , 1997 .

[12]  Chien Wei-zang Method of high-order lagrange multiplier and generalized variational principles of elasticity with more general forms of functionals , 1983 .

[13]  G. Warburton,et al.  Resonant response of orthotropic cylindrical shells , 1977 .

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

[15]  Alan Jeffrey,et al.  Handbook of mathematical formulas and integrals , 1995 .

[16]  Ömer Civalek,et al.  Numerical analysis of free vibrations of laminated composite conical and cylindrical shells , 2007 .

[17]  Mohamad S. Qatu,et al.  Vibration of Laminated Shells and Plates , 2004 .

[18]  Marco Amabili,et al.  Polynomial versus trigonometric expansions for nonlinear vibrations of circular cylindrical shells with different boundary conditions , 2010 .

[19]  Mohamad S. Qatu,et al.  Recent research advances in the dynamic behavior of shells: 1989–2000, Part 2: Homogeneous shells , 2002 .

[20]  C. Bert,et al.  Two new approximate methods for analyzing free vibration of structural components , 1988 .

[21]  Mohamad S. Qatu,et al.  Recent research advances on the dynamic analysis of composite shells: 2000-2009 , 2010 .

[22]  M. Naeem,et al.  Prediction of natural frequencies for thin circular cylindrical shells , 2000 .

[23]  Magdi Mohareb,et al.  Analysis of circular cylindrical shells under harmonic forces , 2010 .

[24]  H. M. Navazi,et al.  Free vibration analysis of functionally graded cylindrical shells including thermal effects , 2007 .

[25]  J. N. Reddy,et al.  A semi-analytical finite element model for the analysis of cylindrical shells made of functionally graded materials , 2009 .

[26]  Xiaoming Zhang,et al.  Vibration analysis of cross-ply laminated composite cylindrical shells using the wave propagation approach , 2001 .

[27]  H. Türkmen STRUCTURAL RESPONSE OF LAMINATED COMPOSITE SHELLS SUBJECTED TO BLAST LOADING: COMPARISON OF EXPERIMENTAL AND THEORETICAL METHODS , 2002 .

[28]  S.M.R. Khalili,et al.  Dynamic response of pre-stressed fibre metal laminate (FML) circular cylindrical shells subjected to lateral pressure pulse loads , 2010 .

[29]  Young-Shin Lee,et al.  On the dynamic response of laminated circular cylindrical shells under impulse loads , 1997 .

[31]  Xinwei Wang,et al.  A NEW APPROACH IN APPLYING DIFFERENTIAL QUADRATURE TO STATIC AND FREE VIBRATIONAL ANALYSES OF BEAMS AND PLATES , 1993 .

[32]  Dimitri E. Beskos,et al.  Dynamic analysis of ring-stiffened circular cylindrical shells , 1981 .

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

[34]  J. Reddy Mechanics of laminated composite plates and shells : theory and analysis , 1996 .

[35]  S. R. Swanson,et al.  Analysis of Simply-Supported Orthotropic Cylindrical Shells Subject to Lateral Impact Loads , 1990 .

[36]  Daniel J. Inman,et al.  2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical shell and annular plate structures , 2009 .

[37]  William James Stronge,et al.  Impact response of composite cylinders , 1997 .

[38]  S.M.R. Khalili,et al.  Transient dynamic response of composite circular cylindrical shells under radial impulse load and axial compressive loads , 2005 .

[39]  Dong-Seong Sohn,et al.  FREE VIBRATION OF CLAMPED–FREE CIRCULAR CYLINDRICAL SHELL WITH A PLATE ATTACHED AT AN ARBITRARY AXIAL POSITION , 1998 .

[40]  K. Washizu Variational Methods in Elasticity and Plasticity , 1982 .

[41]  Arthur W. Leissa,et al.  Modal response of circular cylindrical shells with structural damping , 1981 .

[42]  Mohamad S. Qatu,et al.  Recent research advances in the dynamic behavior of shells: 1989-2000, Part 1: Laminated composite shells , 2002 .

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

[44]  H. Smaoui,et al.  Dynamic stiffness matrix of an axisymmetric shell and response to harmonic distributed loads , 2011 .