Dynamics of Rocking Semicircular, Parabolic, and Semi-Elliptical Disks: Equilibria, Stability, and Natural Frequencies

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Michael J. Mazzoleni ◽  
Michael B. Krone ◽  
Brian P. Mann
Keyword(s):  
Natural Frequency ◽  
Cross Sections ◽  
Experimental Validation ◽  
Natural Frequencies ◽  
Stable Equilibrium ◽  
Pitchfork Bifurcation ◽  
Bistable Behavior ◽  
Elliptical Cross ◽  
Stable Equilibrium Position ◽  
Good Agreement

This paper performs a theoretical and experimental investigation of the natural frequency and stability of rocking semicircular, parabolic, and semi-elliptical disks. Horace Lamb's method for deriving the natural frequency of an arbitrary rocking disk is applied to three shapes with semicircular, parabolic, and semi-elliptical cross sections, respectively. For the case of the semicircular disk, the system's equation of motion is derived to verify Lamb's method. Additionally, the rocking semicircular disk is found to always have one stable equilibrium position. For the cases of the parabolic and semi-elliptical disks, this investigation reveals a supercritical pitchfork bifurcation for changes in a single geometric parameter which indicates that the systems can exhibit bistable behavior. Comparisons between experimental validation and theory show good agreement.

Investigation of Rocking Semicircular and Parabolic Disk Equilibria, Stability, and Natural Frequencies

2014 ◽  
Author(s):  
Michael J. Mazzoleni ◽  
Michael B. Krone ◽  
Brian P. Mann
Keyword(s):  
Natural Frequency ◽  
Cross Sections ◽  
Natural Frequencies ◽  
Stable Equilibrium ◽  
Pitchfork Bifurcation ◽  
Equation Of Motion ◽  
Bistable Behavior ◽  
Wide Range ◽  
Stable Equilibrium Position ◽  
Good Agreement

This paper performs a theoretical and experimental investigation of the natural frequency and stability of rocking semicircular and parabolic disks. Horace Lamb’s method for deriving the natural frequency of an arbitrary rocking disk is applied to two shapes with semicircular and parabolic cross sections, respectively. For the case of the semicircular disk, the system’s equation of motion is derived to verify Lamb’s method. Additionally, the rocking semicircular disk is found to always have one stable equilibrium position. For the case of the parabolic disk, this investigation unveils a super-critical pitchfork bifurcation for changes in a single geometric parameter which reveals that the system can exhibit bistable behavior. Rapid prototyping technology was used to manufacture sample disks across a wide range of parameters, and a laser tachometer was used to experimentally determine the natural frequency of each disk. Comparisons between experiment and theory show good agreement.

Vibrations of an Intermediately Supported U-Bend Tube

1975 ◽  
Vol 97 (1) ◽  
pp. 23-32 ◽  
Author(s):  
L. S. S. Lee
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Experimental Tests ◽  
Bending Stiffness ◽  
Stiffness Ratio ◽  
Plane Vibration ◽  
Straight Beam ◽  
Out Of Plane ◽  
Straight Segments ◽  
Good Agreement

Vibrations of an intermediately supported U-bend tube fall into two independent classes as an incomplete ring of single span does, namely, the in-plane vibration and the coupled twist-bending out-of-plane vibration. Natural frequencies may be expressed in terms of a coefficient p which depends on the stiffness ratio k, the ratio of lengths of spans, and the supporting conditions. The effect of the torsional flexibility of a curved bar acts to release the bending stiffness of a straight beam and hence decrease the natural frequency. Some conclusions for an incomplete ring of single span may not be equally well applicable to the U-tube case due to the effects of intermediate supports and the presence of the supporting straight segments. Results of the analytical predictions and the experimental tests of an intermediately supported U-tube are in good agreement.

Natural Frequencies of Stator in Induction Motors

1997 ◽  
Author(s):  
Isao Suzuki ◽  
Shinichi Noda ◽  
Kazunobu Itomi ◽  
Fuminori Ishibashi
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Induction Motors ◽  
Fem Analysis ◽  
Stator Core ◽  
Second Stage ◽  
Contact Surfaces ◽  
Natural Frequency Analysis ◽  
Spring Constants ◽  
Good Agreement

Abstract Totally enclosed induction motors in which the stator core is pressed in the frame are in general used in industrial machines and manufactured with similar construction around the world. These motors produce a strong electromagnetic noise, which is caused by resonance between the natural frequencies of the stator core and the harmonics of electromagnetic forces. Therefore, it is very important to estimate its natural frequencies at the stage of design. As the first stage of research to estimate the natural frequencies of the stator core pressed into the motor frame, the dual rings were chosen as the object of studies. They are similar to the motor in construction and are easy to use to solve the problems. The purpose of this study is to investigate the effects of the tight fit to the natural frequencies and to find an analytical method by FEM. The authors have found that the introduction of spring elements with radial and circumferential spring constants at the contact surfaces provides accurate calculated results of the natural frequency by FEM. This paper describes about the spring constants obtained from experiments and analysis. As a result, when the spring constants in the radial direction are infinite and those in the circumferential direction are variable, it is clear that the spring constants for natural frequency analysis by FEM were expressed as a function of contact pressure on the contact surfaces. In the second stage, the measurement and calculation of natural frequency in the actual stator core with a frame was performed, and these results showed good agreement. These spring constants will be useful in FEM analysis of stator cores pressed into cylindrical induction motor frames.

Natural frequency response of laminated hybrid composite beams with and without cutouts

2014 ◽  
Vol 34 (9) ◽  
pp. 851-857 ◽  
Author(s):  
Ahmet Erkliğ ◽  
Mehmet Bulut ◽  
Eyüp Yeter
Keyword(s):  
Natural Frequency ◽  
Hybrid Composite ◽  
Fiber Orientation ◽  
Natural Frequencies ◽  
Hybrid Composites ◽  
Fiber Type ◽  
Glass Fibers ◽  
Composite Beams ◽  
Stacking Sequence ◽  
Good Agreement

Abstract This study deals with the effect of hybridization on the natural frequency of woven laminated hybrid composite beams with and without cutouts under the clamped-free boundary condition. Woven carbon, Kevlar and S-glass fibers with epoxy were used for the production of hybrid composites. Natural frequencies of the hybrid composite beams were experimentally determined for [(0/90)3]S stacking sequence. Numerical analyses were performed to investigate the influences of fiber orientation angles, circular and rectangular cutouts, cutout size ratios and positions on natural frequency. Good agreement between experimental and numerical results was found from a comparison of natural frequencies. The results shows that the fiber type used in the layers, cutout size and position on the beam strongly effects the natural frequency.

Improved Modeling of a Dynamic Mirror With Antagonistic Piezoelectric Stack Actuation

2011 ◽  
Author(s):  
James A. Mynderse ◽  
Ann M. Whitney ◽  
George T. C. Chiu
Keyword(s):  
Experimental Data ◽  
Laser Beam ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Beam Steering ◽  
Proposed Model ◽  
Mechanical Compliance ◽  
Charging Dynamics ◽  
Good Agreement ◽  
Shunt Circuit

An enhanced model of a dynamic mirror actuator (DMA) for laser beam steering is presented. The DMA is driven by an antagonistic pair of piezoelectric stack actuators (PESA). The proposed model of the DMA employs explicit PESA charging dynamics and an adjustable PESA shunt circuit to address the frequency-dependent effective mechanical compliance term in several previous models from literature. The proposed DMA model with shunt circuit accurately predicts the first damped natural frequency of the DMA with a shunt circuit across each PESA. Simulation and experimental data are presented. Good agreement is shown between the predicted and measured damped first natural frequencies.

Tire Vibrations

1977 ◽  
Vol 5 (4) ◽  
pp. 202-225 ◽  
Author(s):  
G. R. Potts ◽  
C. A. Bell ◽  
L. T. Charek ◽  
T. K. Roy
Keyword(s):  
Natural Frequencies ◽  
Standing Waves ◽  
Resonant Mode ◽  
Mode Shapes ◽  
Resonant Vibrations ◽  
Resonant Frequencies ◽  
Radial Tire ◽  
Analysis Techniques ◽  
Thin Ring ◽  
Good Agreement

Abstract Natural frequencies and vibrating motions are determined in terms of the material and geometric properties of a radial tire modeled as a thin ring on an elastic foundation. Experimental checks of resonant frequencies show good agreement. Forced vibration solutions obtained are shown to consist of a superposition of resonant vibrations, each rotating around the tire at a rate depending on the mode number and the tire rotational speed. Theoretical rolling speeds that are upper bounds at which standing waves occur are determined and checked experimentally. Digital Fourier transform, transfer function, and modal analysis techniques used to determine the resonant mode shapes of a radial tire reveal that antiresonances are the primary transmitters of vibration to the tire axle.

Dynamic model for high-speed rotors based on their experimental characterization

2017 ◽  
Vol 2 (4) ◽  
pp. 25
Author(s):  
L. A. Montoya ◽  
E. E. Rodríguez ◽  
H. J. Zúñiga ◽  
I. Mejía
Keyword(s):  
Dynamic Model ◽  
High Speed ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Experimental Characterization ◽  
Rotating Systems ◽  
Computing Performance ◽  
The Impact ◽  
Stiffness Distribution ◽  
Good Agreement

Rotating systems components such as rotors, have dynamic characteristics that are of great importance to understand because they may cause failure of turbomachinery. Therefore, it is required to study a dynamic model to predict some vibration characteristics, in this case, the natural frequencies and mode shapes (both of free vibration) of a centrifugal compressor shaft. The peculiarity of the dynamic model proposed is that using frequency and displacements values obtained experimentally, it is possible to calculate the mass and stiffness distribution of the shaft, and then use these values to estimate the theoretical modal parameters. The natural frequencies and mode shapes of the shaft were obtained with experimental modal analysis by using the impact test. The results predicted by the model are in good agreement with the experimental test. The model is also flexible with other geometries and has a great time and computing performance, which can be evaluated with respect to other commercial software in the future.

Analysis of Reinforced Concrete Culvert considering Concrete Creep and Shrinkage

1996 ◽  
Vol 1541 (1) ◽  
pp. 120-126
Author(s):  
Charles J. Oswald
Keyword(s):  
Finite Element ◽  
Reinforced Concrete ◽  
Cross Sections ◽  
Soil Structure ◽  
Silty Clay ◽  
Soil Pressure ◽  
Concrete Creep ◽  
Long Span ◽  
Creep And Shrinkage ◽  
Good Agreement

Measurements made on a long span reinforced concrete arch culvert under 7.3 m (24 ft) of silty clay backfill were compared with results from finite-element analyses of the soil-structure system using the CANDE finite-element code. The culvert strains and deflections and the soil pressure on the culvert were measured during construction and during the following 2.5 years at three instrumented cross sections. The CANDE program was modified to account for the effects of concrete creep and shrinkage strains after it was noted that the measured postconstruction culvert deflection and strains increased significantly whereas the measured soil pressure on the culvert remained relatively constant. Good agreement was generally obtained between measured and calculated values of the culvert strain and deflection and the soil pressure during the entire monitoring period after the code was modified.

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.

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