Effect of Axial Load on Free Vibration of Orthotropic Truncated Conical Shells

1996 ◽  
Vol 118 (2) ◽  
pp. 164-168 ◽  
Author(s):  
L. Tong
Keyword(s):  
Axial Load ◽  
Compressive Load ◽  
Free Vibrations ◽  
Governing Equations ◽  
Conical Shells ◽  
Material Parameters ◽  
Axial Tension ◽  
Wave Numbers ◽  
Axially Loaded ◽  
Circumferential Wave

An analytical solution in the form of a power series is obtained for the three governing equations of free vibrations of axially loaded orthotropic conical shells. Numerical results are presented for the frequency parameters and the associated circumferential wave numbers of the axially loaded shells with different geometric and material parameters and under two types of boundary conditions. It is noted that the axially compressive load decreases the frequency parameters while the axial tension load increases the frequency parameters.

Free Vibration of Axially Loaded Laminated Conical Shells

1999 ◽  
Vol 66 (3) ◽  
pp. 758-763 ◽  
Author(s):  
L. Tong
Keyword(s):  
Free Vibration ◽  
Axial Load ◽  
Governing Equations ◽  
Load Effect ◽  
Critical Buckling Load ◽  
Conical Shells ◽  
Axial Tension ◽  
Axially Loaded ◽  
Constant Axial Load ◽  
Laminated Conical Shells

Analytical solutions for the three displacements are obtained, in the form of power series, directly from the three governing equations for free vibration of laminated conical shells under axial load. Numerical results are presented for free vibration of axially loaded laminated conical shells with different geometric parameters and under two types of boundary conditions. It is found that an axial tension increases the frequencies while an axial compression decreases the frequencies. For the shells studied, the effect of axial load on the lowest frequency of the shell is found to be not sensitive to change in semivertex angle when the applied axial load is kept as a constant fraction of the critical buckling load. However, the axial load effect becomes very sensitive to variation in semivertex angle when a constant axial load is applied.

Axially Loaded Timoshenko Rotors From a Prestressed Continuum Approach

2008 ◽  
Author(s):  
Pradeep Mahadevan ◽  
Anindya Chatterjee
Keyword(s):  
Nonlinear Elasticity ◽  
Timoshenko Beam ◽  
Axial Load ◽  
Constant Speed ◽  
Governing Equations ◽  
Continuum Approach ◽  
Straightforward Application ◽  
Axially Loaded ◽  
The Continuum

We consider an axially loaded Timoshenko rotor rotating at a constant speed and derive its governing equations from a continuum viewpoint. The primary aim of this paper is to understand the source and role of gyroscopic terms, when the rotor is viewed not as a Timoshenko beam but as a genuine 3D continuum. We offer the primary insight that macroscopically observed gyroscopic terms may also, quite equivalently, be viewed as external manifestations of internally existing spin-induced prestresses at the continuum level. To demonstrate this idea with an analytical example (the Timoshenko rotor), we have studied the reliable equations of Choi et al. (Journal of Vibration and Acoustics, 114, 1992, 249–259). Using a straightforward application of our insight in the framework of nonlinear elasticity, we obtain equations that exactly match Choi et al. for the case with no axial load. For the case of axial preload, our straightforward formulation leads to a slightly different set of equations that have negligible numerical consequence for solid rotors. However, we offer a macroscopic, intuitive, justification for modifying our formulation so as to obtain the exact equations of Choi et al. with the axial load included.

Nonlinear Free Vibrations Analysis of Delaminated Composite Conical Shells

2019 ◽  
Vol 20 (01) ◽  
pp. 2050010 ◽  
Author(s):  
Abbas Kamaloo ◽  
Mohsen Jabbari ◽  
Mehdi Yarmohammad Tooski ◽  
Mehrdad Javadi
Keyword(s):  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Laminated Composite ◽  
Middle Surface ◽  
Free Vibrations ◽  
Wave Number ◽  
Vertex Angle ◽  
Conical Shells ◽  
Circumferential Wave ◽  
Delamination Length

This paper examines the nonlinear free vibration of laminated composite conical shells throughout the circumferential delamination. First, based on the energy method, the governing equation of motion for the shell was derived. To simplify the analysis, the nonlinear partial differential equations were reduced into a system of coupled ordinary differential equations using Galerkin’s method. Consequently, the results were obtained by the numerical methods. Finally, the effects of delamination, variations in the delamination length, conical shells characteristics, materials property and circumferential wave number on the nonlinear response of delaminated composite conical shells were examined. The results show that the presence of delamination leads to increase in the amplitude of oscillations for the shells. Besides, the increase in the delamination length and decrease of the circumferential wave number, number of layers, and half vertex angle of the cone and orthotropy bring about a decrease in the nonlinearity of delaminated composite conical shells. However, an increase of the middle surface radius of the shell leads to a reduction of the nonlinearity as well as an increase of the amplitude.

Vibration Analysis of Postbuckled Timoshenko Beams Using a Numerical Solution Methodology

2013 ◽  
Vol 9 (2) ◽  
Author(s):  
M. Faghih Shojaei ◽  
R. Ansari ◽  
V. Mohammadi ◽  
H. Rouhi
Keyword(s):  
Boundary Conditions ◽  
Numerical Solution ◽  
Natural Frequency ◽  
Axial Load ◽  
Continuation Method ◽  
Free Vibrations ◽  
Timoshenko Beams ◽  
Governing Equations ◽  
Technical Interest ◽  
Solution Methodology

In this article, a numerical solution methodology is presented to study the postbuckling configurations and free vibrations of Timoshenko beams undergoing postbuckling. The effect of geometrical imperfection is taken into account, and the analysis is carried out for different types of boundary conditions. Based on Hamilton's principle, the governing equations and corresponding boundary conditions are derived. After introducing a set of differential matrix operators that is used to discretize the governing equations and boundary conditions, the pseudo-arc length continuation method is applied to solve the postbuckling problem. Then, the problem of free vibration around the buckled configurations is solved as an eigenvalue problem using the solution obtained from the nonlinear problem in the previous step. This study shows that, when the axial load in the postbuckling domain increases, the vibration mode shape of buckled beam corresponding to the fundamental frequency may change. Another finding that can be of great technical interest is that, for all types of boundary conditions and in both prebuckling and postbuckling domains, the natural frequency of imperfect beam is higher than that of ideal beam. Also, it is observed that, by increasing the axial load, the natural frequency of both ideal and imperfect beams decreases in the prebuckling domain, while it increases in the postbuckling domain. The reduction of natural frequency in the transition area from the prebuckling domain to the postbuckling domain is due to the severe instability of the structure under the axial load.

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.

scholarly journals Vibration of rotating circular cylindrical shells with distributed springs

2021 ◽  
Vol 37 ◽  
pp. 346-358
Author(s):  
Fuchun Yang ◽  
Xiaofeng Jiang ◽  
Fuxin Du
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Shell Theory ◽  
Rotation Speed ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Governing Equations ◽  
Natural Response ◽  
Circular Cylindrical Shells ◽  
The Galerkin Method

Abstract Free vibrations of rotating cylindrical shells with distributed springs were studied. Based on the Flügge shell theory, the governing equations of rotating cylindrical shells with distributed springs were derived under typical boundary conditions. Multicomponent modal functions were used to satisfy the distributed springs around the circumference. The natural responses were analyzed using the Galerkin method. The effects of parameters, rotation speed, stiffness, and ratios of thickness/radius and length/radius, on natural response were also examined.

Photoelastic Analysis on Different Retention Methods of Implant-Supported Prosthesis

2015 ◽  
Vol 41 (3) ◽  
pp. 258-263 ◽  
Author(s):  
Angélica Castro Pimentel ◽  
Marcello Roberto Manzi ◽  
Cristiane Ibanhês Polo ◽  
Claudio Luiz Sendyk ◽  
Maria da Graça Naclério-Homem ◽  
...  
Keyword(s):  
Stress Distribution ◽  
Axial Load ◽  
Testing Machine ◽  
Compressive Load ◽  
Lower Intensity ◽  
Photoelasticity Method ◽  
Universal Testing ◽  
Isochromatic Fringes ◽  
Photoelastic Analysis ◽  
Compressive Axial Load

The aim of this study was to evaluate the stress distribution of different retention systems (screwed, cemented, and mixed) in 5-unit implant-supported fixed partial dentures through the photoelasticity method. Twenty standardized titanium suprastructures were manufactured, of which 5 were screw retained, 5 were cement retained, and 10 were mixed (with an alternating sequence of abutments), each supported by 5 external hexagon (4.0 mm × 11.5 mm) implants. A circular polariscope was used, and an axial compressive load of 100 N was applied on a universal testing machine. The results were photographed and qualitatively analyzed. We observed the formation of isochromatic fringes as a result of the stresses generated around the implant after installation of the different suprastructures and after the application of a compressive axial load of 100 N. We conclude that a lack of passive adaptation was observed in all suprastructures with the formation of low-magnitude stress in some implants. When cemented and mixed suprastructures were subjected to a compressive load, they displayed lower levels of stress distribution and lower intensity fringes compared to the screwed prosthesis.

Free Vibrations of Thick, Complete Conical Shells of Revolution From a Three-Dimensional Theory

2005 ◽  
Vol 72 (5) ◽  
pp. 797-800 ◽  
Author(s):  
Jae-Hoon Kang ◽  
Arthur W. Leissa
Keyword(s):  
Ritz Method ◽  
Three Dimensional ◽  
Axial Direction ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Vibration Frequencies ◽  
Shells Of Revolution ◽  
Dimensional Theory ◽  
Conical Shells ◽  
Cylindrical Coordinate

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution in which the bottom edges are normal to the midsurface of the shells based upon the circular cylindrical coordinate system using the Ritz method. Comparisons are made between the frequencies and the corresponding mode shapes of the conical shells from the authors' former analysis with bottom edges parallel to the axial direction and the present analysis with the edges normal to shell midsurfaces.

On the Motion of Granular Materials Due to Shear

2000 ◽  
Author(s):  
Mehrdad Massoudi ◽  
Tran X. Phuoc
Keyword(s):  
Finite Difference ◽  
Granular Materials ◽  
Continuum Model ◽  
Theory Model ◽  
Governing Equations ◽  
Flat Plates ◽  
Material Parameters ◽  
Finite Difference Technique ◽  
Linear Differential ◽  
The Continuum

Abstract In this paper we study the flow of granular materials between two horisontal flat plates where the top plate is moving with a constant speed. The constitutive relation used for the stress is based on the continuum model proposed by Rajagopal and Massoudi (1990), where the material parameters are derived using the kinetic theory model proposed by Boyle and Massoudi (1990). The governing equations are non-dimensionalized and the resulting system of non-linear differential equations is solved numerically using finite difference technique.

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