Asymmetric Free Vibrations of Layered Conical Shells

1982 ◽  
Vol 104 (2) ◽  
pp. 453-462 ◽  
Author(s):  
K. Chandrasekaran ◽  
V. Ramamurti
Keyword(s):  
Natural Frequencies ◽  
Middle Surface ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Orthotropic Materials ◽  
Conical Shells ◽  
Shell Models ◽  
Theoretical Predictions ◽  
Parametric Studies ◽  
Ritz Procedure

Asymmetric free vibrations of layered truncated conical shells are studied. Individual layers made of special orthotropic materials and both symmetric and asymmetric stacking with respect to the middle surface are considered. An energy-method based on the Rayleigh-Ritz procedure is employed. The influence of layer arrangements and that of the coupling between bending and stretching on the natural frequencies and mode-shapes are analyzed. Experimental results from tests on two shell models are provided for comparison with theoretical predictions. Numerical results based on extensive parametric studies are presented.

scholarly journals Free Vibrations of Tapered Horseshoe Circular Arch with Constant Volume

2020 ◽  
Vol 10 (16) ◽  
pp. 5431
Author(s):  
Byoung Koo Lee ◽  
Gweon Sik Kim ◽  
Sang Jin Oh ◽  
Tae Eun Lee
Keyword(s):  
Natural Frequencies ◽  
Quadratic Function ◽  
Free Vibrations ◽  
Constant Volume ◽  
Mode Shapes ◽  
Cross Sectional ◽  
Circular Arch ◽  
Taper Function ◽  
Parametric Studies ◽  
Sectional Shape

This paper presents free vibrations of the tapered horseshoe circular arch with a constant volume. The volume of the arch is constant, and the cross-sectional shape of the arch is square and circular. The taper function of the arch is a quadratic function. Differential equations with the boundary conditions that govern the free vibration of such arches are derived and numerically solved to calculate natural frequencies and mode shapes. The natural frequencies of this study agree well with those of the finite element ADINA. Parametric studies of the geometrical and cross-sectional properties of the arch on frequencies and mode shapes are performed and discussed.

scholarly journals Free vibrations of axially functionally graded horseshoe arch

2021 ◽  
Vol 9 (3) ◽  
pp. 251-262
Author(s):  
Gweon Sik Kim ◽  
Sang Jin Oh ◽  
Tae Eun Lee ◽  
Byoung Koo Lee
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Free Vibration ◽  
Natural Frequencies ◽  
Mass Density ◽  
Quadratic Function ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Parametric Studies

This paper deals with free vibrations of the axially functionally graded (AFG) horseshoe arch. The modulus of elasticity and the mass density of AFG material of arch are chosen as a univariate quadratic function. The differential equations with the boundary conditions that govern the free vibration of such arch are derived and numerically solved to calculate natural frequencies and mode shapes. Natural frequencies of this study agree well with those of the finite element ADINA. Parametric studies of the geometrical and mechanical properties of the arch on frequencies and mode shapes are performed and extensively discussed.

Analysis of Free Vibrations of Conical Shells Using Donnell’s Approximations

1995 ◽  
Vol 48 (11S) ◽  
pp. S84-S89
Author(s):  
V. C. M. de Souza ◽  
J. M. F. Saraiva
Keyword(s):  
Shell Theory ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Conical Shells ◽  
Classical Shell Theory ◽  
Clamped Edges

The free vibrations of conical shells, having two open rigidly clamped edges, are investigated by using a variational development of the equations of motion based upon the Classical Shell Theory, and results are compared with those obtained by using Donnell’s approximation in the development of these equations. Through suitable examples, the validity of Donnell’s approximation to compute natural frequencies and mode-shapes of conical shells is shown.

Comparison of Vibration Characteristics of Stiffened Composite Shallow Circular Cylindrical Shell Panels

2002 ◽  
Author(s):  
V. O¨zerciyes ◽  
U. Yuceoglu
Keyword(s):  
Cylindrical Shell ◽  
Natural Frequencies ◽  
Circular Cylindrical Shell ◽  
Free Vibrations ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Shallow Cylindrical Shell ◽  
Parametric Studies ◽  
Complete Set ◽  
Hit And Run

The problem of “Free Vibrations Centrally and Non Centrally Stiffened Composite Shallow Cylindrical Shell Panels” are briefly considered and their vibration characteristics are compared, in detail, in terms of their natural frequencies and the corresponding mode shapes. First, the complete set of composite shallow cylindrical shell equations are reduced to a system of first order ordinary differential equations in “state-vector” form. Then, by making use of the “Modified Transfer Matrix Method”, the effects of the position and the width of the stiffening shell strip in the natural frequencies and the mode shapes of the panel system are plotted and compared. Some significant results of parametric studies and also the possibility of some kind of hit-and-run type of optimization are presented.

OUT-OF-PLANE FREE VIBRATIONS OF CIRCULAR STRIPS WITH VARIABLE BREADTH

2007 ◽  
Vol 07 (03) ◽  
pp. 403-423 ◽  
Author(s):  
BYOUNG KOO LEE ◽  
TAE EUN LEE ◽  
ATHOL J. CARR ◽  
SANG JIN OH
Keyword(s):  
Differential Equations ◽  
Natural Frequencies ◽  
Slenderness Ratio ◽  
Free Vibrations ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
Out Of Plane ◽  
Angle Section ◽  
Parametric Studies ◽  
Experimental Validations

This paper deals with the out-of-plane free vibrations of circular strips with linearly varying breadth. In deriving the differential equations for such strips, the effects of the rotatory and torsional inertias and shear deformation are considered. The differential equations are numerically solved to calculate the natural frequencies and mode shapes. In the numerical examples, three end constraints, i.e. clamped–clamped, clamped-hinged and hinged–hinged ends, are considered. The five lowest frequency parameters and mode shapes are presented. The effects of the rotatory and torsional inertias, and shear parameter on the natural frequencies are evaluated. Parametric studies are carried out for the influence of following parameters of the strip on the natural frequencies: subtended angle, section ratio, thickness ratio, and slenderness ratio. Also presented are the experimental validations of the seven lowest predicted natural frequencies. The natural frequencies obtained by this study agree well with those by the finite element method for both the flexural and torsional modes.

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.

scholarly journals An investigation into the free vibrations of carbon nanotubes using analytical and finite element methods

2021 ◽  
Author(s):  
Ishan Ali Khan
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Eigenvalue Problem ◽  
Natural Frequencies ◽  
Nonlinear Eigenvalue Problem ◽  
Dynamic Stiffness ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Wide Range ◽  
Walled Cnts

Since their discovery, immense attention has been given to carbon nanotubes (CNTs), due to their exceptional thermal, electronic and mechanical properties and, therefore, the wide range of applications in which they are, or can be potentially, employed. Hence, it is important that all the properties of carbon nanotubes are studied extensively. This thesis studies the vibrational frequencies of double-walled and triple-walled CNTs, with and without an elastic medium surrounding them, by using Finite Element Method (FEM) and Dynamic Stiffness Matrix (DSM) formulations, considering them as Euler-Bernoulli beams coupled with van der Waals interaction forces. For FEM modelling, the linear eigenvalue problem is obtained using Galerkin weighted residual approach. The natural frequencies and mode shapes are derived from eigenvalues and eigenvectors, respectively. For DSM formulation of double-walled CNTs, a nonlinear eigenvalue problem is obtained by enforcing displacement and load end conditions to the exact solution of single equation achieved by combining the coupled governing equations. The natural frequencies are obtained using Wittrick-Williams algorithm. FEM formulation is also applied to both double and triple-walled CNTs modelled as nonlocal Euler-Bernoulli beam. The natural frequencies obtained for all the cases, are in agreement with the values provided in literature.

Free Vibrations of Composite Shallow Circular Cylindrical Shell Panels With a Bonded Central Stiffening Shell Strip

2001 ◽  
Author(s):  
U. Yuceoglu ◽  
V. Özerciyes
Keyword(s):  
Shallow Shell ◽  
Natural Frequencies ◽  
Circular Cylindrical Shell ◽  
Adhesive Layer ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Order System ◽  
Theoretical Formulation ◽  
First Order ◽  
Stress Resultant

Abstract This study is concerned with the “Free Vibrations of Composite Shallow Circular Cylindrical Shells or Shell Panels with a Central Stiffening Shell Strip”. The upper and lower shell elements of the stiffened composite system are considered as dissimilar, orthotropic shallow shells. The upper relatively narrow stiffening shell strip is centrally located and adhesively bonded to the lower main shell element In the theoretical formulation, a “First Order Shear Deformation Shell Theory (FSDST)” is employed. The complete set of the shallow shell dynamic equations (including the stress resultant-displacement and the constitutive equations) and the equations of the thin flexible, adhesive layer are first reduced to a set of first order system of ordinary differential equations. This final set forms the governing equations of the problem. Then, they are integrated by means of the “Modified Transfer Matrix Method”. In the adhesive layer, the “hard” and the “soft” adhesive effects are considered. It was found that the material characteristics of the adhesive layer influence the mode shapes and the corresponding natural frequencies of the composite shallow shell panel system. Additionally, some parametric studies on the natural frequencies are presented.

scholarly journals A Study on the Effect of Carbon Nanotubes’ Distribution and Agglomeration in the Free Vibration of Nanocomposite Plates

2020 ◽  
Vol 6 (4) ◽  
pp. 79
Author(s):  
D. S. Craveiro ◽  
M. A. R. Loja
Keyword(s):  
Carbon Nanotubes ◽  
Elastic Properties ◽  
Natural Frequencies ◽  
Mechanical Performance ◽  
Negative Impact ◽  
Free Vibrations ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
Agglomeration Effect ◽  
Performance Predictions

The present work aimed to characterize the free vibrations’ behaviour of nanocomposite plates obtained by incorporating graded distributions of carbon nanotubes (CNTs) in a polymeric matrix, considering the carbon nanotubes’ agglomeration effect. This effect is known to degrade material properties, therefore being important to predict the consequences it may bring to structures’ mechanical performance. To this purpose, the elastic properties’ estimation is performed according to the two-parameter agglomeration model based on the Eshelby–Mori–Tanaka approach for randomly dispersed nano-inclusions. This approach is implemented in association with the finite element method to determine the natural frequencies and corresponding mode shapes. Three main agglomeration cases were considered, namely, agglomeration absence, complete agglomeration, and partial agglomeration. The results show that the agglomeration effect has a negative impact on the natural frequencies of the plates, regardless the CNTs’ distribution considered. For the corresponding vibrations’ mode shapes, the agglomeration effect was shown in most cases not to have a significant impact, except for two of the cases studied: for a square plate and a rectangular plate with symmetrical and unsymmetrical CNTs’ distribution, respectively. Globally, the results confirm that not accounting for the nanotubes’ agglomeration effect may lead to less accurate elastic properties and less structures’ performance predictions.

scholarly journals Effect of Location of Delamination on Free Vibration of Cross-Ply Conical Shells

2012 ◽  
Vol 19 (4) ◽  
pp. 679-692 ◽  
Author(s):  
Sudip Dey ◽  
Amit Karmakar
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Natural Frequencies ◽  
Dynamic Equilibrium ◽  
Twist Angle ◽  
Structural Instability ◽  
Numerical Results ◽  
Mode Shapes ◽  
Iteration Algorithm ◽  
Conical Shells

Location of delamination is a triggering parameter for structural instability of laminated composites. In this paper, a finite element method is employed to determine the effects of location of delamination on free vibration characteristics of graphite-epoxy cross-ply composite pre-twisted shallow conical shells. The generalized dynamic equilibrium equation is derived from Lagrange's equation of motion neglecting Coriolis effect for moderate rotational speeds. The formulation is exercised by using an eight noded isoparametric plate bending element based on Mindlin's theory. Multi-point constraint algorithm is utilized to ensure the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front. The standard eigen value problem is solved by applying the QR iteration algorithm. Finite element codes are developed to obtain the numerical results concerning the effects of location of delamination, twist angle and rotational speed on the natural frequencies of cross-ply composite shallow conical shells. The mode shapes are also depicted for a typical laminate configuration. Numerical results obtained from parametric studies of both symmetric and anti-symmetric cross-ply laminates are the first known non-dimensional natural frequencies for the type of analyses carried out here.

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