Flutter of high-dimension nonlinear system for a FGM truncated conical shell

2017 ◽  
Vol 25 (1) ◽  
pp. 47-61 ◽  
Author(s):  
Y. X. Hao ◽  
S. W. Yang ◽  
W. Zhang ◽  
M. H. Yao ◽  
A. W. Wang
Keyword(s):  
Nonlinear System ◽  
High Dimension ◽  
Conical Shell ◽  
Truncated Conical Shell

scholarly journals Natural Vibrations of the Reinforced Tapered Shell with Taking Into Account the Viscoelastic Properties of the Material

2021 ◽  
Vol 264 ◽  
pp. 01011
Author(s):  
Matlab Ishmamatov ◽  
Nurillo Kulmuratov ◽  
Nasriddin Ахmedov ◽  
Shaxob Хаlilov ◽  
Sherzod Ablakulov
Keyword(s):  
Conical Shell ◽  
Variational Principles ◽  
Variational Equation ◽  
Frequency Equation ◽  
Main Element ◽  
Algebraic Equations ◽  
Natural Vibrations ◽  
Natural Oscillations ◽  
Conical Shells ◽  
Truncated Conical Shell

In this paper, the integro-differential equations of natural oscillations of a viscoelastic ribbed truncated conical shell are obtained based on the Lagrange variational equation. The general research methodology is based on the variational principles of mechanics and variational methods. Geometrically nonlinear mathematical models of the deformation of ribbed conical shells are obtained, considering such factors as the discrete introduction of edges. Based on the finite element method, a method for solving and an algorithm for the equations of natural oscillations of a viscoelastic ribbed truncated conical shell with articulated and freely supported edges is developed. The problem is reduced to solving homogeneous algebraic equations with complex coefficients of large order. For a solution to exist, the main determinant of a system of algebraic equations must be zero. From this condition, we obtain a frequency equation with complex output parameters. The study of natural vibrations of viscoelastic panels of truncated conical shells is carried out, and some characteristic features are revealed. The complex roots of the frequency equation are determined by the Muller method. At each iteration of the Muller method, the Gauss method is used with the main element selection. As the number of edges increases, the real and imaginary parts of the eigenfrequencies increase, respectively.

The Nonlinear Internal Resonance Analysis of a Rotary Truncated Conical Shell

2006 ◽  
Author(s):  
Changping Chen ◽  
Liming Dai
Keyword(s):  
Conical Shell ◽  
Dynamic Properties ◽  
Harmonic Balance Method ◽  
Multiple Scale ◽  
High Order ◽  
Internal Dynamic ◽  
Conical Shells ◽  
System A ◽  
Truncated Conical Shell ◽  
Low Order

Truncated conical shell is an important structure that has been widely applied in many engineering fields. The present paper studies the internal dynamic properties of a truncated rotary conical shell with considerations of intercoupling the high and low order modals by utilizing Harmonic Balance Method. To disclosure the detailed intercoupling characteristics of high order modal and low order modal of the system, a truncated shallow shell is studied and the internal response properties of the system is investigated by using the Multiple Scale Method. Abundant dynamic characteristics are found in the research of this paper. It is found in the research of the paper that the high-order modals of rotating conical shells have significant effects to the amplitude and frequency of the shells.

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

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Chunyu Zhang ◽  
Guoyong Jin ◽  
Zhihao Wang ◽  
Xuqin Qian ◽  
Linghua Tian
Keyword(s):  
Power Series ◽  
Free Vibration ◽  
Conical Shell ◽  
Dynamic Stiffness ◽  
Recursion Formula ◽  
Geometric Dimension ◽  
Mode Shapes ◽  
Elastic Boundary ◽  
Truncated Conical Shell ◽  
Boundary Lines

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.

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