The flutter of truncated conical shell subjected to internal supersonic air flow

2014 ◽  
Vol 10 (1) ◽  
pp. 18-35 ◽  
Author(s):  
Zhang Ruili ◽  
Yang Zhichun ◽  
Gao Yang
Keyword(s):  
Conical Shell ◽  
Correction Term ◽  
Differential Quadrature Method ◽  
Cone Angle ◽  
Computational Effort ◽  
Chamber Pressure ◽  
Content Type ◽  
Conical Shells ◽  
Piston Theory ◽  
Truncated Conical Shell

Purpose – The purpose of this paper is to propose a new approach to determine the aeroelastic instability of truncated conical shells. In the proposed approach the governing equation of flutter for a truncated conical shell is established using Love's thin shell theory and the quasi-steady first-order piston theory. Design/methodology/approach – The derivatives in both the governing equations and the boundary conditions are discretized with the differential quadrature method, and the critical flutter chamber pressure is obtained by eigenvalue analysis. Findings – The influence of the shell geometry parameters, such as semi-cone angle, radius-thickness ratio and length-radius ratio, on the critical flutter chamber pressure is studied. Results are also presented to indicate the stabilizing effects of aerodynamic damping and the destabilizing effects of the curvature correction term of piston theory on flutter of truncated conical shell. Originality/value – The present approach is an efficient method for the free vibration and flutter analysis of truncated conical shells due to its high order of accuracy and less requirement of virtual storage and computational effort.

Stability and vibration analysis of an axially moving thin walled conical shell

2021 ◽  
pp. 107754632199760
Author(s):  
Hossein Abolhassanpour ◽  
Faramarz Ashenai Ghasemi ◽  
Majid Shahgholi ◽  
Arash Mohamadi
Keyword(s):  
Natural Frequency ◽  
Conical Shell ◽  
Shell Theory ◽  
Cone Angle ◽  
Theory Of Elasticity ◽  
Lower Velocity ◽  
Motion Equations ◽  
Conical Shells ◽  
Divergence Instability ◽  
Axially Moving

This article deals with the analysis of free vibration of an axially moving truncated conical shell. Based on the classical linear theory of elasticity, Donnell shell theory assumptions, Hamilton principle, and Galerkin method, the motion equations of axially moving truncated conical shells are derived. Then, the perturbation method is used to obtain the natural frequency of the system. One of the most important and controversial results in studies of axially moving structures is the velocity detection of critical points. Therefore, the effect of velocity on the creation of divergence instability is investigated. The other important goal in this study is to investigate the effect of the cone angle. As a novelty, our study found that increasing or decreasing the cone angle also affects the critical velocity of the structure in addition to changing the natural frequency, meaning that with increasing the cone angle, the instability occurs at a lower velocity. Also, the effect of other parameters such as aspect ratio and mechanical properties on the frequency and instability points is investigated.

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 Thermoelastic Analysis of Rotating Functionally Graded Truncated Conical Shell by the Methods of Polynomial Based Differential Quadrature and Fourier Expansion-Based Differential Quadrature

2018 ◽  
Vol 2018 ◽  
pp. 1-19 ◽  
Author(s):  
Aref Mehditabar ◽  
Gholam H. Rahimi ◽  
Kerameat Malekzadeh Fard
Keyword(s):  
Conical Shell ◽  
Fourier Expansion ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Temperature Fields ◽  
Inertia Force ◽  
Power Law Distribution ◽  
Truncated Conical Shell

This paper focuses on the three-dimensional (3D) asymmetric problem of functionally graded (FG) truncated conical shell subjected to thermal field and inertia force due to the rotating part. The FG properties are assumed to be varied along the thickness according to power law distribution, whereas Poisson’s ratio is assumed to be constant. On the basis of 3D Green-Lagrange theory in general curvilinear coordinate, the fundamental equations are formulated and then two versions of differential quadrature method (DQM) including polynomial based differential quadrature (PDQ) and Fourier expansion-based differential quadrature (FDQ) are applied to discretize the resulting differential equations. The reliability of the present approach is validated by comparing with known literature where good agreement is reached using considerably few grid points. The effects of different mechanical boundary conditions, temperature fields, rotating angular speed, and shell thickness on the distributions of stress components and displacement in thickness direction for both axisymmetric and asymmetric cases are graphically depicted.

Distributed Sensing Signals of Truncated Conical Shells With Clamped-Free Boundary Conditions

2009 ◽  
Author(s):  
H. Li ◽  
Z. B. Chen ◽  
H. S. Tzou
Keyword(s):  
Boundary Conditions ◽  
Conical Shell ◽  
Vibration Isolation ◽  
Free Vibrations ◽  
Distributed Sensing ◽  
The Other ◽  
Helical Line ◽  
Circular Membrane ◽  
Conical Shells ◽  
Truncated Conical Shell

In aerospace structures, vehicles, civil structures, conical shells are used to support a part or connect different parts, such as spacecraft adaptors, fixtures of machine tools. This type of structures has the possibility of vibration isolation. The final purpose of the on-going research is to isolate the supported part from the vibration transferred from the other end. As a phase of the research, the present paper emphasizes on the distributed sensing signals and modal voltages of the truncated conical shell. To simulate free vibrations of supported part, one end of the truncated conical shell is clamped and the other end is free. The piezoelectric patches are attached on top skin of the shell along diagonal helical line. This paper presents an analytical procedure of sensing of truncated conical shell supporting a mass. The displacement functions satisfying the special boundary conditions are given. Based on the thin-shell theory and Donnel-Mushtari-Valsov theory, sensing equations of the piezoelectric stripes are derived. The sensing signals consist of four components, i.e. sensing signals due to meridional and circular membrane strains, meridional and circular bending strains. These components are studied separately to show their distributions to the sensing signals. Finally, a case study is carried out using a sample truncated conical shell model with laminated piezoelectric stripes.

Vibrations of Arbitrarily Laminated Fiber Reinforced Composite Material Truncated Conical Shell

1995 ◽  
Vol 14 (9) ◽  
pp. 923-948 ◽  
Author(s):  
Kamal N. Khatri
Keyword(s):  
Composite Material ◽  
Conical Shell ◽  
Fiber Orientation ◽  
Fiber Reinforced ◽  
Governing Equations ◽  
Conical Shells ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite ◽  
Truncated Conical Shell ◽  
Reinforced Composite Material

Governing equations of motion are presented for arbitrarily laminated fiber reinforced composite material truncated conical shell in which each layer is permitted an arbitrary fixed fiber orientation. Each layer has been considered to be of a specially orthotropic material with its directional elastic properties depending on the fiber orientation. Extension, bending, in-plane shear and transverse shear in all the layers have been considered and inertia effects due to transverse, meridional and rotary motions are taken into account. Convenient trigonometric series are used as solution functions in Galerkin's method to reduce the governing equations to sets of matrix equations. The correspondence principle of linear viscoelasticity has been used for evaluating the damping effectiveness of the shell. Computer programs have been developed for axisymmetric and antisymmetric vibrations of multi-layered conical shells with simply supported edges. The influence of apex angle upon the resonance frequencies and the associated system loss factors of laminated FRP conical shells is investigated.

Vibration characteristics of rotating truncated conical shells reinforced with agglomerated carbon nanotubes

2021 ◽  
pp. 107754632110004
Author(s):  
Hassan Afshari ◽  
Hossein Amirabadi
Keyword(s):  
Carbon Nanotubes ◽  
Differential Quadrature Method ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Governing Equations ◽  
Conical Shells ◽  
First Order ◽  
Effective Mechanical Properties ◽  
Comprehensive Study

In this article, a comprehensive study is conducted on the free vibration analysis of rotating truncated conical shells reinforced with functionally graded agglomerated carbon nanotubes The shell is modeled based on the first-order shear deformation theory, and effective mechanical properties are calculated based on the Eshelby–Mori–Tanaka scheme along with the rule of mixture. By considering centrifugal and Coriolis accelerations and initial hoop tension, the set of governing equations is derived using Hamilton’s principle and is solved numerically using the differential quadrature method Convergence and accuracy of the presented model are confirmed and the effects of different parameters on the forward and backward frequencies of the rotating carbon nanotube-reinforced truncated conical shells are investigated.

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

Torsional vibration of functionally graded carbon nanotube reinforced conical shells

2018 ◽  
Vol 25 (1) ◽  
pp. 41-52 ◽  
Author(s):  
Yaser Kiani
Keyword(s):  
Torsional Vibration ◽  
Conical Shell ◽  
Volume Fraction ◽  
Differential Quadrature Method ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Coupled Equations ◽  
Parametric Studies ◽  
Torsional Frequency ◽  
Generalized Differential

AbstractThe present study deals with the free torsional vibration of a composite conical shell made of a polymeric matrix reinforced with carbon nanotubes (CNTs). Distribution of CNTs across the thickness of the conical shell may be uniform or functionally graded. Five different cases of functionally graded reinforcements are considered. First-order shear deformable shell theory compatible with the Donnell kinematic assumptions is used to establish the motion equations of the shell. These equations are two coupled equations which should be treated as an eigenvalue problem. The generalized differential quadrature method is used to obtain a numerical solution for the torsional frequency parameters and the associated mode shapes of the shell. After validating the results of this study for the cases of isotropic homogeneous cone and annular plates, parametric studies are carried out to analyze the influences of geometrical characteristics of the shell, volume fraction of CNTs, and grading profile of the CNTs. It is shown that volume fraction of CNTs is an important factor with regard to torsional frequencies of the shell; however, grading profile does not change the torsional frequencies significantly.

Differential quadrature method for nonlinear fractional partial differential equations

2018 ◽  
Vol 35 (6) ◽  
pp. 2349-2366 ◽  
Author(s):  
Umer Saeed ◽  
Mujeeb ur Rehman ◽  
Qamar Din
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
High Efficiency ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Operational Matrices ◽  
Fractional Partial Differential Equations ◽  
Infinite Domain ◽  
Partial Differential ◽  
Content Type

Purpose The purpose of this paper is to propose a method for solving nonlinear fractional partial differential equations on the semi-infinite domain and to get better and more accurate results. Design/methodology/approach The authors proposed a method by using the Chebyshev wavelets in conjunction with differential quadrature technique. The operational matrices for the method are derived, constructed and used for the solution of nonlinear fractional partial differential equations. Findings The operational matrices contain many zero entries, which lead to the high efficiency of the method and reasonable accuracy is achieved even with less number of grid points. The results are in good agreement with exact solutions and more accurate as compared to Haar wavelet method. Originality/value Many engineers can use the presented method for solving their nonlinear fractional models.

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