An Approximate Method for the Determination of the Response Frequency of Pipe Whip

1980 ◽  
Vol 102 (2) ◽  
pp. 174-181
Author(s):  
S. A. Haktanir ◽  
G. C. Tolle
Keyword(s):  
Fluid Flow ◽  
Linear Problem ◽  
Natural Frequencies ◽  
Pipe Wall ◽  
Virtual Work ◽  
Fluid Velocity ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Work Technique

This paper is concerned with the effect of fluid flow on the static and dynamic characteristics of a simply supported pipe having a hole through the pipe wall to permit a fluid flow. In this approximate analysis based on the virtual work technique, system natural frequencies and mode shapes are determined and compared to the analytical solution of the linear problem given by G. W. Housner [3] and experimental solution of H. L. Dodds, Jr., and H. L. Runyan [2]. An approximate solution satisfying the initial and boundary conditions is presented for free vibrations and for steady-state forced vibrations for the nonlinear problem. In addition, the critical fluid velocity at which the system becomes statically unstable is verified.

scholarly journals High-Fidelity Sensitivity Analysis of Modal Properties of Mistuned Bladed Disks Regarding Material Anisotropy

2018 ◽  
Author(s):  
Adam Koscso ◽  
Guido Dhondt ◽  
E. P. Petrov
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Finite Element Models ◽  
Coordinate Systems ◽  
Bladed Disks ◽  
Bladed Disk ◽  
Material Orientation

A new method has been developed for sensitivity calculations of modal characteristics of bladed disks made of anisotropic materials. The method allows the determination of the sensitivity of the natural frequencies and mode shapes of mistuned bladed disks with respect to anisotropy angles that define the crystal orientation of the monocrystalline blades using full-scale finite element models. An enhanced method is proposed to provide high accuracy for the sensitivity analysis of mode shapes. An approach has also been developed for transforming the modal sensitivities to coordinate systems used in industry for description of the blade anisotropy orientations. The capabilities of the developed methods are demonstrated on examples of a single blade and a mistuned realistic bladed disk finite element models. The modal sensitivity of mistuned bladed disks to anisotropic material orientation is thoroughly studied.

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.

Determination of the first n modes of a tall building from a reduced eigenvalue problem

1964 ◽  
Vol 54 (4) ◽  
pp. 1233-1254
Author(s):  
Moshe F. Rubinstein
Keyword(s):  
Eigenvalue Problem ◽  
Natural Frequencies ◽  
Tall Building ◽  
Degree Of Freedom ◽  
Mode Shapes ◽  
Story Building

Abstract The first n natural frequencies and mode shapes of an N degree of freedom structure (n < N) are derived from the solution of a reduced eigenvalue problem of order smaller than N. The reduced eigenvalue problem is formulated by using experience to select approximations to the first n modes desired. Accuracy is improved when more than n modes are selected. The method is illustrated by a study on an 18 story building.

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.

The Influence of Internal Pressure on Pipeline Natural Frequency

2009 ◽  
Author(s):  
Andre´ Luiz Lupinacci Massa ◽  
Nelson Szilard Galgoul ◽  
Nestor Oscar Guevara Junior ◽  
Antonio Carlos Fernandes ◽  
Fa´bio Moreira Coelho ◽  
...  
Keyword(s):  
Internal Pressure ◽  
Natural Frequency ◽  
Axial Force ◽  
Natural Frequencies ◽  
Pipe Wall ◽  
Element Model ◽  
Straight Pipe ◽  
Temperature Expansion ◽  
Force Concept

Galgoul et al. (2004) have written a previous paper in which they have pointed out the conservatism of the latest recommendations for pipeline freespan evaluations, associated to the way the axial force is considered in the determination of the pipeline natural frequency. First because it fails to consider the fact, that the axial force of a sagging pipe, subject to temperature expansion, is much smaller than that of a straight pipe. Second because the effective axial force caused by internal pressure should not be used to determine the pipeline natural frequency. Fyrileiv and Collberg (2005) also discussed this aspect. In order to back up their previous arguments the authors decided to perform some tests an axially restrained pipeline at both ends, which was pressurized in order to justify their claims that these pipelines are not only under tension (and not compression), but also that their natural frequencies increase instead of reducing, although they do bend out because of the pressure, reaching a point of instability. The authors understand the effective axial force concept and the enormous simplifications, which it brings to an otherwise cumbersome problem, but wish to emphasize that these advantages are not unlimited and that this is one of these restrictions. To back up the text results a finite element model has been produced, in which the internal pressure is taken into account as it actually is (and not as an axial force) to show that the pipe wall stresses can only be obtained correctly in this manner.

An Extension of the Holzer Method for Redundant Drive Trains

1974 ◽  
Vol 96 (2) ◽  
pp. 697-698 ◽  
Author(s):  
M. S. Hundal
Keyword(s):  
Natural Frequencies ◽  
Mode Shapes ◽  
System Of Equations ◽  
Redundant System ◽  
Drive Trains ◽  
Redundant Drive

A method is described for the determination of natural frequencies and mode shapes of closed drive trains. It is an extension of the Holzer method to a redundant system. The “error” for a given value of frequency is computed by the solution of a tridiagonal system of equations.

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.

scholarly journals On the determination of natural frequencies and mode shapes of cable-stayed bridges

2001 ◽  
Vol 25 (12) ◽  
pp. 1099-1115 ◽  
Author(s):  
F.T.K. Au ◽  
Y.S. Cheng ◽  
Y.K. Cheung ◽  
D.Y. Zheng
Keyword(s):  
Natural Frequencies ◽  
Mode Shapes ◽  
Cable Stayed Bridges
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