The dynamic stability of a nonhomogeneous orthotropic elastic truncated conical shell under a time dependent external pressure

2002 ◽  
Vol 13 (3) ◽  
pp. 329-343 ◽  
Author(s):  
A.H. Sofiyev ◽  
O. Aksogan
Keyword(s):  
Dynamic Stability ◽  
Conical Shell ◽  
External Pressure ◽  
Time Dependent ◽  
Truncated Conical Shell

The dynamic stability of a laminated truncated conical shell with variable elasticity moduli and densities subject to a time-dependent external pressure

2002 ◽  
Vol 37 (3) ◽  
pp. 201-210 ◽  
Author(s):  
O Aksogan ◽  
A. H Sofiyev
Keyword(s):  
Dynamic Stability ◽  
Conical Shell ◽  
External Pressure ◽  
Variable Coefficients ◽  
Time Dependent ◽  
Critical Parameters ◽  
Dynamic Factor ◽  
Elasticity Moduli ◽  
Critical Dynamic ◽  
Truncated Conical Shell

This study considers the dynamic stability of a laminated truncated conical shell with variable elasticity moduli and densities in the thickness direction, subject to a uniform external pressure, which is a power function of time. Initially, the dynamic stability and compatibility equations of a laminated elastic truncated conical shell with variable elasticity moduli and densities, subject to an external pressure, have been obtained. Then, employing Galerkin's method, those equations have been reduced to a system of time-dependent differential equations with variable coefficients. Finally, applying a mixed variational method of Ritz type, the critical dynamic and static loads, the corresponding wave numbers and the dynamic factor have been found analytically. Using those results, the effects of the variations in elasticity moduli and densities, the number and ordering of the layers, the semivertex angle and the power of time in the external pressure expression are studied via pertinent computations. It is observed that these factors have appreciable effects on the critical parameters of the problem in the heading.

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.

Dynamic Stability of a Cylindrical Shell under Alternating Axial External Pressure

2017 ◽  
Vol 60 (4) ◽  
pp. 508-513 ◽  
Author(s):  
V. N. Bakulin ◽  
E. N. Volkov ◽  
A. I. Simonov
Keyword(s):  
Cylindrical Shell ◽  
Dynamic Stability ◽  
External Pressure

Analytical Treatment of In-Plane Parametrically Excited Undamped Vibrations of Simply Supported Parabolic Arches

2003 ◽  
Vol 125 (1) ◽  
pp. 73-79 ◽  
Author(s):  
Dimitris S. Sophianopoulos ◽  
George T. Michaltsos
Keyword(s):  
Differential Equations ◽  
Free Vibration ◽  
Dynamic Stability ◽  
Parametric Excitation ◽  
Stability Problem ◽  
Axial Loading ◽  
Time Dependent ◽  
Analytical Treatment ◽  
Simply Supported ◽  
Forced Motion

The present work offers a simple and efficient analytical treatment of the in-plane undamped vibrations of simply supported parabolic arches under parametric excitation. After thoroughly dealing with the free vibration characteristics of the structure dealt with, the differential equations of the forced motion caused by a time dependent axial loading of the form P=P0+Pt cos θt are reduced to a set of Mathieu-Hill type equations. These may be thereafter tackled and the dynamic stability problem comprehensively discussed. An illustrative example based on Bolotin’s approach produces results validating the proposed method.

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.

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