Multi-Junction, Multi-Branch Torsional Vibration in a Geared Rotating System

2000 ◽  
Author(s):  
Qing Ke Yuan ◽  
David Y. Yao
Keyword(s):  
Torsional Vibration ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Design Stage ◽  
Design Parameters ◽  
Analysis Program ◽  
Vibration System ◽  
Rotating System ◽  
Steel Rolling ◽  
Mining Machinery

Abstract A multi-junction, multi-branch torsional vibration system is often found in a geared rotating system. This is an important part in many types of machinery, such as mining machinery, petroleum machinery, steel rolling machinery and automobiles. If the design parameters of the system are improper, there will be serious torsional vibration, which will cause noticeable sound disturbances, severe shakings, and component fatigue problems. Analyzing and pre-estimating critical speeds or torsional natural frequencies and mode shapes of the vibration systems in the design stage is very important to avoid future disastrous and costly repairs of the machinery. In this paper, a radical and effective method for calculating natural frequencies and mode shapes of multi-junction, multi-branch torsional vibration systems, has been put forward, a program named MJBTVAP (Multi-Junction, multi-Branch Torsional Vibration Analysis Program) based on this method has been developed, actual problems have been solved.

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.

scholarly journals Coupled flexural - torsional vibration and stability analysis of pre-loaded beams using conventional and dynamic finite element methods

2021 ◽  
Author(s):  
Heenkenda Jayasinghe
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Axial Force ◽  
Torsional Vibration ◽  
Natural Frequencies ◽  
Nonlinear Eigenvalue Problem ◽  
Compressive Force ◽  
Mode Shapes ◽  
Dynamic Finite Element ◽  
Starting Point

Dynamic Finite Element (DFE) and conventional finite element formulations are developed to study the flexural - torsional vibration and stability of an isotropic, homogeneous and linearly elastic pre-loaded beam subjected to an axial load and end-moment. Various classical boundary conditions are considered. Elementary Euler - Bernoulli bending and St. Venant torsion beam theories were used as a starting point to develop the governing equations and the finite element solutions. The nonlinear Eigenvalue problem resulted from the DFE method was solved using a program code written in MATLAB and the natural frequencies and mode shapes of the system were determined form the Eigenvalues and Eigenvectors, respectively. Similarly, a linear Eigenvalue problem was formulated and solved using a MATLAB code for the conventional FEM method. The conventional FEM results were validated against those available in the literature and ANSYS simulations and the DFE results were compared with the FEM results. The results confirmed that tensile forces increased the natural frequencies, which indicates beam stiffening. On the contrary, compressive forces reduced the natural frequencies, suggesting a reduction in beam stiffness. Similarly, when an end-moment was applied the stiffness of the beam and the natural frequencies diminished. More importantly, when a force and end-moment were acting in combination, the results depended on the direction and magnitude of the axial force. Nevertheless, the stiffness of the beam is more sensitive to the changes in the magnitude and direction of the axial force compared to the moment. A buckling analysis of the beam was also carried out to determine the critical buckling end-moment and axial compressive force.

Torsional Vibration Analysis of Shafts With Sections of Tapered Diameter

1993 ◽  
Author(s):  
John R. Baker ◽  
Keith E. Rouch
Keyword(s):  
Torsional Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Displacement Function ◽  
The Other ◽  
Mode Shapes ◽  
Axial Distance ◽  
Rotational Degree ◽  
Rotor Systems ◽  
Constant Diameter

Abstract This paper presents the development of two tapered finite elements for use in torsional vibration analysis of rotor systems. These elements are particularly useful in analysis of systems that have shaft sections with linearly varying diameters. Both elements are defined by two end nodes, and inertia matrices are derived based on a consistent mass formulation. One element assumes a cubic displacement function and has two degrees of freedom at each node: rotation about the shaft’s axis and change in angle of rotation with respect to the axial distance along the shaft. The other element assumes a linear displacement function and has one rotational degree of freedom at each node. The elements are implemented in a computer program. Calculated natural frequencies and mode shapes are compared for both tapered shaft sections and constant diameter sections. These results are compared with results from an available constant diameter element. It is shown that the element derived assuming a cubic displacement function offers much better convergence characteristics in terms of calculated natural frequencies, both for tapered sections and constant diameter sections, than either of the other two elements. The finite element code that was developed for implementation of these elements is specifically designed for torsional vibration analysis of rotor systems. Lumped inertia, lumped stiffness, and gear connection elements necessary for rotor system analysis are also discussed, as well as calculation of natural frequencies, mode shapes, and amplitudes of response due to a harmonic torque input.

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.

Free Vibration Characteristics of SPR Joints

2006 ◽  
Author(s):  
Xiaocong He ◽  
Ian Pearson ◽  
Ken Young
Keyword(s):  
Aluminum Alloy ◽  
Free Vibration ◽  
Torsional Vibration ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Advanced Materials ◽  
Mode Shapes ◽  
Stress Distributions ◽  
Numerical Examples ◽  
Different Characteristics

Self-piercing riveting (SPR) has drawn more attention in recent years because it can join some advanced materials that are hard to weld, such as aluminum alloy sheets. In this paper, the free torsional vibration characteristics of single lap-jointed encastre SPR beam are investigated in detail. The focus of the analysis is to reveal the influence on the torsional natural frequencies and mode shapes of the single lap-jointed encastre SPR beam of different characteristics of sheets to be jointed. Numerical examples show that the torsional natural frequencies increase significantly as the Young’s modulus of the sheets increase, but almost no change corresponding to the change in Poisson’s ratio of the sheets to be joint. The mode shapes show that there are different deformations in the jointed section of SPR beam compared with the reference encastre beam without joint. These different deformations may cause different natural frequency values and different stress distributions.

A Parametrization Describing Blisk Airfoil Variations Referring to Modal Analysis

2017 ◽  
Author(s):  
Thomas Backhaus ◽  
Thomas Maywald ◽  
Sven Schrape ◽  
Matthias Voigt ◽  
Ronald Mailach
Keyword(s):  
Modal Analysis ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Design Parameters ◽  
Surface Mesh ◽  
Main Mode ◽  
Airfoil Surface ◽  
Parametrization Method ◽  
Surface Meshes ◽  
Geometric Variation

This paper will present a way to capture the geometric blade by blade variations of a milled from solid blisk as well as the manufacturing scatter. Within this idea it is an essential task to digitize the relevant airfoil surface as good as possible to create a valid surface mesh as the base of the upcoming evaluation tasks. Since those huge surface meshes are not easy to handle and are even worse in getting quantified and easy interpretable results, it should be aimed for an easily accessible way of presenting the geometric variation. The presented idea uses a section based airfoil parametrization that is based on an extended NACA-airfoil structure to ensure the capturing of all occurring characteristic geometry variations. This Paper will show how this adapted parametrization method is suitable to outline all the geometric blade by blade variation and even more, refer those airfoil design parameters to modal analysis results such as the natural frequencies of the main mode shapes. This way, the dependencies between the modal and airfoil parameters will be proven.

scholarly journals Vibration Analysis of Radial Compressor Impellers

1983 ◽  
Author(s):  
J. Wachter ◽  
H. Celikbudak
Keyword(s):  
Dynamic Behavior ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Design Parameters ◽  
Centrifugal Impeller ◽  
Structural Dynamic ◽  
Experimental Procedure ◽  
Radial Compressor ◽  
Comparison Of The Results ◽  
Important Design

There are many problems facing the designers of turbomachines with the demand for ever increasing capabilities and reliability. One problem that requires considerable attention is the vibration characteristics of some components. It is object of this work to determine the dynamic behavior, namely natural frequencies, mode shapes of a centrifugal impeller which are being important design parameters in order to avoid costly failures in the development phase. This work divides into three sections. First, a Finite Element structural dynamic analysis is presented. Then experimental procedure used to determine the natural frequencies and mode shapes is described together with the comparison of the results obtained both theoretically through FEM and experimentally. Finally, interferometric holography technique is used as a means for obtaining the dynamic behavior of the impeller.

An Improved Holzer Procedure for Torsional Vibration Analysis

1975 ◽  
Vol 17 (1) ◽  
pp. 26-30 ◽  
Author(s):  
B. Dawson ◽  
M. Davies
Keyword(s):  
Torsional Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Vibration System

An automatic, root-searching, extended Holzer method is described that is guaranteed to determine all the natural frequencies of a system with the exception of those values lying within prescribed tolerance bandwidth limits. The method is described and illustrated by the determination of the natural frequencies of an eight-rotor free-free torsional vibration system.

Analytical and Experimental Modal Characteristics of Cylindrical Shells

2005 ◽  
Author(s):  
Basem Alzahabi
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Offshore Structures ◽  
Operating Conditions ◽  
Mode Shapes ◽  
Design Stage ◽  
Scaled Model ◽  
Modal Characteristics ◽  
Acoustic Signature

Cylindrical Shells are widely used in many structural designs, such as offshore structures, liquid storage tanks, submarine hulls, and airplane hulls. Most of these structures are required to operate in a dynamic environment. The acoustic signature of submarines is very critical in such high performance structure. Submarines are not only required to sustain very high dynamic loadings at all time, but also being able maneuver and perform their functions under sea without being detected by sonar systems. Reduction of sound radiation is most efficiently achieved at the design stage, and the acoustic signatures may be determined by considering operational scenarios, and modal characteristics. The acoustic signature of submarines is generally of two categories; broadband which has a continuous spectrum; and a tonal noise which has discrete frequencies. Therefore, investigating the dynamic characteristics of cylindrical shells is very critical first step in developing a strategy for modal vibration control for specific operating conditions. Unlike those of beam structure, the lowest natural frequency does not necessarily correspond to the lowest wave index. In fact, the natural frequencies do not fall in ascending order of the wave index in cylindrical shells. Mode shapes associated with each natural frequency are combination of Radial, Longitudinal, and Circumferential modes. In this paper, a scaled model of submarine hull segment under shear diaphragm boundary conditions is analyzed analytically and numerically. Then experimental modal analysis of the scaled model utilizing a fixed response approach was performed to obtain the modal characteristics of the cylindrical shell between 0 and 800 Hz. The cylinder was excited at predetermined points with an impact hammer, while the response was measured using an accelerometer at specified fixed point. Designing a boundary condition that simulate a shear diaphragm is very challenging task by itself. A total of ten natural frequencies were found within that range with their corresponding mode shapes. The experimental data were correlated with those results obtained analytically and numerically using the finite element methods using MSC.NASTRAN software. The results were found to be in excellent agreement.

Structural Undamped Free Vibration Analysis Based on Coefficient Reduced-Basis Method

2014 ◽  
Vol 556-562 ◽  
pp. 4214-4217
Author(s):  
Yong Hong Li ◽  
Shu Zhan Li
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Reduced Basis Method ◽  
Mode Shapes ◽  
Design Parameters ◽  
The Finite Element Method ◽  
Reduced Basis ◽  
Linear Elastic ◽  
Basis Method

Using reduced-basis method, design parameters are needed to be separated from the linear elastic operators, which is time-consuming. So, an improved reduced-basis method - coefficient reduced-basis method is introduced to calculate the low order natural frequencies and mode shapes of structure. In this method, the computing process of design parameters separated from the linear elastic operators is simplified. In this paper, a truck frame is taken as an example, frequencies and mode shapes from coefficient reduced-basis method are obtained. Comparing with results from the finite element method, coefficient reduced-basis method can obtain accurate results efficiently.

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