1/2-Order Subharmonic Resonances in Horizontally Supported Jeffcott Rotor

2011 ◽  
Author(s):  
Nao Yoshida ◽  
Tomoyuki Takano ◽  
Hiroshi Yabuno ◽  
Tsuyoshi Inoue ◽  
Yukio Ishida
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Vertical Direction ◽  
Support Condition ◽  
Restoring Force ◽  
Rotary Machine ◽  
Jeffcott Rotor ◽  
The Difference ◽  
Subharmonic Resonances

A Rotary machine is a significant component of many mechanical systems. It is important to clarify the dynamic characteristics in several conditions. This study deals with nonlinear dynamics of a horizontally supported Jeffcott rotor. The equations of motion are derived by considering the effects of gravity and the cubic nonlinearity of restoring force by the support condition. These effects produce the difference between the linear natural frequencies in the vertical and horizontal directions and make the stiffness in the vertical direction unsymmetric. It is theoretically and experimentally shown that due to such effects, the 1/2-order subharmonic resonances are produced in the cases when the rotational speed is in the neighborhood of twice the natural frequencies in the horizontal and vertical directions, and the frequency response curve of the resonance near twice the horizontal natural frequency is hardening-type, while near twice the vertical natural frequency is softening-type.

INVESTIGATION OF THE PLANE VIBRATION OF AN ELASTIC PLATE WITH A KINEMATIC VIBRATION PROTECTION SYSTEM

2021 ◽  
Vol 75 (3) ◽  
pp. 44-50
Author(s):  
К. Bissembayev ◽  
◽  
Z. Omyrzhanova ◽  
K. Sultanova ◽  
◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Natural Frequency ◽  
Elastic Plate ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Rolling Contact ◽  
Seismic Protection ◽  
Geometrical Parameters ◽  
Plane Vibration ◽  
Hamilton Principle

Creation of vibro-protective devices on rolling contact bearings is widely spread in transportation technology and seismic protection. In this work, mathematical modeling of the oscillation movements of the elastic plate will be considered. The equations of motion for elastic plate on vibration supports bounded by high-order rotation surfaces by the Ostrogradsky-Hamilton principle are obtained. The natural frequencies of elastic plate are determined. It is established that the value of the natural frequencies of elastic plate decreases with increasing height and increases with the width of the bases. The ratio of the natural frequency of the second form to the natural frequency of the first form does not depend on the geometrical parameters of the plate.

Vibration and Stability of a Spinning Disk Under Stationary Distributed Edge Loads

1996 ◽  
Vol 63 (2) ◽  
pp. 439-444 ◽  
Author(s):  
Jen-San Chen
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Modal Interaction ◽  
Reflected Waves ◽  
Reflected Wave ◽  
Nonzero Integer ◽  
Spinning Disk ◽  
The Difference

The vibration and stability of a spinning disk under conservative distributed edge tractions are studied both numerically and analytically. The edge traction is circumferentially stationary in the space. When the compressive traction is uniform, it is found that no modal interaction occurs and the natural frequencies of all nonreflected waves decrease, while the natural frequencies of the reflected waves increase. When the spinning disk is under distributed traction in the form of cos kθ, where k is a nonzero integer, it is found that the eigenvalue only changes slightly under the edge traction if the natural frequency of interest is well separated from others. When two modes are almost degenerate, however, modal interaction may or may not occur. It is observed that when the difference between the number of nodal diameters of these two modes is equal to ±k, frequency veering occurs when both modes are nonreflected, and merging occurs when one of these two modes is a reflected wave. In applying this rule, the number of nodal diameters of the forward and the reflected wave is considered as negative.

Natural Frequency Analysis of Liquid-Filled Tanks

2005 ◽  
Author(s):  
Rouzbeh Amini ◽  
Grant Warner ◽  
Hamid Nayeb-Hashemi
Keyword(s):  
Natural Frequency ◽  
Frequency Analysis ◽  
Natural Frequencies ◽  
Water Levels ◽  
Resonance Phenomenon ◽  
Modal Shape ◽  
Earthquake Excitation ◽  
Element Analysis ◽  
The Difference ◽  
Natural Frequency Analysis

Traditionally, the cantilever modal shape of liquid-filled tanks has been considered as the most critical mode. However, recent research has demonstrated that natural frequencies associated with some circumferential modes might be close to the frequency of earthquake excitation. This can lead to a resonance phenomenon, and consequently failure of the tanks. In this paper, we perform Natural Frequency Analysis of fluid-filled tanks, using finite element analysis. Modeling and solution employ ADINA potential-based flow elements, which require the assumption of inviscid, irrotational and incompressible flow. The problem is solved for different geometries and water levels of tanks; the results are compared with the current results in the literature and the difference is demonstrated.

Size Effect on Natural Frequency of Cantilever Micro-Beams Based on a Modified Couple Stress Theory

2013 ◽  
Vol 694-697 ◽  
pp. 221-224 ◽  
Author(s):  
Sheng Li Kong
Keyword(s):  
Size Effect ◽  
Natural Frequency ◽  
Couple Stress ◽  
Natural Frequencies ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Beam Model ◽  
Stress Theory ◽  
Modified Couple Stress ◽  
The Difference

The natural frequency of cantilever micro-beams is solved analytically on the basis of modified couple stress theory. The governing equations are obtained by a combination of the basic equations of modified couple stress theory and Hamiltons principle. The size effect on natural frequencies of the cantilever micro-beams is analyzed. It is found that the natural frequencies of the cantilever micro-beams predicted by the newly model are size-dependent. The difference between the natural frequencies predicted by the newly established model and classical beam model is assessed.

Modal Experiment Research on Fluid-Solid Coupling Vibration of Hydraulic Long-Straight Pipeline of Shield Machine

2011 ◽  
Vol 105-107 ◽  
pp. 286-293 ◽  
Author(s):  
Jing Hua Xie ◽  
Ke Tian ◽  
Li He ◽  
Tian Ren Yang ◽  
Xiang Heng Zhu
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
Vertical Plane ◽  
Low Frequency ◽  
Pipeline System ◽  
Experiment Research ◽  
Coupling Vibration ◽  
The Difference ◽  
Shield Machine

The hydraulic long-straight pipeline system of the shield machine is to be studied in this paper. Modal parameters of the hydraulic long-straight pipeline whose length is 8m under three kinds of spans (single span, double spans and four spans) were measured and analyzed. Considering the inherent vibration characteristics of the shield machine, we limited the natural frequency of the multi-span long straight pipeline studied within the range of 0~ 200Hz.What the experiment shows is as follows: Firstly, the natural frequency of the hydraulic long-straight pipeline is densely distributed mainly in the low frequency; Secondly, the natural frequencies of vibration in the horizontal plane are slightly higher than those of corresponding orders in the vertical plane, although the difference is little; In addition, by increasing the number of supports, pipeline span can be reduced and the natural frequencies of pipeline can be significantly increased, but this will make the vibration mode change irregularly.

scholarly journals Vibration analysis of a sandwich cylindrical shell in hygrothermal environment

2021 ◽  
Vol 10 (1) ◽  
pp. 414-430
Author(s):  
Chunwei Zhang ◽  
Qiao Jin ◽  
Yansheng Song ◽  
Jingli Wang ◽  
Li Sun ◽  
...  
Keyword(s):  
Cylindrical Shell ◽  
Natural Frequency ◽  
Equations Of Motion ◽  
Single Layer ◽  
Functionally Graded ◽  
Sandwich Shell ◽  
Continuous Change ◽  
Multilayered Structures ◽  
Cylindrical Sandwich Shell ◽  
Vibrational Behavior

Abstract The sandwich structures are three- or multilayered structures such that their mechanical properties are better than each single layer. In the current research, a three-layered cylindrical shell including a functionally graded porous core and two reinforced nanocomposite face sheets resting on the Pasternak foundation is used as model to provide a comprehensive understanding of vibrational behavior of such structures. The core is made of limestone, while the epoxy is utilized as the top and bottom layers’ matrix phase and also it is reinforced by the graphene nanoplatelets (GNPs). The pattern of the GNPs dispersion and the pores distribution play a crucial role at the continuous change of the layers’ properties. The sinusoidal shear deformation shells theory and the Hamilton’s principle are employed to derive the equations of motion for the mentioned cylindrical sandwich shell. Ultimately, the impacts of the model’s geometry, foundation moduli, mode number, and deviatory radius on the vibrational behavior are investigated and discussed. It is revealed that the natural frequency and rotation angle of the sandwich shell are directly related. Moreover, mid-radius to thickness ratio enhancement results in the natural frequency reduction. The results of this study can be helpful for the future investigations in such a broad context. Furthermore, for the pipe factories current study can be effective at their designing procedure.

Elimination of outlier measurements for damage detection of structures under changing environmental conditions

2021 ◽  
pp. 147592172199847
Author(s):  
William Soo Lon Wah ◽  
Yining Xia
Keyword(s):  
Damage Detection ◽  
Multiple Regression ◽  
Natural Frequencies ◽  
Detection Method ◽  
Detection Methods ◽  
Structure Model ◽  
Bridge Structure ◽  
Beam Structure ◽  
Dependent Variables ◽  
The Difference

Damage detection methods developed in the literature are affected by the presence of outlier measurements. These measurements can prevent small levels of damage to be detected. Therefore, a method to eliminate the effects of outlier measurements is proposed in this article. The method uses the difference in fits to examine how deleting an observation affects the predicted value of a model. This allows the observations that have a large influence on the model created, to be identified. These observations are the outlier measurements and they are eliminated from the database before the application of damage detection methods. Eliminating the outliers before the application of damage detection methods allows the normal procedures to detect damage, to be implemented. A multiple-regression-based damage detection method, which uses the natural frequencies as both the independent and dependent variables, is also developed in this article. A beam structure model and an experimental wooden bridge structure are analysed using the multiple-regression-based damage detection method with and without the application of the method proposed to eliminate the effects of outliers. The results obtained demonstrate that smaller levels of damage can be detected when the effects of outlier measurements are eliminated using the method proposed in this article.

scholarly journals Effects of Elliptical Hole on the Correlation of Natural Frequency with Buckling Load of Basalt Laminates Composite Plates

2020 ◽  
Vol 27 (1) ◽  
pp. 216-225
Author(s):  
Buntheng Chhorn ◽  
WooYoung Jung
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Basalt Fiber ◽  
Orientation Angle ◽  
Elliptical Hole ◽  
Composite Plates ◽  
Buckling Load ◽  
Mode Shapes ◽  
Geometric Ratio

AbstractRecently, basalt fiber reinforced polymer (BFRP) is acknowledged as an outstanding material for the strengthening of existing concrete structure, especially it was being used in marine vehicles, aerospace, automotive and nuclear engineering. Most of the structures were subjected to severe dynamic loading during their service life that may induce vibration of the structures. However, free vibration studied on the basalt laminates composite plates with elliptical cut-out and correlation of natural frequency with buckling load has been very limited. Therefore, effects of the elliptical hole on the natural frequency of basalt/epoxy composite plates was performed in this study. Effects of stacking sequence (θ), elliptical hole inclination (ϕ), hole geometric ratio (a/b) and position of the elliptical hole were considered. The numerical modeling of free vibration analysis was based on the mechanical properties of BFRP obtained from the experiment. The natural frequencies as well as mode shapes of basalt laminates composite plates were numerically determined using the commercial program software (ABAQUS). Then, the determination of correlation of natural frequencies with buckling load was carried out. Results showed that elliptical hole inclination and fiber orientation angle induced the inverse proportion between natural frequency and buckling load.

scholarly journals A Vibration-Based Structural Health Monitoring System for Transmission Line Towers

Electronics ◽  
2019 ◽  
Vol 8 (5) ◽  
pp. 515 ◽  
Author(s):  
Long Zhao ◽  
Xinbo Huang ◽  
Ye Zhang ◽  
Yi Tian ◽  
Yu Zhao
Keyword(s):  
Structural Health Monitoring ◽  
Transmission Line ◽  
Natural Frequency ◽  
Health Monitoring ◽  
Structural Changes ◽  
Natural Frequencies ◽  
Transmission Tower ◽  
Health Monitoring System ◽  
Wind Speeds ◽  
Before And After

In this paper, we present a vibration-based transmission tower structural health monitoring system consisting of two parts that identifies structural changes in towers. An accelerometer group realizes vibration response acquisition at different positions and reduces the risk of data loss by data compression technology. A solar cell provides the power supply. An analyser receives the data from the acceleration sensor group and calculates the transmission tower natural frequencies, and the change in the structure is determined based on natural frequencies. Then, the data are sent to the monitoring center. Furthermore, analysis of the vibration signal and the calculation method of natural frequencies are proposed. The response and natural frequencies of vibration at different wind speeds are analysed by time-domain signal, power spectral density (PSD), root mean square (RMS) and short-time Fouier transform (STFT). The natural frequency identification of the overall structure by the stochastic subspace identification (SSI) method reveals that the number of natural frequencies that can be calculated at different wind speeds is different, but the 2nd, 3rd and 4th natural frequencies can be excited. Finally, the system was tested on a 110 kV experimental transmission line. After 18 h of experimentation, the natural frequency of the overall structure of the transmission tower was determined before and after the tower leg was lifted. The results show that before and after the tower leg is lifted, the natural frequencies of each order exhibit obvious changes, and the differences in the average values can be used as the basis for judging the structural changes of the tower.

scholarly journals Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket

2020 ◽  
Vol 25 (2) ◽  
pp. 29
Author(s):  
Desmond Adair ◽  
Aigul Nagimova ◽  
Martin Jaeger
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Algebraic Equations ◽  
Structural Vibrations ◽  
Unknown Parameters ◽  
One Dimensional ◽  
Vibration Problems ◽  
Nonuniform Beam

The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton’s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam.

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