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.

Optimization of Joined Conical Shells Based on Free Vibration

2016 ◽  
Author(s):  
Rayehe Karimi Mahabadi ◽  
Firooz Bakhtiari-Nejad
Keyword(s):  
Genetic Algorithm ◽  
Free Vibration ◽  
Natural Frequency ◽  
Conical Shell ◽  
Fibre Orientation ◽  
Laminated Composite ◽  
Conical Shells ◽  
Design Variables

This work aims at utilizing genetic algorithm (GA) to pursue the optimization of joined conical shells based on free vibration. Semi-vertex angles of cones and fibre orientation of the laminated composite are considered as design variables. First, the model is simulated in ABAQUS, the model is validated by comparing its results to other obtained from the literature. Then the first non-zero natural frequency of isotropic joined conical shell is maximized by changing the two semi-vertex angles of cones. Last the fibre orientation of laminated joined shells are optimized to achieve the maximum natural frequency.

Natural Frequency Analysis of Multilayer Truncated Conical Shells Containing Quiescent Fluid on Elastic Foundation with Different Boundary Conditions

2021 ◽  
Author(s):  
Reza Paknejad ◽  
Faramarz Ashenai Ghasemi ◽  
Keramat Malekzadeh Fard
Keyword(s):  
Boundary Conditions ◽  
Natural Frequency ◽  
Elastic Foundation ◽  
Conical Shell ◽  
Weight Functions ◽  
Conical Shells ◽  
Different Boundary Conditions ◽  
Fundamental Natural Frequency ◽  
Natural Frequency Analysis ◽  
Quiescent Fluid

In this paper, natural frequency of a multilayer truncated conical composite shell conveying quiescent fluid on elastic foundation with different boundary conditions is investigated and analyzed. The governing equations are presented based on the first-order shear deformation theory. Bernoulli’s equation and velocity potential have been used in the shell-fluid interface to obtain the fluid pressure. The fluid used in this study is considered non-compressible and non-viscous. The beam functions and the Galerkin weight functions method are used to describe and solve the coupled system of differential equations. Three types of boundary conditions are considered to investigate the natural frequency of the conical shells. The results show that the presence of the fluid in the conical shell reduces the fundamental natural frequency values. Also, by changing the semi-vertex conical angle from [Formula: see text] to [Formula: see text] for the simply support boundary conditions, the fundamental natural frequency value for the composite conical shell without and with fluid increases, and the presence of the elastic foundation increases the frequencies of the empty and full-fluid composite conical shells.

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.

Stresses and Displacements in a Rotating Conical Shell

1943 ◽  
Vol 10 (2) ◽  
pp. A53-A61
Author(s):  
J. L. Meriam
Keyword(s):  
Conical Shell ◽  
Body Force ◽  
Theory Of Elasticity ◽  
Common Type ◽  
The Body ◽  
Surface Loading ◽  
Thin Walled Structures ◽  
Special Cases ◽  
Engineering Problems ◽  
Rotating Conical Shell

Abstract The analysis of shells is an important subdivision of the general theory of elasticity, and its application is useful in the solution of engineering problems involving thin-walled structures. A common type of shell is one which possesses symmetry with respect to an axis of revolution. A theory for such shells has been developed by various investigators (1, 2, 3, 6) and applied to a few simple cases such as the cylindrical, spherical, and conical shapes. Boundary conditions, for the most part, have been simple static ones, and conditions of surface loading have been included in certain special cases. This paper extends the theory of axially symmetrical shells by including the body force of rotation about the axis and applies the results to the rotating conical shell. The analysis follows a pattern established by several investigators (1, 2, 3, 6) and for this reason is abbreviated to a considerable extent. Only where the inclusion of the body force makes elucidation advisable or where a slightly different method of approach is used are the steps presented in more detail.

Lateral Vibration of Two Axially Translating Beams Interconnected by a Winkler Foundation

2006 ◽  
Vol 129 (3) ◽  
pp. 380-385 ◽  
Author(s):  
Mohamed Gaith ◽  
Sinan Müftü
Keyword(s):  
Natural Frequencies ◽  
Flexural Rigidity ◽  
Mode Shapes ◽  
Winkler Foundation ◽  
Axial Tension ◽  
Winkler Elastic Foundation ◽  
Critical Tension ◽  
Divergence Instability ◽  
Axially Moving Beams ◽  
Axially Moving

Transverse vibration of two axially moving beams connected by a Winkler elastic foundation is analyzed analytically. The two beams are tensioned, translating axially with a common constant velocity, simply supported at their ends, and of different materials and geometry. The natural frequencies and associated mode shapes are obtained. The natural frequencies of the system are composed of two infinite sets describing in-phase and out-of-phase vibrations. In case the beams are identical, these modes become synchronous and asynchronous, respectively. Divergence instability occurs at a critical velocity and a critical tension; and, divergence and flutter instabilities coexist at postcritical speeds, and divergence instability takes place precritical tensions. The effects of the mass, flexural rigidity, and axial tension ratios of the two beams are presented.

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.

A Refined Theory for Laminated Anisotropic, Cylindrical Shells

1974 ◽  
Vol 41 (2) ◽  
pp. 471-476 ◽  
Author(s):  
J. M. Whitney ◽  
C.-T. Sun
Keyword(s):  
Shear Deformation ◽  
Shell Theory ◽  
Theory Of Elasticity ◽  
Small Radius ◽  
Refined Theory ◽  
Normal Strain ◽  
Governing Equations ◽  
Transverse Normal Strain ◽  
Anisotropic Cylindrical Shell ◽  
Good Agreement

A set of governing equations and boundary conditions are derived which describe the static deformation of a laminated anisotropic cylindrical shell. The theory includes both transverse shear deformation and transverse normal strain, as well as expansional strains. The validity of the theory is assessed by comparing solutions obtained from the shell theory to results obtained from exact theory of elasticity. Reasonably good agreement is observed and both shear deformation and transverse normal strain are shown to be of importance for shells having a relatively small radius-to-thickness ratio.

Evaluating actuator distributions in simply supported truncated thin conical shell with embedded piezoelectric layers

2018 ◽  
Vol 29 (12) ◽  
pp. 2641-2659 ◽  
Author(s):  
Rasa Jamshidi ◽  
Ali A Jafari
Keyword(s):  
Conical Shell ◽  
Piezoelectric Layer ◽  
Cone Angle ◽  
Expansion Method ◽  
Longitudinal Direction ◽  
Modal Expansion ◽  
Simply Supported ◽  
Modal Expansion Method ◽  
Layer Segmentation ◽  
Distributed Actuator

In this investigation, distributed modal actuator forces of simply supported truncated conical shell embedded by a piezoelectric layer are studied. Piezoelectric layer is distributed on the conical shell surface as actuators. Three types of distributions are considered: longitudinal, circumferential, and diagonal distributions. First, electromechanical equations of the conical shell with embedded piezoelectric actuator layer are extracted. Then modal expansion method is used to define independent modal characteristics of the conical shell. For each kind of distribution, three case studies are considered and evaluated. Results showed that in the longitudinal and diagonal distributed actuator, membrane force in the longitudinal direction is the dominant force and in the circumferential distributed actuator, the membrane force in the circumferential direction is the dominant force. The effects of cone angle, piezoelectric thickness, and piezoelectric layer segmentation on modal forces of each distributed actuator are also studied. In circumferential distributed actuator, modal forces increase as the cone angle increases. This phenomenon in the longitudinal and diagonal distributed actuator is almost reversed. The piezoelectric layer segmentation effect on the modal forces distribution is also evaluated, and it showed that this phenomenon has a critical effect on the modal forces distribution.

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 Free Vibration Analysis of Composite Conical Shells with Variable Thickness

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Saira Javed ◽  
F. H. H. Al Mukahal ◽  
M. A. Salama
Keyword(s):  
Free Vibration ◽  
Variable Thickness ◽  
Cone Angle ◽  
Spline Approximation ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Axial Direction ◽  
Thickness Variation ◽  
Node Number ◽  
Conical Shells

Free vibration of conical shells of variable thickness is analysed under shear deformation theory with simply supported and clamped free boundary conditions by applying collocation with spline approximation. Sinusoidal thickness variation of layers is assumed in axial direction. Displacements and rotational functions are approximated by Bickley-type splines of order three and a generalized eigenvalue problem is obtained. This problem is solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The vibration of composite conical shells consisting of three layers and five layers where each layer is made up of different materials is analysed. Parametric studies are made for analysing the frequencies of the shell with respect to the coefficients of thickness variations, length ratio, cone angle, circumferential node number, and different ply angles with different combinations of the materials. The results are presented in terms of tables and graphs.

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