Modal Characteristics of Simply Supported Lightweight Long Cylinders

2002 ◽  
Author(s):  
L. Moxey ◽  
H. Hamidzadeh
Keyword(s):  
Analytical Modeling ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Infinite Length ◽  
Solid Cylinder ◽  
Complex Moduli ◽  
Boundary Stress ◽  
Linear Viscoelastic ◽  
Constant Complex

In the study of free vibration of solid cylinders a linear viscoelastic cylinder of an infinite length models the medium. The analytical modeling is based on three dimensional wave propagation utilizing constant complex moduli. The solution is achieved by determining the displacement and stress on the surface, and by complying with requirements at the boundary. Analysis was conducted to express displacement stresses at any point of the solid cylinder to boundary stress. Dimensionless natural frequencies and mode shapes for different circumferential and axial wave numbers are determined.

scholarly journals Free Vibration of Thick Multilayer Cylinders

1995 ◽  
Vol 2 (5) ◽  
pp. 393-401 ◽  
Author(s):  
H. R. Hamidzadeh ◽  
N. N. Sawaya
Keyword(s):  
Free Vibration ◽  
Elastic Moduli ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Single Layer ◽  
Propagator Matrix ◽  
Infinite Extent ◽  
Linear Viscoelastic ◽  
Elastic Cylinders ◽  
Constant Complex

In this study of the free vibration of multilayer thick cylinders, the medium is modeled by laminated linear viscoelastic cylinders of an infinite extent. The analytical modeling is based on three-dimensional wave propagation utilizing constant complex elastic moduli. The solution is achieved by determining the displacements and stresses for each interface and by complying with requirements at the interfaces. A propagator matrix relating the boundary displacements to boundary stresses is developed. Dimensionless natural frequencies and modal loss factors for different circumferential and axial wave numbers are determined. The validity of the proposed method is verified by comparing the results for one-, two-, and three-layer elastic cylinders with properties similar to those reported for an equivalent single layer.

Split Vibration Modes in Acoustically-Coupled Disk Stacks

1995 ◽  
Author(s):  
Jung-Ge Tseng ◽  
Jonathan Wickert
Keyword(s):  
Natural Frequencies ◽  
Three Dimensional ◽  
System Level ◽  
Thin Plates ◽  
Mode Shapes ◽  
Design Parameters ◽  
Phase System ◽  
Acoustic Coupling ◽  
Annular Plates ◽  
Vibration Model

Abstract Vibration of an array of stacked annular plates, in which adjacent plates couple weakly through an acoustic layer, is investigated through experimental and theoretical methods. Such acoustic coupling manifests itself through split natural frequencies, beating in the time responses of adjacent or separated plates, and system-level modes in which plates in the array vibrate in- or out-of-phase at closely-spaced frequencies. Laboratory measurements, including a technique in which the frequency response function of all in-phase modes but no out-of-phase modes, or visa versa, is measured, demonstrate the contribution of coupling to the natural frequency spectrum, and identify the combinations of design parameters for which it is important. For the lower modes of primary interest here, the natural frequencies of the out-of-phase system modes decrease as the air layer becomes thinner, while those of the in-phase mode remain sensibly constant at the in vacuo values. A vibration model comprising N classical thin plates that couple through the three-dimensional acoustic fields established in the annular cavities between plates is developed, and its results are compared with measurements of the natural frequencies and mode shapes.

A Vibrational Mode Analysis of Free Finite-Length Thick Cylinders Using the Finite Element Method

1998 ◽  
Vol 120 (2) ◽  
pp. 371-377 ◽  
Author(s):  
Huan Wang ◽  
Keith Williams ◽  
Wei Guan
Keyword(s):  
Finite Length ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Mode Analysis ◽  
Mode Shapes ◽  
Vibrational Modes ◽  
The Finite Element Method ◽  
Cylinder Length ◽  
Radial Thickness ◽  
Thick Cylinder

Based on their three-dimensional mode shapes, the vibrational modes of free finite length thick cylinders can be classified into 6 categories, consisting of pure radial, radial motion with radial shearing, extensional, circumferential, axial bending, and global modes. This classification, together with the numbers of both the circumferential and the longitudinal nodes, is sufficient to identify each mode of a finite length thick cylinder. The mode classification was verified experimentally by measurements on a thick cylinder. According to the displacement distribution ratio in the radial, tangential and longitudinal directions, the effect of varying cylinder length on the vibrational modes is such that all the modes can be broadly categorized as either pure radial modes, or non pure radial modes. The natural frequencies and mode shapes of the former are dependent upon only the radial dimensions of the models, while the natural frequencies and mode shapes of the latter are dependent upon both the axial length and radial thickness.

In-Plane Vibration Modes of Arbitrarily Thick Disks

1997 ◽  
Author(s):  
Kevin I. Tzou ◽  
Jonathan A. Wickert ◽  
Adnan Akay
Keyword(s):  
Natural Frequencies ◽  
Arbitrary Dimension ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Three Dimensional Model ◽  
Bending Vibration ◽  
Annular Disk ◽  
Out Of Plane ◽  
Plane Bending

Abstract The three-dimensional vibration of an arbitrarily thick annular disk is investigated for two classes of boundary conditions: all surfaces traction-free, and all free except for the clamped inner radius. These two models represent limiting cases of such common engineering components as automotive and aircraft disk brakes, for which existing models focus on out-of-plane bending vibration. For a disk of significant thickness, vibration modes in which motion occurs within the disk’s equilibrium plane can play a substantial role in setting its dynamic response. Laboratory experiments demonstrate that in-plane modes exist at frequencies comparable to those of out-of-plane bending even for thickness-to-diameter ratios as small as 10−1. The equations for three-dimensional motion are discretized through the Ritz technique, yielding natural frequencies and mode shapes for coupled axial, radial, and circumferential deformations. This treatment is applicable to “disks” of arbitrary dimension, and encompasses classical models for plates, bars, cylinders, rings, and shells. The solutions so obtained converge in the limiting cases to the values expected from the classical theories, and to ones that account for shear deformation and rotary inertia. The three-dimensional model demonstrates that for geometries within the technologically-important range, the natural frequencies of certain in- and out-of-plane modes can be close to one another, or even identically repeated.

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.

Forced and Ambient Vibration Tests and Vibration Monitoring of Hakucho Suspension Bridge

2000 ◽  
Vol 1696 (1) ◽  
pp. 57-63 ◽  
Author(s):  
Yozo Fujino ◽  
Masato Abe ◽  
Hajime Shibuya ◽  
Masato Yanagihara ◽  
Masashi Sato ◽  
...  
Keyword(s):  
Natural Frequencies ◽  
Three Dimensional ◽  
Suspension Bridge ◽  
Element Model ◽  
Vibration Monitoring ◽  
Ambient Vibration ◽  
Mode Shapes ◽  
Ambient Vibration Tests ◽  
Bending Mode ◽  
Vibration Tests

Forced and ambient dynamic tests of the Hakucho Bridge were carried out to study the dynamic characteristics of this suspension bridge. Dense-array measurement was employed in order to capture not only natural frequencies and damping, but also the mode shapes of the bridge. The natural frequencies and mode shapes obtained from the forced and ambient vibration tests agreed well with those calculated by a three-dimensional finite element model. A new method that combines the random decrement method with the Ibrahim time domain method is proposed to systematically identify the natural frequencies, damping, and mode shapes. This method is successfully applied to ambient vibration data. It is shown that the natural frequency of the first vertical bending mode decreases noticeably as the wind speed increases. It is also shown that the shape of the first vertical bending mode changes slightly near the towers, depending on the wind velocity; this finding indicates that the change may be associated with friction in the bearings at the towers. Finally, application of the Global Positioning System to measure static displacement of the girder is explained.

Modal Analysis Based on Finite Element Jaw Crusher Rotor

2014 ◽  
Vol 599-601 ◽  
pp. 547-550
Author(s):  
Mei Ling Hao ◽  
Guang Juan Cheng
Keyword(s):  
Finite Element ◽  
Modal Analysis ◽  
Natural Frequencies ◽  
Weak Link ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Complex Dynamic ◽  
Three Dimensional Modeling ◽  
Dimensional Modeling ◽  
Analysis Of Results

The vertical shaft impact crusher the material is accelerated , while the rotor bear complex dynamic loads , finite element method for three-dimensional modeling of the rotor body and modal analysis , discussion and analysis of results. Won the first 20 natural frequencies and mode shapes , as well as the weak link parts may exist , making the crusher prone resonance attention away from the source at work , as well as designers kinetic design provides some guidance basis.

Modal Analysis of Ballooning Strings With Small Sag

1999 ◽  
Author(s):  
Rongjun Fan ◽  
Sushil K. Singh ◽  
Christopher D. Rahn
Keyword(s):  
Steady State ◽  
High Speed ◽  
Natural Frequencies ◽  
Rotation Speed ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Theoretical Predictions ◽  
Nonlinear Equations Of Motion

Abstract During the manufacture and transport of textile products, yarns are rotated at high speed and form balloons. The dynamic response of the balloon to varying rotation speed, boundary excitation, and disturbance forces governs the quality of the associated process. Resonance, in particular, can cause large tension variations that reduce product quality and may cause yarn breakage. In this paper, the natural frequencies and mode shapes of a single loop balloon are calculated to predict resonance. The three dimensional nonlinear equations of motion are simplified via small steady state displacement (sag) and vibration assumptions. Axial vibration is assumed to propagate instantaneously or in a quasistatic manner. Galerkin’s method is used to calculate the mode shapes and natural frequencies of the linearized equations. Experimental measurements of the steady state balloon shape and the first two natural frequencies and mode shapes are compared with theoretical predictions.

Large amplitude free vibration study of non-uniform plates with in-plane material inhomogeneity

2016 ◽  
Vol 232 (5) ◽  
pp. 371-387 ◽  
Author(s):  
Saurabh Kumar ◽  
Anirban Mitra ◽  
Haraprasad Roy
Keyword(s):  
Free Vibration ◽  
Large Amplitude ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Static Problem ◽  
Solution Procedure ◽  
Mode Shapes ◽  
Material Inhomogeneity ◽  
Contour Plots ◽  
Variational Form

Free vibration study of non-uniform plates with in-plane material inhomogeneity is carried out in the present work considering geometric nonlinearity. Inhomogeneous plates where the material properties vary along only x-axis (unidirectional) and along both x- and y-axis (bidirectional) are considered. The analysis is performed for two boundary conditions namely clamped and simply supported at all edges, under the action of a transverse uniformly distributed load. The large amplitude problem is formulated using nonlinear strain–displacement relations along with a variational form of energy method. A two-step solution procedure is utilised where, in the first part the static problem is solved and undetermined coefficients are found, subsequently the dynamic problem is taken up on the basis of previously determined coefficients. Validity of the results is successfully confirmed by comparison with the works of other researchers. The analysis reveals that the amplitude and taper parameter affect the loaded natural frequencies significantly. Three-dimensional mode shapes for linear and nonlinear cases are presented along with their respective contour plots.

In-Plane Vibration Modes of Arbitrarily Thick Disks

1998 ◽  
Vol 120 (2) ◽  
pp. 384-391 ◽  
Author(s):  
K. I. Tzou ◽  
J. A. Wickert ◽  
A. Akay
Keyword(s):  
Natural Frequencies ◽  
Arbitrary Dimension ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Three Dimensional Model ◽  
Bending Vibration ◽  
Annular Disk ◽  
Out Of Plane ◽  
Plane Bending

The three-dimensional vibration of an arbitrarily thick annular disk is investigated for two classes of boundary conditions: all surfaces traction-free, and all free except for the clamped inner radius. These two models represent limiting cases of such common engineering components as automotive and aircraft disk brakes, for which existing models focus on out-of-plane bending vibration. For a disk of significant thickness, vibration modes in which motion occurs within the disk’s equilibrium plane can play a substantial role in-setting its dynamic response. Laboratory experiments demonstrate that in-plane modes exist at frequencies comparable to those of out-of-plane bending even for thickness-to-diameter ratios as small as 10−1. The equations for three-dimensional motion are discretized through the Ritz technique, yielding natural frequencies and mode shapes for coupled axial, radial, and circumferential deformations. This treatment is applicable to “disks” of arbitrary dimension, and encompasses classical models for plates, bars, cylinders, rings, and shells. The solutions so obtained converge in the limiting cases to the values expected from the classical theories, and to ones that account for shear deformation and rotary inertia. The three-dimensional model demonstrates that for geometries within the technologically-important range, the natural frequencies of certain in- and out-of-plane modes can be close to one another, or even identically repeated.

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