Spatial Modulation of Repeated Vibration Modes in Rotationally Periodic Structures

1997 ◽  
Vol 122 (1) ◽  
pp. 62-68 ◽  
Author(s):  
M. Kim ◽  
J. Moon ◽  
J. A. Wickert
Keyword(s):  
Mode Shape ◽  
Natural Frequencies ◽  
Periodic Structures ◽  
Spatial Modulation ◽  
Vibration Modes ◽  
Algebraic Relation ◽  
Axisymmetric Structure ◽  
Technical Interest ◽  
Diagrammatic Method ◽  
Model Features

When a structure deviates from axisymmetry because of circumferentially varying model features, significant changes can occur to its natural frequencies and modes, particularly for the doublet modes that have non-zero nodal diameters and repeated natural frequencies in the limit of axisymmetry. Of technical interest are configurations in which inertia, dissipation, stiffness, or domain features are evenly distributed around the structure. Aside from the well-studied phenomenon of eigenvalue splitting, whereby the natural frequencies of certain doublets split into distinct values, modes of the axisymmetric structure that are precisely harmonic become contaminated with certain additional wavenumbers. From analytical, numerical, and experimental perspectives, this paper investigates spatial modulation of the doublet modes, particularly those retaining repeated natural frequencies for which modulation is most acute. In some cases, modulation can be sufficiently severe that a mode shape will “beat” spatially as harmonics with commensurate wavenumbers combine, just as the superposition of time records having nearly equal frequencies leads to classic temporal beating. An algebraic relation and a diagrammatic method are discussed with a view towards predicting the wavenumbers present in modulated eigenfunctions given the number of nodal diameters in the base mode and the number of equally spaced model features. [S0739-3717(00)01501-4]

Spatial Modulation of Repeated Vibration Modes in Rotationally Periodic Structures

1997 ◽  
Author(s):  
Mintae Kim ◽  
Joonho Moon ◽  
Jonathan A. Wickert
Keyword(s):  
Mode Shape ◽  
Natural Frequencies ◽  
Periodic Structures ◽  
Spatial Modulation ◽  
Vibration Modes ◽  
Algebraic Relation ◽  
Natural Frequencies And Modes ◽  
Axisymmetric Structure ◽  
Technical Interest ◽  
Model Features

Abstract When a structure deviates from axisymmetry because of circumferentially varying model features, significant changes can occur to its natural frequencies and modes, particularly for the doublet modes that have non-zero nodal diameters and repeated natural frequencies in the limit of axisymmetry. Of technical interest are configurations in which inertia, dissipation, stiffness, or domain features are evenly distributed around the structure. Aside from the well-studied phenomenon of eigenvalue splitting, whereby the natural frequencies of certain doublets split into distinct values, modes of the axisymmetric structure that are precisely harmonic become contaminated by certain additional wavenumbers in the presence of periodically spaced model features. From analytical, numerical, and experimental perspectives, this paper investigates spatial modulation of the doublet modes, particularly those retaining repeated natural frequencies for which modulation is most acute. In some cases, modulation can be sufficiently severe that a mode shape will beat spatially as harmonics with commensurate wavenumbers combine, just as the superposition of time records having nearly equal frequencies leads to classic temporal beating. A straightforward algebraic relation and a graphical checkerboard diagram are discussed with a view towards predicting the wavenumbers present in modulated eigenfunctions given the number of nodal diameters in the base mode and the number of equally spaced model features.

Simple Models for Periodic Lattices

1991 ◽  
Author(s):  
Serge Abrate
Keyword(s):  
Natural Frequencies ◽  
Periodic Structures ◽  
Optimal Solution ◽  
Mode Shapes ◽  
Design Stage ◽  
Continuum Models ◽  
Original Structure ◽  
Vibration Modes ◽  
Equivalent Properties

Abstract In many applications, the dynamic behavior of large periodic structures must be modeled accurately, thus requiring the determination of a significant number of natural frequencies and mode shapes. In order to perform that task most efficiently, a continuum modeling approach can be adopted. The discrete structure is then replaced by a continuum model which can be analyzed more efficiently. Therefore, at the design stage many analyses can be performed while searching for the optimal solution. Known structural models are usually used as continuum models, and several methods are available to determine the equivalent properties from the properties of the original structure. This task is usually cumbersome, and in addition, in certain cases, continuum models cannot represent all modes of deformation. In this article, a simple approach to develop continuum models without explicit reference to an existing structural theory is presented. Very accurate results are obtained, and all vibration modes can now be handled easily.

Measurement of Young’s Modulus and Shear Modulus of Some Structures Welded Using Flux Cored Wire by Vibration Tests

2014 ◽  
Vol 216 ◽  
pp. 151-156 ◽  
Author(s):  
Liviu Bereteu ◽  
Mircea Vodǎ ◽  
Gheorghe Drăgănescu
Keyword(s):  
Shear Modulus ◽  
Arc Welding ◽  
Natural Frequencies ◽  
Free Vibrations ◽  
Vibration Modes ◽  
Cored Wire ◽  
Flux Cored Arc Welding ◽  
Longitudinal Elastic Modulus ◽  
Vibration Tests ◽  
Non Destructive

The aim of this work was to determine by vibration tests the longitudinal elastic modulus and shear modulus of welded joints by flux cored arc welding. These two material properties are characteristic elastic constants of tensile stress respectively torsion stress and can be determined by several non-destructive methods. One of the latest non-destructive experimental techniques in this field is based on the analysis of the vibratory signal response from the welded sample. An algorithm based on Pronys series method is used for processing the acquired signal due to sample response of free vibrations. By the means of Finite Element Method (FEM), the natural frequencies and modes shapes of the same specimen of carbon steel were determined. These results help to interpret experimental measurements and the vibration modes identification, and Youngs modulus and shear modulus determination.

scholarly journals Vibration of Rotating and Revolving Planet Rings with Discrete and Partially Distributed Stiffnesses

2020 ◽  
Vol 11 (1) ◽  
pp. 127
Author(s):  
Fuchun Yang ◽  
Dianrui Wang
Keyword(s):  
High Speed ◽  
Differential Operators ◽  
Natural Frequencies ◽  
Rotation Speed ◽  
Distribution Area ◽  
Vibration Modes ◽  
Governing Equations ◽  
Vibration Properties ◽  
Wide Range ◽  
Forced Responses

Vibration properties of high-speed rotating and revolving planet rings with discrete and partially distributed stiffnesses were studied. The governing equations were obtained by Hamilton’s principle based on a rotating frame on the ring. The governing equations were cast in matrix differential operators and discretized, using Galerkin’s method. The eigenvalue problem was dealt with state space matrix, and the natural frequencies and vibration modes were computed in a wide range of rotation speed. The properties of natural frequencies and vibration modes with rotation speed were studied for free planet rings and planet rings with discrete and partially distributed stiffnesses. The influences of several parameters on the vibration properties of planet rings were also investigated. Finally, the forced responses of planet rings resulted from the excitation of rotating and revolving movement were studied. The results show that the revolving movement not only affects the free vibration of planet rings but results in excitation to the rings. Partially distributed stiffness changes the vibration modes heavily compared to the free planet ring. Each vibration mode comprises several nodal diameter components instead of a single component for a free planet ring. The distribution area and the number of partially distributed stiffnesses mainly affect the high-order frequencies. The forced responses caused by revolving movement are nonlinear and vary with a quasi-period of rotating speed, and the responses in the regions supported by partially distributed stiffnesses are suppressed.

Vibration-Based Crack Detection in L-Frames

2014 ◽  
Vol 658 ◽  
pp. 261-268
Author(s):  
Jean Louis Ntakpe ◽  
Gilbert Rainer Gillich ◽  
Florian Muntean ◽  
Zeno Iosif Praisach ◽  
Peter Lorenz
Keyword(s):  
Strain Energy ◽  
Crack Detection ◽  
Natural Frequencies ◽  
Vibration Modes ◽  
Structural Elements ◽  
Element Analysis ◽  
Accurate Localization ◽  
Mathematical Expressions ◽  
Measurement Results ◽  
Non Destructive

This paper presents a novel non-destructive method to locate and size damages in frame structures, performed by examining and interpreting changes in measured vibration response. The method bases on a relation, prior contrived by the authors, between the strain energy distribution in the structure for the transversal vibration modes and the modal changes (in terms of natural frequencies) due to damage. Using this relation a damage location indicator DLI was derived, which permits to locate cracks in spatial structures. In this paper an L-frame is considered for proving the applicability of this method. First the mathematical expressions for the modes shapes and their derivatives were determined and simulation result compared with that obtained by finite element analysis. Afterwards patterns characterizing damage locations were derived and compared with measurement results on the real structure; the DLI permitted accurate localization of any crack placed in the two structural elements.

Dynamic Characteristics of a Long-Span Cable-Stayed Bridge

2011 ◽  
Vol 480-481 ◽  
pp. 1496-1501
Author(s):  
Liu Hui
Keyword(s):  
Finite Element ◽  
Dynamic Characteristics ◽  
Iteration Method ◽  
Natural Frequencies ◽  
Element Model ◽  
Vibration Modes ◽  
Cable Stayed Bridge ◽  
Long Span ◽  
Subspace Iteration ◽  
Floating System

In order to study the dynamic characteristics of a super-long-span cable-stayed bridge which is semi-floating system, the spatial finite element model of this cable-stayed bridge was established in ANSYS based on the finite element theory.Modal solution was conducted using subspace iteration method, and natural frequencies and vibration modes were obtained.The dynamic characteristics of this super-long-span cable-stayed bridge were then analyzed.Results showed that the super-long-span cable-stayed bridge of semi-floating system has long basic cycle, low natural frequencies, dense modes and intercoupling vibration modes.

scholarly journals Influence of the flexibility of beams and slabs in static response and dynamic properties

2016 ◽  
Vol 9 (6) ◽  
pp. 842-855 ◽  
Author(s):  
J. R. BUENO ◽  
◽  
D. D. LORIGGIO ◽  
Keyword(s):  
Finite Element Method ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Vibration Modes ◽  
Linear Regime ◽  
Static Response ◽  
The Finite Element Method ◽  
Standard Code ◽  
The Relationship ◽  
Brazilian Standard

Abstract This article examines numerically the flexibility influence of support beams in static response and dynamic properties of a symmetric plate formed by massive slabs of reinforced concrete in elastic linear regime, using the Finite Element Method. In the static response the variation of bending mo-ments and displacements are evaluated, which depend on the relationship between the flexibility of the slab and the beam. The evaluation of dynamic properties is held in undamped free vibration, through which the vibration modes and the values of the natural frequencies is obtained, which are compared with the limits of the Brazilian standard code for design of concrete structures. Results show that the response may show great variation due to the change in the relationship between bending stiffness of the slabs and the beams.

Natural Frequencies and Normal Modes of a Spinning Timoshenko Beam With General Boundary Conditions

1992 ◽  
Vol 59 (2S) ◽  
pp. S197-S204 ◽  
Author(s):  
Jean Wu-Zheng Zu ◽  
Ray P. S. Han
Keyword(s):  
Boundary Conditions ◽  
Mode Shape ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Normal Modes ◽  
Single Mode ◽  
Mode Shapes ◽  
Simulation Studies ◽  
Classical Boundary ◽  
First Time

A free flexural vibrations of a spinning, finite Timoshenko beam for the six classical boundary conditions are analytically solved and presented for the first time. Expressions for computing natural frequencies and mode shapes are given. Numerical simulation studies show that the simply-supported beam possesses very peculiar free vibration characteristics: There exist two sets of natural frequencies corresponding to each mode shape, and the forward and backward precession mode shapes of each set coincide identically. These phenomena are not observed in beams with the other five types of boundary conditions. In these cases, the forward and backward precessions are different, implying that each natural frequency corresponds to a single mode shape.

Vibration Response of a Thin-Walled Cylindrical Pipe with Liquid

2012 ◽  
Vol 189 ◽  
pp. 345-349
Author(s):  
Yu Lan Wei ◽  
Bing Li ◽  
Li Gao ◽  
Ying Jun Dai
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Element Model ◽  
Beam Model ◽  
Vibration Modes ◽  
Timoshenko Beam Model ◽  
Cylindrical Pipe ◽  
Bending Vibration ◽  
Beam Bending ◽  
Thin Walled

Vibration characteristics of the thin-walled cylindrical pipe are affected by the liquid within the pipe. The natural frequencies and vibration modes of the pipe without liquid are analyzed by the theory of beam bending vibration and finite element model, which is based on the Timoshenko beam model. The first three natural frequencies and vibration modes of the pipe with or without liquid are acquired by experiments. As shown in the experiment results, the natural frequencies of the containing liquid pipe are lower than the natural frequencies of the pipe without liquid.

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.

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