Dynamic Stiffness Formulation for Free Vibration of Truncated Conical Shell and Its Combinations with Uniform Boundary Restraints

This paper presents a dynamic stiffness formulation for the free vibration analysis of truncated conical shell and its combinations with uniform boundary restraints. The displacement fields are expressed as power series, and the coefficients of the series are obtained as recursion formula by substituting the power series into the governing equations. Then, the general solutions can be replaced by an algebraic sum which contains eight base functions, which can diminish the number of degrees of freedom directly. The dynamic stiffness matrix is formulated based on the relationship between the force and displacement along the boundary lines. In the formulation, arbitrary elastic boundary restraints can be realized by introducing four sets of boundary springs along the displacement directions at the boundary lines. The modeling methodology can be easily extended to the combinations of conical shells with different thickness and semivertex angles. The convergence and accuracy of the present formulation are demonstrated by comparing with the finite element method using several numerical examples. Effects of the elastic boundary condition and geometric dimension on the free vibration characteristics are investigated, and several representative mode shapes are depicted for illustrative purposes.

[1]  Weiguo Wu,et al.  Structural and Acoustic Response of a Finite Stiffened Conical Shell , 2015 .

[2]  J. Banerjee,et al.  Free vibration of functionally graded beams and frameworks using the dynamic stiffness method , 2018 .

[3]  J. Banerjee,et al.  Free flexural vibration of tapered beams , 2019, Computers & Structures.

[4]  Q. Cao,et al.  Free vibration of truncated conical shells with elastic boundary constraints and added mass , 2019, International Journal of Mechanical Sciences.

[5]  Moshe Eisenberger,et al.  Exact vibration frequencies of segmented axisymmetric shells , 2006 .

[6]  M. Nefovska-Danilović,et al.  In-plane free vibration and response analysis of isotropic rectangular plates using the dynamic stiffness method , 2015 .

[7]  Phillip L. Gould,et al.  Free Vibration of Shells of Revolution Using FEM , 1974 .

[8]  Xiang Liu,et al.  An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies , 2021 .

[9]  Stephen J. Elliott,et al.  Wave interpretation of numerical results for the vibration in thin conical shells , 2014 .

[10]  Hui Li,et al.  Dynamic stiffness formulation for in-plane and bending vibrations of plates with two opposite edges simply supported , 2018 .

[11]  Y. Kerboua,et al.  Vibration analysis of truncated conical shells subjected to flowing fluid , 2010 .

[12]  M. Eslami,et al.  Free vibration of joined conical-conical shells , 2017 .

[13]  X. Liu,et al.  Coupled axial-bending dynamic stiffness matrix and its applications for a Timoshenko beam with mass and elastic axes eccentricity , 2020 .

[14]  Tiangui Ye,et al.  Harmonic response analysis of coupled plate structures using the dynamic stiffness method , 2018, Thin-Walled Structures.

[15]  A. N. Bergin,et al.  Natural frequencies of cross-ply laminated singly curved panels , 1996 .

[16]  Ömer Civalek,et al.  Discrete singular convolution method for the free vibration analysis of rotating shells with different material properties , 2017 .

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

[18]  Guoyong Jin,et al.  A modified Fourier series solution for vibration analysis of truncated conical shells with general boundary conditions , 2014 .

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

[20]  Meixia Chen,et al.  An analytic method for free and forced vibration analysis of stepped conical shells with arbitrary boundary conditions , 2017 .

[21]  M. Nefovska-Danilović,et al.  Dynamic stiffness method in the vibration analysis of circular cylindrical shell , 2016 .

[22]  J. Banerjee,et al.  Dynamic stiffness matrix of a conical bar using the Rayleigh-Love theory with applications , 2020 .

[23]  Jun Li,et al.  Free vibration analyses of axially loaded laminated composite beams using a unified higher-order shear deformation theory and dynamic stiffness method , 2016 .

[24]  David P. Thambiratnam,et al.  Axisymmetric free vibration analysis of conical shells , 1993 .

[25]  N. Cuong,et al.  FREE VIBRATION ANALYSIS OF JOINED COMPOSITE CONICAL-CONICAL-CONICAL SHELLS CONTAINING FLUID , 2016 .

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

[27]  Reza Ansari,et al.  A novel variational numerical method for analyzing the free vibration of composite conical shells , 2015 .

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

[29]  N. Ganesan,et al.  Frequency response of shell-plate combinations , 1996 .

[30]  M. A. Kouchakzadeh,et al.  Free vibration analysis of joined conical shells: Analytical and experimental study , 2014 .

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

[32]  Guang Meng,et al.  A Domain Decomposition Method for Vibration Analysis of Conical Shells With Uniform and Stepped Thickness , 2013 .

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

[34]  J. R. Banerjee,et al.  Free vibration analysis for plates with arbitrary boundary conditions using a novel spectral-dynamic stiffness method , 2016 .

[35]  M. Mahmoud.  Natural frequency of axially functionally graded, tapered cantilever beams with tip masses , 2019, Engineering Structures.

[36]  Robin S. Langley,et al.  A dynamic stiffness technique for the vibration analysis of stiffened shell structures , 1992 .