scholarly journals NUMERICAL ANALYSIS OF THE EFFECTS OF THE BENDING STIFFNESS OF THE CABLE AND THE MASS OF STRUCTURAL MEMBERS ON FREE VIBRATIONS OF SUSPENSION BRIDGES

2015 ◽  
Vol 21 (7) ◽  
pp. 948-957 ◽  
Author(s):  
Tatjana Grigorjeva
Keyword(s):  
Natural Frequencies ◽  
Mass Density ◽  
Suspension Bridge ◽  
Free Vibrations ◽  
Bending Stiffness ◽  
Suspension System ◽  
Mode Shapes ◽  
Suspension Bridges ◽  
Fe Method ◽  
Bridge Model

The article determines natural frequencies of vibration and the corresponding mode shapes of a suspension bridge with the varying bending stiffness of cables and examines variations that occur in these characteristics with respect to parametric changes in the bridge. A single span suspension steel footbridge with flexible cables has been selected as an initial model used for studying the dynamic characteristics of a suspension system. With the help of the finite elements (FE) method, parameter studies of the bridge model are presented in which vibration characteristics are studied as a function of structural and material parameters such as the flexural stiffness of the cable and the mass density of structural components. It has been generally found that the bending stiffness of the main cable contributes to a considerable effect on natural frequencies for this type of the suspension system. A simplified expression of predicting natural bending frequencies of the suspension bridge taking into account the bending stiffness of the cable has been developed for the application as the first step in the design process.

The Free Vibrations of Stiffened Drill Strings With Static Curvature

1967 ◽  
Vol 89 (1) ◽  
pp. 23-29 ◽  
Author(s):  
D. A. Frohrib ◽  
R. Plunkett
Keyword(s):  
Natural Frequencies ◽  
Free Vibrations ◽  
Drill String ◽  
Bending Stiffness ◽  
Mode Shapes ◽  
Static Tension ◽  
Lateral Vibration ◽  
Governing Equations ◽  
Deflection Curve ◽  
Wide Range

The natural frequencies of lateral vibration of a long drill string in static tension under its own weight are primarily the same as those of the equivalent catenary. These frequencies and the mode shapes are affected to a certain extent by the bending stiffness and to a greater extent by the static deflection curve due to lateral deflection of the bottom end. In this paper, the governing equations are derived and general solutions are given in an asymptotic expansion with the bending stiffness as the parameter. Specific numerical results are given in dimensionless form for the first three natural frequencies for a very wide range of horizontal tension and several appropriate values of bending stiffness for zero vertical static force at the bottom.

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 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.

In-Plane Free Vibration of Uniform Circular Arches Made of Axially Functionally Graded Materials

2019 ◽  
Vol 19 (08) ◽  
pp. 1950084 ◽  
Author(s):  
Joon Kyu Lee ◽  
Byoung Koo Lee
Keyword(s):  
Free Vibration ◽  
Young’S Modulus ◽  
Natural Frequencies ◽  
Dynamic Equilibrium ◽  
Young's Modulus ◽  
Mass Density ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Governing Equations ◽  
Direct Integral

This study focused on the in-plane free vibration of uniform circular arches made of axially functionally graded (AFG) materials. Based on the dynamic equilibrium of an arch element, the governing equations for the free vibration of an AFG arch are derived in this study, where arbitrary functions for the Young’s modulus and mass density are acceptable. For the purpose of numerical analysis, quadratic polynomials for the Young’s modulus and mass density are considered. To calculate the natural frequencies and corresponding mode shapes, the governing equations are solved using the direct integral method enhanced by the trial eigenvalue method. For verification purposes, the predicted frequencies are compared to those obtained by the general purpose software ADINA. A parametric study of the end constraint, rotatory inertia, modular ratio, radius parameter, and subtended angle for the natural frequencies is conducted and the corresponding mode shapes are reported.

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.

Dynamic Characteristics of Tsing Ma Suspension Bridge

1996 ◽  
Vol 1541 (1) ◽  
pp. 43-50 ◽  
Author(s):  
Siu Kui Au ◽  
Neil Mickleborough ◽  
Paul N. Roschke
Keyword(s):  
Analytical Solutions ◽  
Bridge Deck ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Suspension Bridge ◽  
Mode Shapes ◽  
Out Of Plane ◽  
Quantitative Results ◽  
Suspension Cable ◽  
Bending Modes

Numerical simulation was carried out to determine the dynamic properties of the Tsing Ma Suspension Bridge. Both the structure as a whole and individual subcomponents were modeled. Classical analytical solutions for simplified models from the available literature were compared with the results obtained from a finite-element code. Quantitative results for static deflection, natural frequencies, and mode shapes were compared with analytical solutions from linear theory. Out-of-plane modes were shown to be dominant. For in-plane antisymmetric and symmetric bending modes, in which the suspension cable and bridge deck vibrate in the same direction, the natural frequency of the main span of the bridge is determined to be approximately equal to the square root of the sum of the squares of the frequencies of the cable and bridge deck.

An Exact Solution for the Natural Frequencies of Flexible Beams Undergoing Overall Motions

2003 ◽  
Vol 9 (11) ◽  
pp. 1221-1229 ◽  
Author(s):  
Ali H Nayfeh ◽  
S.A. Emam ◽  
Sergio Preidikman ◽  
D.T. Mook
Keyword(s):  
Exact Solution ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Beam Theory ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Flexible Beam ◽  
Bernoulli Beam ◽  
Flexible Beams ◽  
Euler Bernoulli Beam

We investigate the free vibrations of a flexible beam undergoing an overall two-dimensional motion. The beam is modeled using the Euler-Bernoulli beam theory. An exact solution for the natural frequencies and corresponding mode shapes of the beam is obtained. The model can be extended to beams undergoing three-dimensional motions.

Research on Dynamic Characteristics for Large Span Cable-Stayed Suspension Bridges with CFRP Cables

2013 ◽  
Vol 683 ◽  
pp. 845-850
Author(s):  
Rong Gui Liu ◽  
Guo Ying Feng ◽  
Bei Chen
Keyword(s):  
Dynamic Characteristics ◽  
Natural Vibration ◽  
Natural Frequencies ◽  
Suspension Bridge ◽  
Suspension Bridges ◽  
Bridge Structure ◽  
Reinforced Plastics ◽  
New Type ◽  
Carbon Fibre Reinforced Plastics ◽  
Cable Stayed Bridges

Cable-stayed suspension bridge with Carbon Fibre Reinforced Plastics(CFRP) cables is a new type of bridge structure. To study the dynamic characteristics for this kind of bridges, and its differences from cable-stayed bridges of the same span level, finite element dynamic modle of a Cable-stayed suspension bridge with main span of 1488 meters is established and a series of calculations is done. The results show that, natural frequencies of cable-stayed suspension bridges with CFRP cables are relatively small, integral frequencies are stepped and discontinuous; Its modes are centralized and the natural vibration modes show a lot of coupling; The natural frequencies of this kind of bridges are smaller than cable-stayed bridges of the same span level, the entire stiffness decreased.

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.

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