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.

Split Vibration Modes in Acoustically-Coupled Disk Stacks

1998 ◽  
Vol 120 (1) ◽  
pp. 234-239 ◽  
Author(s):  
J.-G. Tseng ◽  
J. A. Wickert
Keyword(s):  
Natural Frequencies ◽  
Three Dimensional ◽  
System Level ◽  
Thin Plates ◽  
Mode Shapes ◽  
Design Parameters ◽  
Phase System ◽  
Acoustic Coupling ◽  
Annular Plates ◽  
Vibration Model

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.

Direct Coupling of a Two-Dimensional Fan Model in a Turbofan Engine Performance Simulation

2016 ◽  
Author(s):  
Ioannis Templalexis ◽  
Alexios Alexiou ◽  
Vassilios Pachidis ◽  
Ioannis Roumeliotis ◽  
Nikolaos Aretakis
Keyword(s):  
Three Dimensional ◽  
Engine Performance ◽  
System Level ◽  
Design Parameters ◽  
High Fidelity ◽  
Two Dimensional ◽  
Performance Simulation ◽  
Cfd Models ◽  
Component Design ◽  
Complex Phenomena

Coupling of high fidelity component calculations with overall engine performance simulations (zooming) can provide more accurate physics and geometry based estimates of component performance. Such a simulation strategy offers the ability to study complex phenomena and their effects on engine performance and enables component design changes to be studied at engine system level. Additionally, component interaction effects can be better captured. Overall, this approach can reduce the need for testing and the engine development time and cost. Different coupling methods and tools have been proposed and developed over the years ranging from integrating the results of the high fidelity code through conventional performance component maps to fully-integrated three-dimensional CFD models. The present paper deals with the direct integration of an in-house two-dimensional (through flow) streamline curvature code (SOCRATES) in a commercial engine performance simulation environment (PROOSIS) with the aim to establish the necessary coupling methodology that will allow future advanced studies to be performed (e.g. engine condition diagnosis, design optimization, mission analysis, distorted flow). A notional two-shaft turbofan model typical for light business jets and trainer aircraft is initially created using components with conventional map-defined performance. Next, a derivative model is produced where the fan component is replaced with one that integrates the high fidelity code. For both cases, an operating line is simulated at sea-level static take-off conditions and their performances are compared. Finally, the versatility of the approach is further demonstrated through a parametric study of various fan design parameters for a better thermodynamic matching with the driving turbine at design point operation.

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.

Modeling and Free Vibration of Flex Circuits in Hard Disk Drives

2003 ◽  
Author(s):  
Jonathan Wickert
Keyword(s):  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Equilibrium Shape ◽  
Local Equilibrium ◽  
Hard Disk Drives ◽  
Laser Interferometry ◽  
Hard Disk ◽  
System Level ◽  
Mode Shapes ◽  
Free Length

A flex circuit connects the stationary electronic components in a hard disk drive to the rotating arm that carries the read/write heads and positions them above data tracks on the disk. Flex circuits are conventionally formed as a laminate of polyimide substrate, adhesive, and copper conductors. Deformation of a flex circuit is discussed in the context of the following stages: the initial unstressed shape, configurations in which stresses set and relax in response to elevated temperature, equilibrium, and small amplitude vibration. The model involves displacements of the flex circuit in the directions tangent and normal to the local equilibrium shape, and those motions couple with the arm’s dynamics. Nonlinearity associated with finite curvature, partial elastic springback, and the arm’s geometry and inertia properties are incorporated within the vibration model to predict system-level natural frequencies, mode shapes, and coupling factors between the circuit and the arm. Laboratory measurements using noncontact laser interferometry validate the model with respect to the circuit’s shape, stiffness, restoring moment, and natural frequencies. The primary degrees of freedom for optimizing flex circuit design are the thicknesses of the individual layers within the circuit, free length, and the locations and slopes of the circuit’s attachment points to the arm and electronics block. The model’s predictions and trends developed from a case study in free length are discussed with a view toward reducing coupling between the circuit and arm in certain vibration modes.

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.

Mechanical Behavior of an Electrostatically Actuated Microplate

2003 ◽  
Author(s):  
Xiaopeng Zhao ◽  
Eihab M. Abdel-Rahman ◽  
Ali H. Nayfeh
Keyword(s):  
Differential Equations ◽  
Natural Frequencies ◽  
Finite Dimension ◽  
Equations Of Motion ◽  
Galerkin Approximation ◽  
Mode Shapes ◽  
Design Parameters ◽  
Electrostatically Actuated ◽  
Linear Eigenvalue Problem ◽  
Electrically Actuated

We present a nonlinear model of electrically actuated microplates. The model accounts for the nonlinearity in the electric forcing as well as mid-plane stretching of the plate. We use a Galerkin approximation to reduce the partial-differential equations of motion to a finite-dimension system of nonlinearly coupled second-order ordinary-differential equations. We find the deflection of the microplate under DC voltage and study the pull-in phenomenon. The natural frequencies and mode shapes are then obtained around the deflected position of the microplate by solving the linear eigenvalue problem. The effect of various design parameters on both the static response and the dynamic characteristics are studied.

Frequency Clusters in the Spectrum of Annular Cylinders

1998 ◽  
Vol 65 (4) ◽  
pp. 797-803 ◽  
Author(s):  
K. I. Tzou ◽  
J. A. Wickert ◽  
A. Akay
Keyword(s):  
Natural Frequencies ◽  
Spectral Characteristics ◽  
Three Dimensional ◽  
Longitudinal Shear ◽  
Forced Response ◽  
Infinite Cylinder ◽  
Propagation Theory ◽  
Cylinder Length ◽  
Vibration Model ◽  
Shear Modes

As the length of a traction-free annular cylinder is increased, distinct members within any family of radial or longitudinal shear modes have natural frequencies that asymptotically approach a common nonzero value. Such modes, potentially having significantly different numbers of nodes along the cylinder’s generator, can have natural frequencies that are indistinguishable from one another within the resolution of test equipment or numerical simulation. The three-dimensional vibration model discussed here predicts the formation of narrow “frequency clusters” with the cylinder’s increasing length, the converged value of which bounds from below the frequencies of all modes within a particular family. In addition to these spectral characteristics, frequency clusters have implications for the forced response of annular cylinders. For the particular families of modes that are of interest here, the steady-state harmonic response at frequencies near a cluster can be spatially confined with displacements that decay rapidly away from the point of maximum response. At other driving frequencies, the response is distributed more uniformly along the length of the cylinder. The derived analytical model is compared with results from laboratory measurements, and from the predictions of wave propagation theory in the limit of infinite cylinder length.

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.

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