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.

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.

Analysis of Modal Parameters of Adhesively Bonded Double-Strap Joints by the Modal Strain Energy Method

1993 ◽  
Author(s):  
Mohan D. Rao ◽  
Krishna M. Gorrepati
Keyword(s):  
Strain Energy ◽  
Natural Frequencies ◽  
Structural Parameters ◽  
Flexural Vibration ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Adhesively Bonded ◽  
Modal Strain Energy ◽  
Joint System ◽  
Damping Material

Abstract This paper presents the analysis of modal parameters (natural frequencies, damping ratios and mode shapes) of a simply supported beam with adhesively bonded double-strap joint by the finite-element based Modal Strain Energy (MSE) method using ANSYS 4.4A software. The results obtained by the MSE method are compared with closed form analytical solutions previously obtained by the first author for flexural vibration of the same system. Good agreement has been obtained between the two methods for both the natural frequencies and system loss factors. The effects of structural parameters and material properties of the adhesive on the modal properties of the joint system are also studied which are useful in the design of the joint system for passive vibration and noise control. In order to evaluate the MSE and analytical results, some experiments were conducted using aluminum double-strap joint with 3M ISD112 damping material. The experimental results agreed well with both analytical and MSE results indicating the validity of both analytical and MSE methods. Finally, a comparative study has been conducted using various commercially available damping materials to evaluate their relative merits for use in the design of these joints.

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.

Research on Feasibility and Applicability of Delamination Localization Methods for Composite Laminated Beams

2014 ◽  
Vol 599-601 ◽  
pp. 92-95
Author(s):  
Hang Ma ◽  
Ping Lu ◽  
Tao Jiang ◽  
Sheng Feng Shi ◽  
Jian Bin Wei ◽  
...  
Keyword(s):  
Strain Energy ◽  
Damage Index ◽  
Energy Difference ◽  
Laminated Beams ◽  
Modal Strain Energy ◽  
Laminated Beam ◽  
Modal Strain Energy Method ◽  
Response Method ◽  
Strain Energy Ratio ◽  
Delamination Damage

The feasibility and applicability of delamination damages localization methods with various defined damage indexes for the damaged composite laminated beam were studied. The results indicate that, for the modal strain energy method, damage indexes defined by strain energy difference are more effective to locate the delamination damage than that of strain energy ratio. For energy response method, damage index defined by the second difference can effectively locate the delamination damage in the composite laminated beams.

Analysis of Modal Parameters of Adhesively Bonded Double-Strap Joints by the Modal Strain Energy Method

1996 ◽  
Vol 118 (1) ◽  
pp. 28-35 ◽  
Author(s):  
K. M. Gorrepati ◽  
M. D. Rao
Keyword(s):  
Strain Energy ◽  
Natural Frequencies ◽  
Structural Parameters ◽  
Flexural Vibration ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Adhesively Bonded ◽  
Modal Strain Energy ◽  
Joint System ◽  
Damping Material

This paper presents the analysis of modal parameters (natural frequencies, damping and mode shapes) of a simply supported beam with adhesively bonded double-strap joint by the finite-element based Modal Strain Energy (MSE) method using ANSYS 4.4A software. The results obtained by the MSE method are compared with closed form analytical solutions previously obtained by the author for flexural vibration of the same system. Good agreement has been obtained between the two methods for both the natural frequencies and system loss factors. The effects of structural parameters and material properties of the adhesive on the modal properties of the joint system are also studied which are useful in the design of the joint system for passive vibration and noise control. In order to evaluate the MSE and analytical results, some experiments were conducted using aluminum double-strap joints with 3M ISD112 damping material. The experimental results agreed well with both analytical and MSE results indicating the validity of both analytical and MSE methods. Finally, a comparative study has been conducted using various commercially available damping materials to evaluate their relative merits for use in the design of these joints.

scholarly journals DEVELOPMENT OF A DESIGN METHOD FOR DETERMINING THE ATTACHMENT OF THE EXHAUST MOUNTING MOUNTS

Akustika ◽  
2019 ◽  
Vol 34 ◽  
pp. 141-147
Author(s):  
Rakhmatjon Rakhmatov ◽  
Vitaliy Krutolapov ◽  
Valeriy Zuzov
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Strain Energy ◽  
Natural Frequencies ◽  
Design Method ◽  
Exhaust System ◽  
Element Model ◽  
Vehicle Body ◽  
Vibration Modes ◽  
The Finite Element Model

The article presents the developed method of determining the attachment points of the mounts of the exhaust system to the vehicle body. The requirements for the construction of a finite element model of the exhaust system are presented, the finite element model of the exhaust system is created, the results of natural frequencies and vibration modes and the strain energy of the structure are shown.

Viscoelastic Damping Calculations Using a p-Type Finite Element Code

1992 ◽  
Vol 59 (3) ◽  
pp. 696-699 ◽  
Author(s):  
C. J. Wilson ◽  
P. Carnevali ◽  
R. B. Morris ◽  
Y. Tsuji
Keyword(s):  
Finite Element ◽  
Strain Energy ◽  
Natural Frequencies ◽  
Computation Time ◽  
Viscoelastic Damping ◽  
Modal Strain Energy ◽  
Modal Strain Energy Method ◽  
Solution Convergence ◽  
Cantilevered Beam ◽  
P Type

Damping factors of viscoelastically damped structures can be calculated using the modal strain energy method, implemented with a sequence of undamped modal analysis computations. There are significant advantages in performing these calculations using p-type finite element codes. These include ease of mesh design, an indicator of degree of solution convergence, modest computation time, and an insensitivity to element aspect ratio. Capitalizing on these advantages an algorithm is defined, which is effective in solving for the natural frequencies and modal loss factors of damped structures. The algorithm is demonstrated using a sandwiched cantilevered beam as an example.

scholarly journals Effects of molecule force on free vibration for a micro electromagnetic harmonic drive system

2021 ◽  
Vol 22 ◽  
pp. 12
Author(s):  
Dan Zhao ◽  
Lizhong Xu ◽  
Yuming Fu
Keyword(s):  
Free Vibration ◽  
Lower Order ◽  
Natural Frequencies ◽  
Van Der Waals ◽  
Drive System ◽  
Van Der Waals Force ◽  
Vibration Modes ◽  
Harmonic Drive ◽  
Force Dynamics ◽  
Flexible Ring

In this paper, a micro electromagnetic harmonic drive system is proposed. Considering Van der Waals force, dynamics equation of the flexible ring for the micro drive system is deduced and resolved. Using the equations, the effects of the molecule force on the natural frequencies and vibration modes of the drive system are investigated. Results show that considering molecule force, natural frequencies of the flexible ring are reduced and its vibration modes are changed. For lower order modes, smaller clearance between the flexible ring and stator, smaller thickness of the flexible ring and larger radius of the flexible ring, the effects of the molecule force on the natural frequencies and vibration modes are more obvious.

Effect of Semi-Geodesic Winding on the Vibration Characteristics of Filament Wound Shells of Revolution

2011 ◽  
Vol 78 (6) ◽  
Author(s):  
Altan Kayran ◽  
Can Serkan İbrahimoğlu
Keyword(s):  
Free Vibration ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Vibration Modes ◽  
Integration Technique ◽  
Shells Of Revolution ◽  
Spherical Shells ◽  
Filament Wound ◽  
Winding Angle ◽  
Dominant Parameter

The effect of semigeodesic winding on the free vibration characteristics of filament wound shells of revolution is studied. For this purpose multisegment numerical integration technique is extended to the solution of the free vibration problem of composite shells of revolution which are wound along the semigeodesic fiber paths counting on the preset friction used during the winding process. Sample results are obtained for truncated conical and spherical shells of revolution and the effect of preset friction on the vibration characteristics of filament wound shells of revolution is particularly analyzed. Results show that when the preset friction is increased natural frequencies of higher circumferential vibration modes also increase irrespective of the initial winding angle, and the circumferential bending stiffness stands out as the dominant parameter governing the natural frequencies of higher circumferential vibration modes.

scholarly journals Vibration Analysis of Viscoelastically Damped Sandwich Shells

1996 ◽  
Vol 3 (6) ◽  
pp. 403-417 ◽  
Author(s):  
Ji-Fan He ◽  
Bang-An Ma
Keyword(s):  
Asymptotic Solution ◽  
Strain Energy ◽  
Natural Frequencies ◽  
Governing Equations ◽  
Modal Strain Energy ◽  
Simply Supported ◽  
Modal Strain Energy Method ◽  
Sandwich Shells ◽  
Method Accuracy ◽  
Loss Factors

The simplified governing equations and corresponding boundary conditions of vibration of viscoelastically damped unsymmetrical sandwich shells are given. The asymptotic solution to the equations is then discussed. If only the first terms of the asymptotic solution of all variables are taken as an approximate solution, the result is identical with that obtained from the modal strain energy method. By taking more terms of the asymptotic solution with successive calculations and use of the Padé approximants method, accuracy of natural frequencies and modal loss factors of sandwich shells can be improved. The lowest three or four natural frequencies and modal loss factors of simply supported cylindrical sandwich shells are calculated.

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