Simplified setup for the vibration study of plates with simply-supported boundary conditions

Dumond, Patrick; Monette, Dominic; Alladkani, Fadi; Akl, James; Chikhaoui, Inès

doi:10.1016/j.mex.2019.09.023

Cited by 10 publications

(7 citation statements)

References 14 publications

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“…These results have been instrumental in enhancing our understanding of the behavior of carbon steel under varying conditions and will undoubtedly serve as a valuable resource in future studies. The unilaterally reinforced perimeter conditions of P. Dumond et al [53] and K. Luo et al [54] have consistent results with both studies, as shown in Table 7. Determining the modal constraint frequency of a workpiece is a complex process that involves various factors.…”

supporting

confidence: 75%

The Vibration Analysis Based on Experimental and Finite Element Modeling for Investigating the Effect of a Multi-Notch Location of a Steel Plate

Charoensuk,

Sethaput

2023

Applied Sciences

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Vibration is challenging and significant in solving engineering problems. The issue of vibration in loaded objects by utilizing a three-dimensional model and experiments. Typically, an object is subjected to a random frequency, which changes the notch shape depending on the frequency model. The investigations determined the performance difference by conducting modal analysis with the finite element method and examining the various forms of each mode. We simulated metal plates with V notch and multiple notch locations on both sides and one side of the notch. The test kits included an accelerometer and a force sensor for correcting the national frequency via Simulink Matlab® and verifying the result from the finite element methods. The V-shaped vibration testing provided significant insights into its accuracy and potential for predicting damage and fracture through experimentation and the finite element method. The tested specimen analyzed the behavior of two models and found that the two V-shaped exhibited varying natural frequency values. Specifically, the double-sided V-shaped increased natural frequency, whereas the single-sided notched V-shaped cutting showed a significant decrease in natural frequency. Accordingly, this investigative approach, the result of the experiment, and the finite element shows that correlation disposition can be utilized to forecast various random frequencies for vibration analysis.

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supporting

confidence: 75%

The Vibration Analysis Based on Experimental and Finite Element Modeling for Investigating the Effect of a Multi-Notch Location of a Steel Plate

Charoensuk,

Sethaput

2023

Applied Sciences

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“…As the mount and inner portion of the rim flexed upward, the outer portion of the rim flexed downward, and visa-versa. The characteristic oscillating central bulge in the backboard plate prominent in Figure 9 can also be found in [10][11][12][13].…”

Section: Methodsmentioning

confidence: 57%

“…The missed modes at 29 Hz and 49 Hz comprised the reciprocating rotational motion of the rim and mount about the Z-axis. The missed mode at 29 Hz had previously perplexed the authors' empirical modal analysis [9] as that was a common mode of vibrations in plates [11][12][13]. But we now understand that the lack of vertical motion of the rim in Figure 9 meant that any signal from the vertically-oriented accelerometer could have easily been overlooked as noise.…”

Section: Methodsmentioning

confidence: 93%

Finite Element Analysis versus Empirical Modal Analysis of a Basketball Rim and Backboard

Winarski,

Nygren,

Winarski

2024

Preprint

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The ANSYS 2024R1 student edition was used to create a finite element model of a basketball rim and backboard. This finite element model included the use of steel for the rim and its mount, a tempered glass backboard, and an aluminum frame behind the backboard. After a mesh was created, fixed support boundary conditions were applied to the four corners of the aluminum frame. The subsequently calculated mode shapes and frequencies were compared to empirical modal analysis previously done at the United States Military Academy at West Point, New York. Four mode shapes and frequencies agreed rather well between the theoretical finite element analysis and previously published empirical modal analysis, specifically where the rim was vibrating in the vertical direction, which was the direction that the accelerometer was aligned for modal analysis. However, three mode shapes missed by the empirical modal analysis were found where the vibration of the rim was confined to the horizontal plane, which was orthogonal to the orientation of our accelerometer.

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“…Looking beyond our first two modes of vibration, Dumond [5] provided valuable insight for modes 5-6, and the indicial notation used in this article was adopted for the quantification of plate-vibration-dominated modes 3-6. Irvine provided valuable insight for visualizing mode 4 [6] and dome-shaped mode 5 [7], especially since the plates that Irvine analyzed had the same aspect ratio of 1.5:1 as the basketball backboard in this study.…”

Section: Introductionmentioning

confidence: 99%

Modes of Vibration in Basketball Rims and Backboards and the Energy Rebound Testing Device

Winarski,

Nygren,

Winarski

2023

Vibration

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Six mode shapes, including bending and torsion, were documented for five different basketball rims and backboards at the United States Military Academy, West Point, New York, NY, USA. The frequency and damping ratio of each mode shape were also determined. The empirical process began with the time-domain excitation and response of each rim-backboard system. The impulse of excitation came from an impact hammer separately applied sequentially to each node. The sinusoidal response was gathered from an accelerometer at a fixed location (node 1). Each time-domain excitation response was then converted to a frequency-domain Bode plot for each node by a Brüel & Kjær 2034 Signal Analyzer, giving transfer functions of output/input versus frequency. Structural Measurements System (SMS) StarStruc software was used to fit mode shapes to the Bode plots. Each of the six mode shapes was fitted to the Bode plots of each node at a specific modal frequency. Each of the six mode shapes was a function of the locations of the nodes, and the Bode plots gathered at each node. The first and second modes were critical for showing that the Energy Rebound Testing Device statistically correlated with the energy transferred to the rim and backboard. A known perturbation mass was selectively attached to the rim to help isolate the dynamic masses and spring rates for the rim and backboard and to ascertain that the kinetic energy transferred to the rim had a 95.67% inverse correlation with rim stiffness.

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Simplified setup for the vibration study of plates with simply-supported boundary conditions

Abstract: Graphical abstract

Cited by 10 publications

References 14 publications

The Vibration Analysis Based on Experimental and Finite Element Modeling for Investigating the Effect of a Multi-Notch Location of a Steel Plate

The Vibration Analysis Based on Experimental and Finite Element Modeling for Investigating the Effect of a Multi-Notch Location of a Steel Plate

Finite Element Analysis versus Empirical Modal Analysis of a Basketball Rim and Backboard

Modes of Vibration in Basketball Rims and Backboards and the Energy Rebound Testing Device

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