Theory of Receptance Applied to Modal Analysis of a Spinning Disk With Interior Multi-Point Supports

1992 ◽  
Vol 114 (4) ◽  
pp. 468-476 ◽  
Author(s):  
S. C. Huang ◽  
B. S. Hsu
Keyword(s):  
Modal Analysis ◽  
Vibration Analysis ◽  
Critical Speed ◽  
Rotation Speed ◽  
Frequency Equation ◽  
Numerical Results ◽  
Mode Shapes ◽  
Spinning Disk ◽  
Nodal Pattern ◽  
Receptance Method

The theory of receptance applied to the modal analysis of a spinning disk with interior multi-point supports is developed. Traveling modes are first introduced for the vibration analysis of a spinning disk. The receptance method is then applied to join the spinning disk and the point supports. The frequency equation and mode shapes are then formulated. An important property, conjugate pairing of the cross receptances is derived. This feature has never been described before in the literature. Numerical results for various numbers of point supports are illustrated. The results show that the nodal pattern of a spinning disk with point supports is varying periodically. The change of rotation speed further causes the mode exchange phenomenon. The change of first critical speed due to point supports is also discussed.

The Use of Modan 3D in Experimental Modal Analysis

2013 ◽  
Vol 486 ◽  
pp. 36-41 ◽  
Author(s):  
Róbert Huňady ◽  
František Trebuňa ◽  
Martin Hagara ◽  
Martin Schrötter
Keyword(s):  
Modal Analysis ◽  
Vibration Analysis ◽  
High Speed ◽  
Mechanical Vibration ◽  
Steel Sample ◽  
Experimental Modal Analysis ◽  
Image Correlation ◽  
Optical Methods ◽  
Mode Shapes ◽  
Vibration Modes

Experimental modal analysis is a relatively young part of dynamics, which deals with the vibration modes identification of machines or their parts. Its development has started since the beginning of the eighties, when the computers hardware equipment has improved and the fast Fourier transform (FFT) could be used for the results determination. Nowadays it provides an uncountable set of vibration analysis possibilities starting with conventional contact transducers of acceleration and ending with modern noncontact optical methods. In this contribution we mention the use of high-speed digital image correlation by experimental determination of mode shapes and modal frequencies. The aim of our work is to create a program application called Modan 3D enabling the performing of experimental modal analysis and operational modal analysis. In this paper the experimental modal analysis of a thin steel sample performed with Q-450 Dantec Dynamics is described. In Modan 3D the experiment data were processed and the vibration modes were determined. The reached results were verified by PULSE modulus specialized for mechanical vibration analysis.

scholarly journals Three Dimensional Vibration Analysis of a Class of Traction-Free Solid Elastic Bodies with an Eccentric Cavity

2012 ◽  
Vol 19 (6) ◽  
pp. 1341-1357 ◽  
Author(s):  
Seyyed M. Hasheminejad ◽  
Yaser Mirzaei
Keyword(s):  
Vibration Analysis ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Numerical Results ◽  
Mode Shapes ◽  
Computational Techniques ◽  
Published Data ◽  
Elastic Structures ◽  
Wide Range ◽  
Vibrational Characteristics

A three-dimensional elasticity-based continuum model is developed for describing the free vibrational characteristics of an important class of isotropic, homogeneous, and completely free structural bodies (i.e., finite cylinders, solid spheres, and rectangular parallelepipeds) containing an arbitrarily located simple inhomogeneity in form of a spherical or cylindrical defect. The solution method uses Ritz minimization procedure with triplicate series of orthogonal Chebyshev polynomials as the trial functions to approximate the displacement components in the associated elastic domains, and eventually arrive at the governing eigenvalue equations. An extensive review of the literature spanning over the past three decades is also given herein regarding the free vibration analysis of elastic structures using Ritz approach. Accuracy of the implemented approach is established through proper convergence studies, while the validity of results is demonstrated with the aid of a commercial FEM software, and whenever possible, by comparison with other published data. Numerical results are provided and discussed for the first few clusters of eigen-frequencies corresponding to various mode categories in a wide range of cavity eccentricities. Also, the corresponding 3D mode shapes are graphically illustrated for selected eccentricities. The numerical results disclose the vital influence of inner cavity eccentricity on the vibrational characteristics of the voided elastic structures. In particular, the activation of degenerate frequency splitting and incidence of internal/external mode crossings are confirmed and discussed. Most of the results reported herein are believed to be new to the existing literature and may serve as benchmark data for future developments in computational techniques.

Free Vibration Analysis of Shafts on Resilient Bearings Using Timoshenko Beam Theory

1999 ◽  
Vol 121 (2) ◽  
pp. 256-258 ◽  
Author(s):  
S. Karunendiran ◽  
J. W. Zu
Keyword(s):  
Free Vibration ◽  
Timoshenko Beam ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Frequency Equation ◽  
Timoshenko Beam Theory ◽  
Mode Shapes ◽  
Complex Eigenvalues ◽  
First Time

This paper presents an analytical method adopted for the free vibration analysis of a shaft, both ends of which are supported by resilient bearings. The shaft is modeled by Timoshenko beam theory. Based on this model exact frequency equation to calculate complex eigenvalues is derived and presented in complex compact form for the first time. Explicit expressions to compute the corresponding mode shapes are also presented.

scholarly journals Vibration Modes and Parameter Analysis of V-Shaped Electrothermal Microactuators

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Zhuo Zhang ◽  
Yueqing Yu ◽  
Xuping Zhang
Keyword(s):  
Modal Analysis ◽  
Natural Frequencies ◽  
Frequency Equation ◽  
Parameter Analysis ◽  
Mode Shapes ◽  
Element Analysis ◽  
Shaped Beam ◽  
The Finite Element Analysis ◽  
Parametric Studies ◽  
First Time

Comprehensive analysis on the modal characteristics of V-shaped electrothermal microactuators is presented in this paper for the first time. Considering the unique geometric characteristics of the V-shaped beam, that is, two inclined beams supporting a movable shuttle, both the lateral and longitudinal deflections are taken into account in the modal analysis. Boundary and continuity conditions are employed to obtain the frequency equation. Natural frequencies are then obtained by solving the frequency equation. Mode shapes corresponding to their natural frequencies are also calculated analytically. The theoretical modal analysis is verified with the finite element analysis using ANSYS software. Based on the model analysis, this paper further investigates the relationship between natural frequencies and the volume scaling of the V-shaped beam. Finally, comprehensive parametric studies in terms of material properties and structural dimensions are conducted to provide insights and guidance in designing the V-shaped beam electrothermal microactuators.

Modal Analysis of the Cylinder Mechanism Based on ANSYS Workbench

2013 ◽  
Vol 561 ◽  
pp. 496-500
Author(s):  
De Gong Chang ◽  
Hong Yun Dou ◽  
Fu Qin Yang ◽  
Rong Zong
Keyword(s):  
Modal Analysis ◽  
High Speed ◽  
Optimization Design ◽  
Critical Speed ◽  
Structural Characteristics ◽  
Safety Evaluation ◽  
Mode Shapes ◽  
Bearing Stiffness ◽  
Working Principle ◽  
Ansys Workbench

According to the working principle and structural characteristics of cylinder mechanism, the simplified model is built by the Pro/E software. Then we carry on the modal analysis for cylinder mechanism combined with ANSYS Workbench [1], and obtain the natural frequency and mode shapes of all steps. It provides the basis for optimization design and safety evaluation of cylinder mechanism. Finally, we study the influence of bearing stiffness on the critical speed, which provides the basis for the research of high-speed cylinder.

Free Vibration Analysis of a Beam Under Axial Load Carrying a Mass-Spring-Mass

2012 ◽  
Author(s):  
O. R. Barry ◽  
Y. Zhu ◽  
J. W. Zu ◽  
D. C. D. Oguamanam
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Axial Load ◽  
Equations Of Motion ◽  
Tensile Load ◽  
Free Vibration Analysis ◽  
Frequency Equation ◽  
Mode Shapes ◽  
Mass System ◽  
Mass Spring

This paper deals with the free vibration analysis of a beam subjected to an axial tensile load with an attached in-span mass-spring-mass system. The equations of motion are derived by means of the Hamilton principle and an explicit expression of the frequency equation is presented. The formulation is validated with results in the literature and the finite element method. Parametric studies are done to investigate the effect of the axial load, the magnitude and location of the mass-spring-mass system on the lowest five natural frequencies and mode shapes. The results indicate that the fundamental mode is independent of the tension and the in-span mass. However, a significant change in all modes is observed when the position of the mass-spring-mass is varied.

Modal Analysis of a Spinning Cylindrical Shell with Interior Point or Circular Line Supports

1993 ◽  
Vol 115 (4) ◽  
pp. 535-543 ◽  
Author(s):  
Shyh-Chin Huang ◽  
Bih-Sheng Hsu
Keyword(s):  
Cylindrical Shell ◽  
Modal Analysis ◽  
Physical Interpretation ◽  
Interior Point ◽  
Rotational Speed ◽  
Frequency Equation ◽  
Mode Shapes ◽  
Point Support ◽  
Frequency Changes ◽  
Circular Line

An approach to the modal analysis of a spinning cylindrical shell with interior multipoint or circular-line supports is developed. Receptance theory is applied for joining the shell and supports. The frequency equation and mode shapes are then formulated. Conjugate pairing in cross receptances is found in the point support case, but not in the circular line support case. Numerical results for various numbers of point supports are illustrated, and physical interpretation of those results is given. Effects of rotational speed on frequency changes are also addressed.

Three-Dimensional Vibration Analysis of a Truncated Quadrangular Pyramid

1987 ◽  
Vol 54 (1) ◽  
pp. 115-120 ◽  
Author(s):  
T. Irie ◽  
G. Yamada ◽  
Y. Tagawa
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Three Dimensional ◽  
Frequency Equation ◽  
The Body ◽  
Mode Shapes ◽  
Algebraic Polynomials ◽  
Transformation Of Variables ◽  
Unit Edge

An analysis is presented for the three-dimensional vibration problem of determining the natural frequencies and the mode shapes of a truncated quadrangular pyramid. For this purpose, the body is transformed into a right quadrangular prism with unit edge lengths by a transformation of variables. With the displacements of the transformed prism assumed in the forms of algebraic polynomials, the dynamical energies of the prism are evaluated, and the frequency equation is derived by the Ritz method. This method is applied to quadrangular pyramids in which the base is clamped and the other sides are free, and the natural frequencies (the eigenvalues of vibration) and the mode shapes are calculated numerically, from which the vibration characteristics arising in the pyramids are studied.

Modal and Vibration Analysis of a Trator Frame Based on FEM

2013 ◽  
Vol 373-375 ◽  
pp. 16-19 ◽  
Author(s):  
Kang Li Shao ◽  
Feng Wang ◽  
Yong Hai Wu
Keyword(s):  
Modal Analysis ◽  
Dynamic Characteristics ◽  
Vibration Analysis ◽  
Geometric Model ◽  
Excitation Frequency ◽  
Mode Shapes ◽  
Characteristics Analysis ◽  
Dynamic Characteristics Analysis

Modal analysis and vibration analysis is the foundation of dynamic characteristics analysis and it is the most important methods to analyze the inherent characteristics and mode shapes of the system. In this paper, the airport tractor frame is taken as the research object and its geometric model is established by Pro / E, 10 order modal and shapes of tractor frame is obtained by ANSYS. The results showed that: the first and second frequency of the frame is avoided the engine idling, the outbreak frequency, and excitation frequency in normal driving road. The entire frame meets the requirement of the dynamic characteristics.

Assessment of Serviceability of the Footbridge Across Opatovska Street

2016 ◽  
Vol 827 ◽  
pp. 263-266
Author(s):  
Vladimír Sana
Keyword(s):  
Theoretical Analysis ◽  
Modal Analysis ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Fe Model ◽  
Matlab Code ◽  
Forced Vibration Analysis

This paper is focused on the assessment of serviceability of the footbridge structure, which has been excited by pedestrians and vandals. The three dimensional FE model of the footbridge structure was created for the necessities of theoretical modal analysis. Computed mode shapes and natural frequencies were subsequently used for the forced vibration analysis as an input files into MATLAB code. Results obtained by the theoretical analysis were compared with the experimental results. At the end of this paper, the comfort criterion of crossing pedestrians has been evaluated.

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