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

Round 1

Reviewer 1 Report (Previous Reviewer 1)

Comments and Suggestions for Authors

Dear authors,

The study “Finite Element Analysis versus Empirical Modal Analysis of a Basketball Rim and Backboard” brings novel information about the process of creating a geometry, mesh, and boundary conditions for a basketball rim, mount, backboard, and border frame. The authors improved the main aspects, so, in my opinion, the article should be accepted for publication.

Best regards

 

Author Response

Dear Reviewers and Editors,

 

These changes have been made to the manuscript “Finite Element Analysis versus Empirical Modal Analysis of a Basketball Rim and Backboard,” 3001068.

 

Figure 3 may have inadvertently moved slightly out of position.  Could our editor please check this? Could our editor also please check for consistency of font type and font size across the entire manuscript?  Thank you.

 

ADDED TO THE DESCRIPTION OF FIGURE 2:  The wing brace, as well as both the inner and outer flanges, were modeled as 3/16 inch [4.7625mm] thick steel plate.

 

ADDED TO THE DESCRIPTION OF FIGURE 3:  made of half-inch [12.7mm] thick tempered glass

 

NEW FIGURE 4:  New Figure 4 has been added, to address one reviewer’s request for an overview of the major dimensions of the rim and backboard.  We sincerely apologize, but basketball equipment is specified by the NCAA (United States) using “English inches” as primary.  The corresponding System International measurements in millimeters are shown in brackets.  The subsequent Figures were renumbered in the manuscript, Graphical Abstract, and Video Abstract.

 

Figure 4 gave the major dimensions of the basketball rim and backboard which were used in the 29 steps listed in Figures 1-3. These dimensions, in English inches followed by the respective millimeter equivalents in brackets, came from NCAA specifications [5] and Gared specifications [6], except for the 7.5 inch [190.5mm] dimension which was measured with calipers. The upper-left top-view in Figure 4 came from Gared [6]. The upper-right top-view and the lower front-view came from our finite element model.

 

 

FIVE NEW REFERENCES:  To accommodate the request for more references by reviewers 3 and 4, five more references have been added.  We authors originally looked for the narrow topic of finite elements as applied to basketball rims and backboards.  To accommodate reviewers 3 and 4, we broadened our search to sports-related finite element analysis.  This produced the following new and very useful references, all published by MDPI:

 

[9] Covill, Derek, and Jean-Marc Drouet. "On the Effects of Tube Butting on the Structural Performance of Steel Bicycle Frames." Proceedings. Vol. 2. No. 6. MDPI, 2018.

 

[10] Tanaka, Katsumasa, and Kazuhiro Sekizawa. "Construction of a finite element model of golf clubs and influence of shaft stiffness on its dynamic behavior." Proceedings. Vol. 2. No. 6. MDPI, 2018.

 

[11] Matsuda, Akihiro, Motoho Nakui, and Tomohiro Hashiguchi. "Simulation of Mechanical Characteristics of Tennis Racket String Bed Considering String Pattern." Proceedings. Vol. 2. No. 6. MDPI, 2018.

 

[12] Takizawa, Masatomo, Akihiro Matsuda, and Tomohiro Hashiguchi. "A Study on the Mechanical Characteristics of String Planes of Badminton Racquets by Nonlinear Finite Element Analysis." Proceedings. Vol. 49. No. 1. MDPI, 2020.

 

[13] Yin, Shih-Rong, Hung-Chih Chang, and Kuangyou B. Cheng. "Impact Characteristics of a Badminton Racket with Realistic Finite Element Modeling." Proceedings. Vol. 49. No. 1. MDPI, 2020.

 

The manuscript was modified to say in Page 6:  Figure 5 was inspired by the sports-related application of finite elements in [9-13], as these references listed what types of finite elements were used. 

 

The manuscript was modified to say in Page 7:  This mesh refinement was inspired by [9]. Both Tables 1 and 2 were dominated by tetrahedron elements, which was the primary element used in [9].

 

 

ABSTRACT AND CONCLUSIONS:  Both were reorganized to better emphasize the goals of this study.

 

Abstract: The first goal of this research was to document the use of the MODAL Analysis System of the ANSYS 2024R1 student edition to create a finite element model of the modes and frequencies of vibration of one basketball rim and backboard design. 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, before beginning the theoretical modal analysis.  The second goal was to validate this model by comparing the finite element calculated mode shapes and frequencies to empirical modal analysis previously measured at the United States Military Academy at West Point, New York. Five 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 the empirical modal analysis. These five modes were addressed from a finite element model validation standpoint by a 99.5% confidence in a 98.09% cross-correlation with empirical modal analysis data, and from a verification standpoint by employing a refined-mesh.  However, three theoretical 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.

 

5. Conclusions:

Via an ANSYS Tree Outline, 29 steps were documented in detail for the use of the ANSYS MODAL Analysis System to create a geometry, mesh, and boundary conditions for a basketball rim, mount, backboard, and border frame.

The purpose of this theoretical finite element analysis was the identification of theoretical modes and frequencies of vibration of one basketball hoop and backboard design. Five empirical modes of vibration compared favorably with this theoretical finite element analysis. These five modes were addressed from a finite element model validation standpoint by statistical correlations with empirical modal analysis data and from a verification standpoint by employing a refined-mesh. The original finite element mesh, generated by default parameters in ANSYS, had a 99.5% confidence in a 97.187% cross-correlation. The refined-mesh, which increased the number of finite elements by 82%, had a 99.5% confidence in a slightly higher 98.09% cross-correlation. The high correlations between the theoretical finite element modeling and the empirical modal analysis was considered a validation of our work. That the refined-mesh did not alter the mode shapes and only made minor changes to the mode frequencies was considered a verification of our finite element model.

There are many possible designs of rims, backboards, and frames which meet NCAA standards, so this study was not comprehensive across the sport of basketball. However, our efforts of finite element analysis did reasonably match empirically measured mode shapes and frequencies of our previously published data.  Also, we showed the potential need for a triaxial accelerometer for any future empirical modal analysis efforts involving basketball rims and backboards.

 

 

We authors sincerely thank the insightful comments of our four reviewers, as their collective input has resulted in substantial improvements to our proposed paper.

 

Sincerely,

Daniel Winarski (corresponding author).

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

this research is very interesting and I believe it deserves to be published. I advise the authors to expand the references section (also looking for recent works) and to make minor changes of English language.

Comments on the Quality of English Language

Minor revision must be required

Author Response

Dear Reviewers and Editors,

 

These changes have been made to the manuscript “Finite Element Analysis versus Empirical Modal Analysis of a Basketball Rim and Backboard,” 3001068.

 

Figure 3 may have inadvertently moved slightly out of position.  Could our editor please check this? Could our editor also please check for consistency of font type and font size across the entire manuscript?  Thank you.

 

ADDED TO THE DESCRIPTION OF FIGURE 2:  The wing brace, as well as both the inner and outer flanges, were modeled as 3/16 inch [4.7625mm] thick steel plate.

 

ADDED TO THE DESCRIPTION OF FIGURE 3:  made of half-inch [12.7mm] thick tempered glass

 

NEW FIGURE 4:  New Figure 4 has been added, to address one reviewer’s request for an overview of the major dimensions of the rim and backboard.  We sincerely apologize, but basketball equipment is specified by the NCAA (United States) using “English inches” as primary.  The corresponding System International measurements in millimeters are shown in brackets.  The subsequent Figures were renumbered in the manuscript, Graphical Abstract, and Video Abstract.

 

Figure 4 gave the major dimensions of the basketball rim and backboard which were used in the 29 steps listed in Figures 1-3. These dimensions, in English inches followed by the respective millimeter equivalents in brackets, came from NCAA specifications [5] and Gared specifications [6], except for the 7.5 inch [190.5mm] dimension which was measured with calipers. The upper-left top-view in Figure 4 came from Gared [6]. The upper-right top-view and the lower front-view came from our finite element model.

 

 

FIVE NEW REFERENCES:  To accommodate the request for more references by reviewers 3 and 4, five more references have been added.  We authors originally looked for the narrow topic of finite elements as applied to basketball rims and backboards.  To accommodate reviewers 3 and 4, we broadened our search to sports-related finite element analysis.  This produced the following new and very useful references, all published by MDPI:

 

[9] Covill, Derek, and Jean-Marc Drouet. "On the Effects of Tube Butting on the Structural Performance of Steel Bicycle Frames." Proceedings. Vol. 2. No. 6. MDPI, 2018.

 

[10] Tanaka, Katsumasa, and Kazuhiro Sekizawa. "Construction of a finite element model of golf clubs and influence of shaft stiffness on its dynamic behavior." Proceedings. Vol. 2. No. 6. MDPI, 2018.

 

[11] Matsuda, Akihiro, Motoho Nakui, and Tomohiro Hashiguchi. "Simulation of Mechanical Characteristics of Tennis Racket String Bed Considering String Pattern." Proceedings. Vol. 2. No. 6. MDPI, 2018.

 

[12] Takizawa, Masatomo, Akihiro Matsuda, and Tomohiro Hashiguchi. "A Study on the Mechanical Characteristics of String Planes of Badminton Racquets by Nonlinear Finite Element Analysis." Proceedings. Vol. 49. No. 1. MDPI, 2020.

 

[13] Yin, Shih-Rong, Hung-Chih Chang, and Kuangyou B. Cheng. "Impact Characteristics of a Badminton Racket with Realistic Finite Element Modeling." Proceedings. Vol. 49. No. 1. MDPI, 2020.

 

The manuscript was modified to say in Page 6:  Figure 5 was inspired by the sports-related application of finite elements in [9-13], as these references listed what types of finite elements were used. 

 

The manuscript was modified to say in Page 7:  This mesh refinement was inspired by [9]. Both Tables 1 and 2 were dominated by tetrahedron elements, which was the primary element used in [9].

 

 

ABSTRACT AND CONCLUSIONS:  Both were reorganized to better emphasize the goals of this study.

 

Abstract: The first goal of this research was to document the use of the MODAL Analysis System of the ANSYS 2024R1 student edition to create a finite element model of the modes and frequencies of vibration of one basketball rim and backboard design. 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, before beginning the theoretical modal analysis.  The second goal was to validate this model by comparing the finite element calculated mode shapes and frequencies to empirical modal analysis previously measured at the United States Military Academy at West Point, New York. Five 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 the empirical modal analysis. These five modes were addressed from a finite element model validation standpoint by a 99.5% confidence in a 98.09% cross-correlation with empirical modal analysis data, and from a verification standpoint by employing a refined-mesh.  However, three theoretical 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.

 

5. Conclusions:

Via an ANSYS Tree Outline, 29 steps were documented in detail for the use of the ANSYS MODAL Analysis System to create a geometry, mesh, and boundary conditions for a basketball rim, mount, backboard, and border frame.

The purpose of this theoretical finite element analysis was the identification of theoretical modes and frequencies of vibration of one basketball hoop and backboard design. Five empirical modes of vibration compared favorably with this theoretical finite element analysis. These five modes were addressed from a finite element model validation standpoint by statistical correlations with empirical modal analysis data and from a verification standpoint by employing a refined-mesh. The original finite element mesh, generated by default parameters in ANSYS, had a 99.5% confidence in a 97.187% cross-correlation. The refined-mesh, which increased the number of finite elements by 82%, had a 99.5% confidence in a slightly higher 98.09% cross-correlation. The high correlations between the theoretical finite element modeling and the empirical modal analysis was considered a validation of our work. That the refined-mesh did not alter the mode shapes and only made minor changes to the mode frequencies was considered a verification of our finite element model.

There are many possible designs of rims, backboards, and frames which meet NCAA standards, so this study was not comprehensive across the sport of basketball. However, our efforts of finite element analysis did reasonably match empirically measured mode shapes and frequencies of our previously published data.  Also, we showed the potential need for a triaxial accelerometer for any future empirical modal analysis efforts involving basketball rims and backboards.

 

 

We authors sincerely thank the insightful comments of our four reviewers, as their collective input has resulted in substantial improvements to our proposed paper.

 

Sincerely,

Daniel Winarski (corresponding author).

Reviewer 3 Report (New Reviewer)

Comments and Suggestions for Authors

I would like to congrats the author for this great study related to the analyses of new rims and blackboard for basketball. It is a great idea and new paradigm for this sport modality. Thus, i would like to encourage and support this group of author to continues with this research line to obtain significant results related to the use of new rims in basketball. 

Author Response

Dear Reviewers and Editors,

 

These changes have been made to the manuscript “Finite Element Analysis versus Empirical Modal Analysis of a Basketball Rim and Backboard,” 3001068.

 

Figure 3 may have inadvertently moved slightly out of position.  Could our editor please check this? Could our editor also please check for consistency of font type and font size across the entire manuscript?  Thank you.

 

ADDED TO THE DESCRIPTION OF FIGURE 2:  The wing brace, as well as both the inner and outer flanges, were modeled as 3/16 inch [4.7625mm] thick steel plate.

 

ADDED TO THE DESCRIPTION OF FIGURE 3:  made of half-inch [12.7mm] thick tempered glass

 

NEW FIGURE 4:  New Figure 4 has been added, to address one reviewer’s request for an overview of the major dimensions of the rim and backboard.  We sincerely apologize, but basketball equipment is specified by the NCAA (United States) using “English inches” as primary.  The corresponding System International measurements in millimeters are shown in brackets.  The subsequent Figures were renumbered in the manuscript, Graphical Abstract, and Video Abstract.

 

Figure 4 gave the major dimensions of the basketball rim and backboard which were used in the 29 steps listed in Figures 1-3. These dimensions, in English inches followed by the respective millimeter equivalents in brackets, came from NCAA specifications [5] and Gared specifications [6], except for the 7.5 inch [190.5mm] dimension which was measured with calipers. The upper-left top-view in Figure 4 came from Gared [6]. The upper-right top-view and the lower front-view came from our finite element model.

 

 

FIVE NEW REFERENCES:  To accommodate the request for more references by reviewers 3 and 4, five more references have been added.  We authors originally looked for the narrow topic of finite elements as applied to basketball rims and backboards.  To accommodate reviewers 3 and 4, we broadened our search to sports-related finite element analysis.  This produced the following new and very useful references, all published by MDPI:

 

[9] Covill, Derek, and Jean-Marc Drouet. "On the Effects of Tube Butting on the Structural Performance of Steel Bicycle Frames." Proceedings. Vol. 2. No. 6. MDPI, 2018.

 

[10] Tanaka, Katsumasa, and Kazuhiro Sekizawa. "Construction of a finite element model of golf clubs and influence of shaft stiffness on its dynamic behavior." Proceedings. Vol. 2. No. 6. MDPI, 2018.

 

[11] Matsuda, Akihiro, Motoho Nakui, and Tomohiro Hashiguchi. "Simulation of Mechanical Characteristics of Tennis Racket String Bed Considering String Pattern." Proceedings. Vol. 2. No. 6. MDPI, 2018.

 

[12] Takizawa, Masatomo, Akihiro Matsuda, and Tomohiro Hashiguchi. "A Study on the Mechanical Characteristics of String Planes of Badminton Racquets by Nonlinear Finite Element Analysis." Proceedings. Vol. 49. No. 1. MDPI, 2020.

 

[13] Yin, Shih-Rong, Hung-Chih Chang, and Kuangyou B. Cheng. "Impact Characteristics of a Badminton Racket with Realistic Finite Element Modeling." Proceedings. Vol. 49. No. 1. MDPI, 2020.

 

The manuscript was modified to say in Page 6:  Figure 5 was inspired by the sports-related application of finite elements in [9-13], as these references listed what types of finite elements were used. 

 

The manuscript was modified to say in Page 7:  This mesh refinement was inspired by [9]. Both Tables 1 and 2 were dominated by tetrahedron elements, which was the primary element used in [9].

 

 

ABSTRACT AND CONCLUSIONS:  Both were reorganized to better emphasize the goals of this study.

 

Abstract: The first goal of this research was to document the use of the MODAL Analysis System of the ANSYS 2024R1 student edition to create a finite element model of the modes and frequencies of vibration of one basketball rim and backboard design. 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, before beginning the theoretical modal analysis.  The second goal was to validate this model by comparing the finite element calculated mode shapes and frequencies to empirical modal analysis previously measured at the United States Military Academy at West Point, New York. Five 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 the empirical modal analysis. These five modes were addressed from a finite element model validation standpoint by a 99.5% confidence in a 98.09% cross-correlation with empirical modal analysis data, and from a verification standpoint by employing a refined-mesh.  However, three theoretical 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.

 

5. Conclusions:

Via an ANSYS Tree Outline, 29 steps were documented in detail for the use of the ANSYS MODAL Analysis System to create a geometry, mesh, and boundary conditions for a basketball rim, mount, backboard, and border frame.

The purpose of this theoretical finite element analysis was the identification of theoretical modes and frequencies of vibration of one basketball hoop and backboard design. Five empirical modes of vibration compared favorably with this theoretical finite element analysis. These five modes were addressed from a finite element model validation standpoint by statistical correlations with empirical modal analysis data and from a verification standpoint by employing a refined-mesh. The original finite element mesh, generated by default parameters in ANSYS, had a 99.5% confidence in a 97.187% cross-correlation. The refined-mesh, which increased the number of finite elements by 82%, had a 99.5% confidence in a slightly higher 98.09% cross-correlation. The high correlations between the theoretical finite element modeling and the empirical modal analysis was considered a validation of our work. That the refined-mesh did not alter the mode shapes and only made minor changes to the mode frequencies was considered a verification of our finite element model.

There are many possible designs of rims, backboards, and frames which meet NCAA standards, so this study was not comprehensive across the sport of basketball. However, our efforts of finite element analysis did reasonably match empirically measured mode shapes and frequencies of our previously published data.  Also, we showed the potential need for a triaxial accelerometer for any future empirical modal analysis efforts involving basketball rims and backboards.

 

 

We authors sincerely thank the insightful comments of our four reviewers, as their collective input has resulted in substantial improvements to our proposed paper.

 

Sincerely,

Daniel Winarski (corresponding author).

Reviewer 4 Report (New Reviewer)

Comments and Suggestions for Authors

Introduction must be improved by establishing a topic, indicating a gap between other similar studies and stating the aim of the research.

In result section if it is possible can you report research result?

Discussion needs improvement. 

Contextualizing the study (e.g. better referring to established knowledge)

Consolidate result

Explain specific research outcomes

State research conclusion

Author Response

Dear Reviewers and Editors,

 

These changes have been made to the manuscript “Finite Element Analysis versus Empirical Modal Analysis of a Basketball Rim and Backboard,” 3001068.

 

Figure 3 may have inadvertently moved slightly out of position.  Could our editor please check this? Could our editor also please check for consistency of font type and font size across the entire manuscript?  Thank you.

 

ADDED TO THE DESCRIPTION OF FIGURE 2:  The wing brace, as well as both the inner and outer flanges, were modeled as 3/16 inch [4.7625mm] thick steel plate.

 

ADDED TO THE DESCRIPTION OF FIGURE 3:  made of half-inch [12.7mm] thick tempered glass

 

NEW FIGURE 4:  New Figure 4 has been added, to address one reviewer’s request for an overview of the major dimensions of the rim and backboard.  We sincerely apologize, but basketball equipment is specified by the NCAA (United States) using “English inches” as primary.  The corresponding System International measurements in millimeters are shown in brackets.  The subsequent Figures were renumbered in the manuscript, Graphical Abstract, and Video Abstract.

 

Figure 4 gave the major dimensions of the basketball rim and backboard which were used in the 29 steps listed in Figures 1-3. These dimensions, in English inches followed by the respective millimeter equivalents in brackets, came from NCAA specifications [5] and Gared specifications [6], except for the 7.5 inch [190.5mm] dimension which was measured with calipers. The upper-left top-view in Figure 4 came from Gared [6]. The upper-right top-view and the lower front-view came from our finite element model.

 

 

FIVE NEW REFERENCES:  To accommodate the request for more references by reviewers 3 and 4, five more references have been added.  We authors originally looked for the narrow topic of finite elements as applied to basketball rims and backboards.  To accommodate reviewers 3 and 4, we broadened our search to sports-related finite element analysis.  This produced the following new and very useful references, all published by MDPI:

 

[9] Covill, Derek, and Jean-Marc Drouet. "On the Effects of Tube Butting on the Structural Performance of Steel Bicycle Frames." Proceedings. Vol. 2. No. 6. MDPI, 2018.

 

[10] Tanaka, Katsumasa, and Kazuhiro Sekizawa. "Construction of a finite element model of golf clubs and influence of shaft stiffness on its dynamic behavior." Proceedings. Vol. 2. No. 6. MDPI, 2018.

 

[11] Matsuda, Akihiro, Motoho Nakui, and Tomohiro Hashiguchi. "Simulation of Mechanical Characteristics of Tennis Racket String Bed Considering String Pattern." Proceedings. Vol. 2. No. 6. MDPI, 2018.

 

[12] Takizawa, Masatomo, Akihiro Matsuda, and Tomohiro Hashiguchi. "A Study on the Mechanical Characteristics of String Planes of Badminton Racquets by Nonlinear Finite Element Analysis." Proceedings. Vol. 49. No. 1. MDPI, 2020.

 

[13] Yin, Shih-Rong, Hung-Chih Chang, and Kuangyou B. Cheng. "Impact Characteristics of a Badminton Racket with Realistic Finite Element Modeling." Proceedings. Vol. 49. No. 1. MDPI, 2020.

 

The manuscript was modified to say in Page 6:  Figure 5 was inspired by the sports-related application of finite elements in [9-13], as these references listed what types of finite elements were used. 

 

The manuscript was modified to say in Page 7:  This mesh refinement was inspired by [9]. Both Tables 1 and 2 were dominated by tetrahedron elements, which was the primary element used in [9].

 

 

ABSTRACT AND CONCLUSIONS:  Both were reorganized to better emphasize the goals of this study.

 

Abstract: The first goal of this research was to document the use of the MODAL Analysis System of the ANSYS 2024R1 student edition to create a finite element model of the modes and frequencies of vibration of one basketball rim and backboard design. 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, before beginning the theoretical modal analysis.  The second goal was to validate this model by comparing the finite element calculated mode shapes and frequencies to empirical modal analysis previously measured at the United States Military Academy at West Point, New York. Five 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 the empirical modal analysis. These five modes were addressed from a finite element model validation standpoint by a 99.5% confidence in a 98.09% cross-correlation with empirical modal analysis data, and from a verification standpoint by employing a refined-mesh.  However, three theoretical 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.

 

5. Conclusions:

Via an ANSYS Tree Outline, 29 steps were documented in detail for the use of the ANSYS MODAL Analysis System to create a geometry, mesh, and boundary conditions for a basketball rim, mount, backboard, and border frame.

The purpose of this theoretical finite element analysis was the identification of theoretical modes and frequencies of vibration of one basketball hoop and backboard design. Five empirical modes of vibration compared favorably with this theoretical finite element analysis. These five modes were addressed from a finite element model validation standpoint by statistical correlations with empirical modal analysis data and from a verification standpoint by employing a refined-mesh. The original finite element mesh, generated by default parameters in ANSYS, had a 99.5% confidence in a 97.187% cross-correlation. The refined-mesh, which increased the number of finite elements by 82%, had a 99.5% confidence in a slightly higher 98.09% cross-correlation. The high correlations between the theoretical finite element modeling and the empirical modal analysis was considered a validation of our work. That the refined-mesh did not alter the mode shapes and only made minor changes to the mode frequencies was considered a verification of our finite element model.

There are many possible designs of rims, backboards, and frames which meet NCAA standards, so this study was not comprehensive across the sport of basketball. However, our efforts of finite element analysis did reasonably match empirically measured mode shapes and frequencies of our previously published data.  Also, we showed the potential need for a triaxial accelerometer for any future empirical modal analysis efforts involving basketball rims and backboards.

 

 

We authors sincerely thank the insightful comments of our four reviewers, as their collective input has resulted in substantial improvements to our proposed paper.

 

Sincerely,

Daniel Winarski (corresponding author).

Round 2

Reviewer 4 Report (New Reviewer)

Comments and Suggestions for Authors

Author made enough changes

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Dear Authors,

The study “Finite Element Analysis versus Empirical Modal Analysis of a 2 Basketball Rim and Backboard” brings novel information about the process of creating a geometry, mesh, and boundary conditions for a basketball rim, mount, backboard, and border frame. General comments are provided to improve the article.

General Comments

The abstract is sufficiently informative and presents the main objectives and conclusions of the study.

In the introduction section the objectives of the study could be better described. Please add the hypothesis if they can be formulated.

In materials and methods section there is a detailed explanation of the procedures, but this section also includes the results. Please add a results section comparing Finite Element Analysis data with Empirical Modal Analysis data. 

It was applied any statistical analysis?

Are there any suggestions for additional studies in the discussion section?

Best regards,

Author Response

Dear Reviewers.

First of all, we thank each of you for your valued comments.  Change tracker was used to mark all changes and additions.  If you feel our revisions still do not meet what you have asked for, please let us know and additional work will be done.

• Added Figure 10, showing torsion mode of basketball rim at 131.61 Hz.  Added this torsional mode of rim to Table 2.
• Finite Element Frequencies in Table 2 and captions for Figures 6-10 now match what is in Video Abstract.
• What was Figure 9 (3 missed modes) is now Figure 11 due to new Figure 10 (Torsion mode) and new Figure 4 (parabolic elements).
• 5 modes compared empirical modal vs theoretical FEM (previously 4) in Table 2, abstract, and conclusions.

Reviewer 1:  

In materials and methods section there is a detailed explanation of the procedures, but this section also includes the results. Please add a results section comparing Finite Element Analysis data with Empirical Modal Analysis data. 

Done….thank you, as this greatly improved the organization of the paper.

It was applied any statistical analysis? 

Correlation of 97.2% at a confidence of 99.5% calculated.  Thank you for this invaluable suggestion.

In the introduction section the objectives of the study could be better described. Please add the hypothesis if they can be formulated. 

Added to the end of the first paragraph of the introduction.  Thanks again for your valuable insight.

Reviewer 2 Report

Comments and Suggestions for Authors

This article  compares theoretical finite element analysis to empirical modal analysis for a basketball rim and backboard. It utilizes the ANSYS 2024R1 student edition for simulations and compares results with empirical data. The methodology for creating and analyzing the geometry, mesh, and boundary conditions. The paper demonstrates the potential need for a triaxial accelerometer in future analyses and suggests that while their finite element analysis aligns with some empirical data, broader basketball equipment designs need consideration for comprehensive applicability.

General Comments:

- The article has no scientific contribution.

- The importance or significance of the work is not justified in the document.

 

- What is presented in the manuscript should be part of the discussion of the results of the article. https://doi.org/10.3390/vibration6040045

 

Recommendation: restate the manuscript by proposing a new experimental case study where the simulation results help the modal planning of the experiment. 

 

 

Author Response

Dear Reviewers.

First of all, we thank each of you for your valued comments.  Change tracker was used to mark all changes and additions.  If you feel our revisions still do not meet what you have asked for, please let us know and additional work will be done.

• Added Figure 10, showing torsion mode of basketball rim at 131.61 Hz.  Added this torsional mode of rim to Table 2.
• Finite Element Frequencies in Table 2 and captions for Figures 6-10 now match what is in Video Abstract.
• What was Figure 9 (3 missed modes) is now Figure 11 due to new Figure 10 (Torsion mode) and new Figure 4 (parabolic elements).
• 5 modes compared empirical modal vs theoretical FEM (previously 4) in Table 2, abstract, and conclusions.

Reviewer 2

Added after Figure 11:  This showed us that first obtaining simulation results via finite element analysis could help the planning of subsequent modal analysis experiments.

 

Reviewer 3 Report

Comments and Suggestions for Authors

1. Given the focus on vibration applications in the bundled education from Cornell University, how did the authors incorporate this knowledge into their analysis and interpretation of the results? Did it influence any specific aspects of the study design or methodology?

2. Considering the availability of the ANSYS 2024R1 Student Edition, how accessible are the methods and tools used in this study to other researchers or practitioners in the field? Are there any barriers or challenges that might limit broader adoption or replication of the proposed approach?

3. How did the authors ensure the accuracy of the geometry created in ANSYS DesignModeler, especially considering the complex shapes involved in modeling the basketball rim, mount, backboard, and frame? 

4. Regarding the mesh creation process, why were all mesh parameters set to program defaults? Please mention the considerations for adjusting these parameters based on the specific characteristics of the basketball system being modeled. 

5. Considering the complex geometry and multiple parts involved in the model, how did the authors ensure that the meshing process accurately represented the structural features and boundaries of the basketball system? 

6. The manuscript could benefit from a thorough round of extensive revision in the overall writing, grammar checks, and an extensive literature review. 

Author Response

Dear Reviewers.

First of all, we thank each of you for your valued comments.  Change tracker was used to mark all changes and additions.  If you feel our revisions still do not meet what you have asked for, please let us know and additional work will be done.

• Added Figure 10, showing torsion mode of basketball rim at 131.61 Hz.  Added this torsional mode of rim to Table 2.
• Finite Element Frequencies in Table 2 and captions for Figures 6-10 now match what is in Video Abstract.
• What was Figure 9 (3 missed modes) is now Figure 11 due to new Figure 10 (Torsion mode) and new Figure 4 (parabolic elements).
• 5 modes compared empirical modal vs theoretical FEM (previously 4) in Table 2, abstract, and conclusions.

Reviewer 3:  

1. Given the focus on vibration applications in the bundled education from Cornell University, how did the authors incorporate this knowledge into their analysis and interpretation of the results? Did it influence any specific aspects of the study design or methodology?  

In this course, emphasis was placed on using the ANSYS Tree Outline to organize one’s efforts, which we fully adopted along with all methodology taught.  If you need further detail, please let us know.

 

2.1 Considering the availability of the ANSYS 2024R1 Student Edition, how accessible are the methods and tools used in this study to other researchers or practitioners in the field?

ANSYS makes this totally accessible.  

2.2 Are there any barriers or challenges that might limit broader adoption or replication of the proposed approach?  

There are no barriers or challenges seen.

3. How did the authors ensure the accuracy of the geometry created in ANSYS DesignModeler, especially considering the complex shapes involved in modeling the basketball rim, mount, backboard, and frame?

Citations of the use of the NCAA and GARED 3500 specifications added to the manuscript.  We actually purchased the GARED 3500 unit to measure anything not explicitly specified.

4. Regarding the mesh creation process, why were all mesh parameters set to program defaults? Please mention the considerations for adjusting these parameters based on the specific characteristics of the basketball system being modeled. 

We did add a discussion of the four parabolic elements used in our study in new FIGURE 4 and added a description. We could have downgraded to linear elements, at a possible loss of accuracy.

5. Considering the complex geometry and multiple parts involved in the model, how did the authors ensure that the meshing process accurately represented the structural features and boundaries of the basketball system?

We were able to reasonably match five modal shapes and frequencies.

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

General Comments:

- The article has no scientific contribution.

- The importance or significance of the work is not justified in the document.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have not adequately responded to the review comments. One-line answers with no justifications do not provide a whole lot of confidence in addressing any of the queries. The authors should provide extensive justification and should be careful enough to justify their claims with proper established references. The writing style and the presentation style are very poor with no scholarly impact whatsoever.

Author Response

Please see the attachment

Author Response File: Author Response.docx