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.

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.

The Three-Dimensional Dynamics for Toroidal Drive

2012 ◽  
Vol 562-564 ◽  
pp. 536-539
Author(s):  
Li Zhong Xu ◽  
Jin Liang Li ◽  
Ya Jun Li
Keyword(s):  
Natural Frequencies ◽  
Cone Angle ◽  
Three Dimensional ◽  
Drive System ◽  
Vibration Modes ◽  
Mesh Stiffness ◽  
Coupled Modes ◽  
Bearing Stiffness ◽  
Rigid Body Motions ◽  
Half Cone

In this paper, a model to simulate the dynamic behavior of the toroidal drive is developed. The three-dimensional dynamic model includes all six rigid body motions of the stator, worm, rotor and the planets. Using the model, the natural frequencies and vibration modes of the drive system are investigated. The vibration modes are classified into single modes and coupled modes. The single modes include planet mode, worm mode and stator mode. The vibration and frequency characteristics of different modes are obtained. The relation between modes and half cone angle of the planet tooth is discussed. The relation between vibrations and bearing stiffness is also discussed. When the bearing stiffness is about 10 times of the mesh stiffness, some vibration displacements of the drive system are quite small and can be neglected. Meanwhile, the dynamic equations for the drive system can be simplified.

Free Vibration and Stability of a Spinning Disk-Spindle System

1999 ◽  
Vol 121 (3) ◽  
pp. 391-396 ◽  
Author(s):  
R. G. Parker ◽  
P. J. Sathe
Keyword(s):  
Free Vibration ◽  
Strain Energy ◽  
Natural Frequencies ◽  
Vibration Modes ◽  
Modal Strain Energy ◽  
Spindle System ◽  
Disk Rotation ◽  
High Speeds ◽  
Elastic Disk ◽  
Strain Energy Ratio

This work examines the free vibration and stability of a spinning, elastic disk-spindle system. The extended operator formulation is exploited to discretize the system using Galerkin’s method (Parker, 1999). The coupled vibration modes of the system consist of disk modes, in which the disk dominates the system deformation, and spindle modes, in which the spindle dominates the system deformation. Both the natural frequencies and vibration modes are strongly affected by disk flexibility. If the membrane stresses associated with disk rotation are neglected then the system exhibits flutter instabilities, but these instabilities are not present when membrane stresses are modeled. Natural frequency veering between disk and spindle frequencies is prominent at low speeds and substantially affects the spectrum and stability. No veering is observed at high speeds where rotational stress stiffening diminishes disk-spindle coupling and causes the natural frequencies to converge to those of a rotating spindle carrying a rigid disk. Changes to the vibration modes are examined in terms of a strain energy ratio measuring the contribution of the disk strain energy to the total modal strain energy.

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.

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.

scholarly journals Vibration Analysis of a Tire in Ground Contact under Varied Conditions

2017 ◽  
Vol 47 (1) ◽  
pp. 3-17 ◽  
Author(s):  
Murat Karakus ◽  
Aydin Cavus ◽  
Mehmet Colakoglu
Keyword(s):  
Free Vibration ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Concrete Block ◽  
Ground Contact ◽  
Tire Model ◽  
Inflation Pressure ◽  
Monitoring Method ◽  
The Impact ◽  
Good Agreement

Abstract The effect of three different factors, which are inflation pressure, vertical load and coefficient of friction on the natural frequencies of a tire (175/70 R13) has been studied. A three dimensional tire model is constructed, using four different material properties and parts in the tire. Mechanical properties of the composite parts are evaluated. After investigating the free vibration, contact analysis is carried out. A concrete block and the tire are modelled together, using three different coefficients of friction. Experiments are run under certain conditions to check the accuracy of the numerical model. The natural frequencies are measured to describe free vibration and vibration of the tire contacted by ground, using a damping monitoring method. It is seen, that experimental and numerical results are in good agreement. On the other hand, investigating the impact of three different factors together is quite difficult on the natural frequencies. When some of these factors are assumed to be constant and the variables are taken one by one, it is easier to assess the effects.

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.

Virtual Detection of a Radial-Ply Tire’s Three-Dimensional Free Vibration Modes Transmissibility

2003 ◽  
Author(s):  
Y. P. Chang
Keyword(s):  
Free Vibration ◽  
Transient Response ◽  
Three Dimensional ◽  
Nonlinear Finite Element ◽  
Vibration Modes ◽  
Tire Model ◽  
Response Characteristics ◽  
Beam Elements ◽  
Fea Model ◽  
Response Information

A full nonlinear finite element P205/70R14 passenger car-radial-ply tire model was developed and run on a 1.7-meter-diameter spinning test drum model at a constant speed of 50 km/h in order to investigate the tire transient response characteristics, i.e. the tire three-dimensional free vibration modes transmissibility in X, Y and Z directions. The tire model was constructed in extreme detail with three-dimensional solid, layered membrane, and beam elements. The reactions forces of the tire axle in longitudinal (X axis), lateral (Y axis) and vertical (Z axis) directions were recorded when the tire rolled over a cleat on the test drum, and then the FFT algorithm was applied to examine the transient response information in the frequency domain. The result showed that this tire has clear peaks of 45, 40, and 84 Hz transmissibility in the longitudinal, lateral and vertical directions. This result was validated against previous studies by analytical, experimental, and FEA model approaches and showed excellent agreement. The parameters adopted in this FEA tire model were also compared with experimental work and the extraordinary agreement was also confirmed. The tire three dimensional free vibration modes transmissibility was successfully detected virtually.

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.

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