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.

scholarly journals Vibration analysis of multi-stepped and multi-damaged parabolic arches using GDQ

2014 ◽  
Vol 2 (1) ◽  
Author(s):  
Erasmo Viola ◽  
Marco Miniaci ◽  
Nicholas Fantuzzi ◽  
Alessandro Marzani
Keyword(s):  
Boundary Conditions ◽  
Cross Sections ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Internal Boundary ◽  
Radius Of Curvature ◽  
Inertia Effects ◽  
Circular Arch

AbstractThis paper investigates the in-plane free vibrations of multi-stepped and multi-damaged parabolic arches, for various boundary conditions. The axial extension, transverse shear deformation and rotatory inertia effects are taken into account. The constitutive equations relating the stress resultants to the corresponding deformation components refer to an isotropic and linear elastic material. Starting from the kinematic hypothesis for the in-plane displacement of the shear-deformable arch, the equations of motion are deduced by using Hamilton’s principle. Natural frequencies and mode shapes are computed using the Generalized Differential Quadrature (GDQ) method. The variable radius of curvature along the axis of the parabolic arch requires, compared to the circular arch, a more complex formulation and numerical implementation of the motion equations as well as the external and internal boundary conditions. Each damage is modelled as a combination of one rotational and two translational elastic springs. A parametric study is performed to illustrate the influence of the damage parameters on the natural frequencies of parabolic arches for different boundary conditions and cross-sections with localizeddamage.Results for the circular arch, derived from the proposed parabolic model with the derivatives of some parameters set to zero, agree well with those published over the past years.

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.

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.

Vibrational Analysis of Human Femur Bone

2018 ◽  
Author(s):  
Reza Sadeghi ◽  
Firooz Bakhtiari-Nejad ◽  
Taha Goudarzi
Keyword(s):  
Natural Frequencies ◽  
Vibrational Analysis ◽  
Bone Geometry ◽  
The Body ◽  
Mode Shapes ◽  
Pelvic Bone ◽  
Cross Sectional ◽  
Femur Bone ◽  
Bone Structures ◽  
Elderly Falls

Femur bone is the longest and largest bone in the human skeleton. This bone connects the pelvic bone to the knee and carries most of the body weight. The static behavior of femur bone has been a center of investigation for many years while little attention has been given to its dynamic and vibrational behavior, which is of great importance in sports activities, car crashes and elderly falls. Investigation of natural frequencies and mode shapes of bone structures are important to understand the dynamic and vibrating behaviors. Vibrational analysis of femoral bones is presented using finite element method. In the analysis, the bone was modeled with isotropic and orthotropic mechanical properties. The effect of surrounding bone muscles has also been accounted for as a viscoelastic medium embedding the femur bone. Natural frequencies extracted considering the effects of age aggravated by weakening the elastic modulus and density loss. The effects of real complex bone geometry on natural frequencies are studied and are compared with a simple circular cross-sectional model.

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.

scholarly journals Improved Riccati Transfer Matrix Method for Free Vibration of Non-Cylindrical Helical Springs Including Warping

2012 ◽  
Vol 19 (6) ◽  
pp. 1167-1180 ◽  
Author(s):  
A.M. Yu ◽  
Y. Hao
Keyword(s):  
Free Vibration ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Axial Deformation ◽  
Cross Sectional ◽  
Helical Springs

Free vibration equations for non-cylindrical (conical, barrel, and hyperboloidal types) helical springs with noncircular cross-sections, which consist of 14 first-order ordinary differential equations with variable coefficients, are theoretically derived using spatially curved beam theory. In the formulation, the warping effect upon natural frequencies and vibrating mode shapes is first studied in addition to including the rotary inertia, the shear and axial deformation influences. The natural frequencies of the springs are determined by the use of improved Riccati transfer matrix method. The element transfer matrix used in the solution is calculated using the Scaling and Squaring method and Pad'e approximations. Three examples are presented for three types of springs with different cross-sectional shapes under clamped-clamped boundary condition. The accuracy of the proposed method has been compared with the FEM results using three-dimensional solid elements (Solid 45) in ANSYS code. Numerical results reveal that the warping effect is more pronounced in the case of non-cylindrical helical springs than that of cylindrical helical springs, which should be taken into consideration in the free vibration analysis of such springs.

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.

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