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.

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.

Tunable Three-Dimensional Vibrational Structures for Concurrent Determination of Thin Film Modulus and Density

2021 ◽  
pp. 1-15
Author(s):  
Hairui Wang ◽  
Chen Wei ◽  
Yao Zhang ◽  
Yinji Ma ◽  
Ying Chen ◽  
...  
Keyword(s):  
Thin Film ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Theoretical Models ◽  
Structural Vibration ◽  
Small Scale ◽  
Vibration Modes ◽  
Film Material ◽  
Film Properties ◽  
Out Of Plane

Abstract The real-time characterization of thin film properties can provide insights into the behavior of film material during process such as phase-transition, hydration and chemical reaction. The shift of reasonant frequency in structural vibration serves as the basis of an effective approach to determine film properties, but encounters the difficulty that multiple to-be-determined quantites (e.g. film modulus and density) are often related to the resonant frequency simultaneously and therefore cannot be determined by a structure with fixed shape and vibration mode. Determinsitic mechanical buckling provides an effective route for the vibrational structure to rapidly switch between designed shapes and vibration modes. Here, we adopt a ribbon structure in the flat state and buckled state to yield two distinct vibration modes. Theoretical models of the natural frequencies are established for first-order out-of-plane modes of the ribbon with patterned thin films in these two states, respectively. The model suggests that with optimized film pattern the sensitivity of the natural frequencies to the film modulus and density can be partially decoupled. The results lead to a simple and effective method based on tunable vibration to characterize the thin film modulus and density at small scale.

Pre-Stressed Modal Analysis of the Shaft Based on ANSYS Workbench

2014 ◽  
Vol 1028 ◽  
pp. 105-110
Author(s):  
Xin Wang Song ◽  
Yan Wu ◽  
Yu An He ◽  
Fu Yang Chen
Keyword(s):  
Modal Analysis ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Drive Shaft ◽  
Stepper Motor ◽  
Vibration Modes ◽  
Three Dimensional Model ◽  
Speed Range ◽  
Stepper Motors ◽  
Ansys Workbench

This paper is based on the research on the drive shaft of the toothpaste tube conveyor, using Solidworks to create the three dimensional model of the frame of the soft tube conveyor and the drive shaft. And natural frequencies and vibration modes of preceding 6 modalities of pre-stress modal analysis are calculated with ANSYS Workbench. By analyzing the natural frequencies of the drive shaft and the resonance range of stepper motors, the reasonable speed range of the stepper motor can be acquired, in order to avoid the resonance between the drive shaft and stepper motor. At the same time, the reasonable installation location of synchronous belt wheels can be attained by analyzing each vibration mode.

Theoretical Analysis and FEM Simulation of Piezoelectric Vibrator Used in Ultrasonic EDM System

2013 ◽  
Vol 694-697 ◽  
pp. 3020-3024
Author(s):  
Hong Bing Wang ◽  
Zhi Rong Li ◽  
Chun Hua Sun
Keyword(s):  
Theoretical Analysis ◽  
Natural Frequencies ◽  
Dynamic Performance ◽  
Three Dimensional ◽  
Fem Simulation ◽  
Model Analysis ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Piezoelectric Vibrator ◽  
Working Frequency

The dynamic performance of the piezoelectric vibrator used in ultrasonic EDM machine in natural frequencies has a great effect on machining precision. Firstly, Through theoretical analysis the dynamic characteristics of the piezoelectric vibrator is obtained. Then the three-dimensional model of the piezoelectric vibrator is constructed by using PRO/E software, and model analysis is carried by using FEM software. Through theoretical analysis and FEM simulation, the appropriate working frequency and mode of the piezoelectric vibrator was found, and the piezoelectric vibrator was fabricated. Experimented results show that the model analysis of frequency is accord with that of FEM.

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.

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.

Free Vibration of Coupled Disk-Hat Structures

1999 ◽  
Author(s):  
Jun-Chul Bae ◽  
Jonathan Wickert
Keyword(s):  
Free Vibration ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Phase Relationship ◽  
Vibration Modes ◽  
Pure Bending ◽  
Brake Rotors ◽  
Automotive Brake ◽  
Ordered Pairs

Abstract The free vibration of disk-hat structures, such as automotive brake rotors, is investigated analytically and through laboratory experimentation. Of particular interest are the role played by the hat element’s depth in influencing the three-dimensional vibration of the disk, and the manner in which the bending and in-plane modes of the disk alone evolve as a hat of increasing depth is incorporated in the model. The lower vibration modes of disk-hat structures are shown to be characterized by the numbers of nodal circles NC and diameters ND present on the disk, as well as the phase relationship between the disk’s transverse and radial displacements due to coupling with the hat element. Such modes map continuously back to the pure bending and in-plane modes of the disk alone, appear in ordered pairs, and can exist at close frequencies. Those characteristics are explored particularly with respect to sensitivities in the disk’s thickness and the hat’s depth with a view towards shifting particular natural frequencies, or minimizing transverse disk motion in certain vibration modes. Results obtained through analysis and measurement of a prototypical disk-hat structure are applied in a case study with a ventilated automotive brake rotor.

Finite Element Analysis of Elliptical Chord

2013 ◽  
Vol 3 (4) ◽  
pp. 44-61
Author(s):  
K. S. Narayana ◽  
R. T. Naik ◽  
R. C. Mouli ◽  
L. V. V. Gopala Rao ◽  
R. T. Babu Naik
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Compressive Load ◽  
Dynamic Strength ◽  
Element Analysis ◽  
T Joints ◽  
Shell Elements ◽  
Tubular Joints ◽  
Plane Bending

The work presents the Finite element study of the effect of elliptical chords on the static and dynamic strength of tubular T-joints using ANSYS. Two different geometry configurations of the T-joints have been used, namely Type-1 and Type-2. An elastic analysis has been considered. The Static loading conditions used are: axial load, compressive load, In-plane bending (IPB) and Out-plane bending (OPB). The natural frequencies analysis (dynamic loading condition) has also been carried out. The geometry configurations of the T-joints have been used, vertical tubes are called brace and horizontal tubes are called chords. The joint consists of brace joined perpendicular to the circular chord. In this case the ends of the chord are held fixed. The material used is mild steel. Using ANSYS, finite element modeling and analysis of T-joint has been done under the aforementioned loading cases. It is one of the most powerful methods in use but in many cases it is an expensive analysis especially due to elastic–plastic and creep problems. Usually, three dimensional solid elements or shell elements or the combination of two types of elements are used for generating the tubular joints mesh. In tubular joints, usually the fluid induced vibrations cause the joint to fail under resonance. Therefore the natural frequencies analysis is also an important issue here. Generally the empirical results are required as guide or comparison tool for finite element investigation. It is an effective way to obtain confidence in the results derived. Shell elements have been used to model the assembled geometry. Finite element ANSYS results have been validated with the LUSAS FEA and experimental results, that is within the experimentation error limit of ten percentage.

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