Vibration of an Eccentrically Clamped Annular Plate

1993 ◽  
Author(s):  
Jung-Ge Tseng ◽  
Jonathan A. Wickert
Keyword(s):  
Data Storage ◽  
Natural Frequencies ◽  
Annular Plate ◽  
Outer Edge ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Laboratory Measurements ◽  
Free Response ◽  
Amplitude Vibration ◽  
Natural Frequency Spectrum

Abstract Small amplitude vibration of an eccentric annular plate, which is free along its outer edge and clamped along the interior, is investigated through experimental and analytical methods. A disk with this geometry, or a stacked array in which the clamping and symmetry axes of each disk are nominally coincident, is common in data storage and brake systems applications. In the present case, the geometric imperfections on the boundary can have important implications for the disk’s dynamic response. Changes that occur in the natural frequency spectrum, the mode shapes, and the free response under eccentric mounting are studied through laboratory measurements and an approximate discrete model of the plate. The natural frequencies and modes are found through global discretization of the Kamke quotient for a classical thin plate. For the axisymmetric geometry, the natural frequencies of the “sine” and “cosine” vibration modes for a specified number of nodal diameters are repeated. With increasing eccentricity, on the other hand, each pair of repeated frequencies splits at a rate that depends on the number of nodal diameters. Over a range of clamping and eccentricity ratios, the model’s predictions are compared to the measured results.

Vibration of an Eccentrically Clamped Annular Plate

1994 ◽  
Vol 116 (2) ◽  
pp. 155-160 ◽  
Author(s):  
J.-G. Tseng ◽  
J. A. Wickert
Keyword(s):  
Data Storage ◽  
Natural Frequencies ◽  
Annular Plate ◽  
Outer Edge ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Laboratory Measurements ◽  
Free Response ◽  
Amplitude Vibration ◽  
Natural Frequency Spectrum

Small amplitude vibration of an eccentric annular plate, which is free along its outer edge and clamped along the interior, is investigated through experimental and analytical methods. A disk with this geometry, or a stacked array in which the clamping and symmetry axes of each disk are nominally coincident, is common in data storage and brake systems applications. In the present case, the geometric imperfections on the boundary can have important implications for the disk’s dynamic response. Changes that occur in the natural frequency spectrum, the mode shapes, and the free response under eccentric mounting are studied through laboratory measurements and an approximate discrete model of the plate. The natural frequencies and modes are found through global discretization of the Kamke quotient for a classical thin plate. For the axisymmetric geometry, the natural frequencies of the “sine” and “cosine” vibration modes for a specified number of nodal diameters are repeated. With increasing eccentricity, on the other hand, each pair of repeated frequencies splits at a rate that depends on the number of nodal diameters. Over a range of clamping and eccentricity ratios, the model’s predictions are compared to the measured results.

On the Vibration of Bolted Plate and Flange Assemblies

1994 ◽  
Vol 116 (4) ◽  
pp. 468-473 ◽  
Author(s):  
J.-G. Tseng ◽  
J. A. Wickert
Keyword(s):  
Data Storage ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
Annular Plate ◽  
Approximate Model ◽  
Outer Edge ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Laboratory Measurements ◽  
Structural Imperfections

The vibration of an annular plate that is free along its outer edge, and that is connected to a flange along its inner edge by bolts that are equally spaced in the circumferential direction, is studied. A disk with this geometry, or a stacked array of such disks, is common in applications involving data storage, rotating machinery, or brake systems. The periodic structural imperfections that are associated with the bolt pattern can have interesting implications for the plate’s dynamic response. Changes that occur in the natural frequencies and mode shapes as a result of such deviations from an ideally clamped inner edge are studied through laboratory measurements, and through an approximate model that captures the rotationally periodic character of the bolted plate and flange system. In the axisymmetric case, the natural frequencies of the plate’s “sine” and “cosine” vibration modes are repeated for a specified number of nodal diameters. Under the influence of a regular bolt pattern, and the resulting local variations of the stiffness and compression at the plate/flange interface, some natural frequencies are repeated and others split. This process depends on the number of bolts used to mount the plate, and on the number of nodal diameters present in a specific vibration mode. A straightforward criterion to predict the split and repeated modes is discussed.

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.

Structural Response of Pipeline Free Spans Based on Beam Theory

2002 ◽  
Author(s):  
Olav Fyrileiv ◽  
Kim Mo̸rk
Keyword(s):  
Natural Frequencies ◽  
Structural Response ◽  
Beam Theory ◽  
Vertical Vibration ◽  
Mode Shapes ◽  
Ocean Current ◽  
Vibration Modes ◽  
Wave Loading ◽  
Vortex Induced Vibrations ◽  
Subsea Pipelines

One of the main risk factors for subsea pipelines exposed on the seabed is fatigue failure of free spans due to ocean current or wave loading. This paper describes how the structural response of a free span, as input to the fatigue analyses, can be assessed in a simple and still accurate way by using improved beam theory formulations. In connection with the release of the DNV Recommended Practice, DNV-RP-F105 “Free Spanning Pipelines”, the simplified structural response quantities have been improved compared to previous codes. The boundary condition coefficients for the beam theory formulations have been updated based an effective span length concept. This concept is partly based on theoretical studies and partly on a large number of FE analyses. The updated expressions are general and fit all types of soil and pipe dimensions for lower lateral and vertical vibration modes. The present paper focus on estimation of simplified response quantities such as lower natural frequencies and associated mode shapes. Hydrodynamical aspects of Vortex Induced Vibrations (VIV) are outside the scope of this paper.

Modal Analysis of Annular Plate with Crack and its Effect on Natural Frequency

2015 ◽  
Vol 813-814 ◽  
pp. 910-914 ◽  
Author(s):  
R. Pramod ◽  
M.E. Shashi Kumar ◽  
S. Mohan Kumar
Keyword(s):  
Natural Frequency ◽  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Annular Plate ◽  
Structural Member ◽  
Vibration Modes ◽  
Static And Dynamic Characteristics ◽  
Annular Plates ◽  
Theoretical Frequency ◽  
Theoretical Results

The study of the dynamic behavior of annular plates with circumferential cracks can find many applications in several machine components such as flywheels, clutch plates, compact discs etc. A crack on a structural member introduces a local increase of flexibility in that region then; this affects the static and dynamic characteristics. The effects of cracks on the dynamic characteristics of structures, especially on the natural frequencies and modes, were extensively studied. In this study, the natural frequencies of annular plates with circumferential cracks are investigated by using finite element method. The cracks were non-propagating and open. The annular plate with different cracks was subjected to different boundary conditions and final variation in the natural frequency was obtained, which was compared with the theoretical frequency and the change in the natural frequency was studied. The results of this study with improved elements are compared with the theoretical results in the literature. It is observed that the location and the number of cracks have various effects on the natural frequencies related to the vibration modes.

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.

Approximate Linear Theories for the Dynamics of Slack Cables Supporting a Discrete Mass

1991 ◽  
Author(s):  
S.-P. Cheng ◽  
N. C. Perkins
Keyword(s):  
Three Dimensional ◽  
Small Mass ◽  
Mode Shapes ◽  
Mass Model ◽  
Free Response ◽  
Eigen Solutions ◽  
Technical Interest ◽  
Spatially Varying ◽  
Discrete Mass ◽  
Natural Frequency Spectrum

Abstract A continuum model is presented that describes the three-dimensional response of an elastic cable that supports a single attached mass. Two asymptotic forms of this model are analyzed for the free, linear response of slack suspensions having small equilibrium curvature (sag) and level supports. The first model, which is valid for relatively small attached masses, assumes that the cable stretches quasi-statically and results in uniform dynamic cable tension. The quasi-static stretching assumption is partially relaxed in the second model which accounts for spatially varying dynamic tension in an approximate manner. The eigen-solutions associated with free response are compared for the two models. Results indicate that the “small mass model” provides excellent approximations to the natural frequency spectrum and vibration mode shapes for most cables and modes of technical interest. A simple criterion is presented which governs the range of validity of the small mass model.

Bending Flexibility of Bolted Flanges and Its Effect on Dynamical Behavior of Structures

1989 ◽  
Vol 111 (4) ◽  
pp. 392-398 ◽  
Author(s):  
A. Lifson ◽  
A. J. Smalley
Keyword(s):  
Natural Frequencies ◽  
Dynamical Behavior ◽  
Measured Data ◽  
Model Verification ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Reciprocating Compressor ◽  
Southwest Research Institute ◽  
Piping Systems ◽  
Good Agreement

This paper presents a basis for determining the bending flexibility of flanged joints in complex piping systems for use in predicting natural frequencies, mode shapes, and response to excitation forces. Data was developed by a combination of laboratory testing and analysis. Highly instrumented testing initially identified and isolated the contributing deformations in a flanged joint and later provided overall flexibilities of flanged assemblies for verification of the analytical model. The analysis, its results, and model verification are presented in the paper. Further results are provided which compare predicted dynamic characteristics of reciprocating compressor manifold piping systems with measured data obtained in the field for vibration modes which are sensitive to flange flexibility. Consistent good agreement has been achieved of the techniques utilized in some 50 design and field analyses conducted at the Center for Applied Machinery and Piping Technology (CAMPT) at Southwest Research Institute.

Some Remarks on the Dynamic Behaviour of Integrally Shrouded Blade Rows

2011 ◽  
Author(s):  
N. Bachschmid ◽  
S. Bistolfi ◽  
S. Chatterton ◽  
M. Ferrante ◽  
E. Pesatori
Keyword(s):  
Steam Turbine ◽  
Natural Frequencies ◽  
Low Pressure ◽  
Contact Forces ◽  
Mode Shapes ◽  
Torsional Vibrations ◽  
Vibration Modes ◽  
Nodal Diameter ◽  
Blade Row ◽  
Pressure Steam

Actual trend in steam turbine design is to use blades with integral shrouds, for high pressure and intermediate pressure steam turbine sections, as well as also for the long blades of the low pressure sections. The blades are inserted with their root into the seat on the shaft in such a way that the blades are slightly forced against each other in correspondence of the shrouds. In long blades of low pressure stages the forcing can be obtained by the untwisting of twisted blades due to the effect of the huge centrifugal forces. The dynamic behavior of these blade rows is difficult to predict due to the nonlinear effect of the contact forces and due to friction. Different models for the contact are proposed and compared. The resulting natural frequencies of the blade row as a function of the different nodal diameter mode shapes are highly depending on the assumed models. For avoiding resonant conditions with engine order excitations, the natural frequencies must be calculated with good accuracy. Some of the modes of the blade row, typically for the last stage of the low pressure steam turbine, can couple with some vibration modes of the rotor: flexural vibrations of the shaft couple with 1 nodal diameter mode shape of the row in axial direction and torsional vibrations of the shaft couple with the 0 nodal diameter mode in tangential direction. Therefore analyses of lateral and torsional vibrations of low pressure steam turbine shafts require also an accurate analysis of the blade row vibration modes.

Modeling of Annular Plate With Piezoelectric Actuators for Active Vibration Control

2002 ◽  
Author(s):  
El Mostafa Sekouri ◽  
Yan-Ru Hu ◽  
Anh Dung Ngo
Keyword(s):  
Analytical Approach ◽  
Natural Frequencies ◽  
Annular Plate ◽  
Electrical Response ◽  
Active Vibration Control ◽  
Piezoelectric Actuators ◽  
Mode Shapes ◽  
State Behavior ◽  
Element Approach ◽  
Active Vibration

This paper presents an analytical approach for modeling the mechanical-electrical response of annular plate components of space structures containing distributed piezoelectric under static as well as dynamic mechanical or electrical loadings. The analytical approach used in this paper is based on the Kirchhoff plate model. The equations governing the dynamics of the plate, relating the strains in the piezoelectric elements to the strain induced in the system, are derived for annular plate using the partial differential equation. The natural frequencies and mode shapes of the structures were determined by modal analysis. In addition, the harmonic analysis is performed for analyzing the steady-state behavior of the structures subjected to cyclic sinusoidal loads. Numerical simulation results are obtained using finite element approach. Experiments using a thin circular aluminum plate structure with distributed piezoelectric actuators were also conducted to verify the analysis and the computer simulations. Relatively good agreements between the results of these three approaches are observed. Finally, the results show that the model can predict natural frequencies and modes shapes of the plate very accurately.

Sign in / Sign up

Export Citation Format

Share Document