Proposition of a New High Speed and High Efficiency Control Method for Plural Eigen Frequencies by Changing Topology

Toshie Sasaki; Yang Yang; Ichiro Hagiwara

doi:doi:10.11648/j.ijmea.20221006.12

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Proposition of a New High Speed and High Efficiency Control Method for Plural Eigen Frequencies by Changing Topology

Toshie Sasaki, Yang Yang, Ichiro Hagiwara

Published in International Journal of Mechanical Engineering and Applications (Volume 10, Issue 6)

Received: 3 November 2022 Accepted: 17 November 2022 Published: 29 November 2022

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Abstract

We have developed many types of transport boxes by origami-operation and space filling operation. But it has not been solved that the fruits, vegetables, strawberries, cells, blood and a bottle of liquor are damaged, broken during transportation. It is the greatest factor in this situation that there is a danger vibration frequency band where these are easy to scratch and are prone to death. If there are eigen frequencies within this danger frequency band, it needs that those eigen frequencies within this danger frequency band are moved out of the band. But it is difficult to apply the existing topology optimization methods using homogenization method or density method to control plural eigen frequencies for two reasons. One reason is that even if homogenization method or density method is used, finally after convergence, holes are made on finite elements of which the size of the homogenizing element or the thickness is smaller than the threshold by keeping the rest the original size. In such processing, there is a possibility that the converged solution again deviates from the convergence value. Another reason is that it is difficult to control plural eigen frequencies simultaneously because some eigen frequencies go up and some ones go down no matter where it is reinforced although displacement at any point goes down in static problem. Although in such way, it is very difficult to control plural eigen frequencies, here we propose a new high precision and high efficiency method for controlling plural eigen frequencies simultaneously using the kinetic energy density and the strain energy density.

Published in	International Journal of Mechanical Engineering and Applications (Volume 10, Issue 6)
DOI	10.11648/j.ijmea.20221006.12
Page(s)	135-143
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Origami Engineering, Transportation Box, Topology Optimization, Density Method, Index of Generalized Eigen Frequency, Kinetic Energy Density, Strain Energy Density, Danger Frequency Band

References

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[2]	Nishiwaki, S. (2020). Optimization Concept and its Trends. Journal of the Japan Society of Precision Engineering, 86 (6), 391-394.
[3]	Kikuchi, N. (1993). Optimum Theory based on Homogenization Method. JSIAM 3 (1), 2-26.
[4]	Ma, Z. D., Kikuchi, N., Cheng, H. C. & Hagiwara, I. (1993). Development of Structural Optimization Method for Vibration Reduction (1st Report, Structural Optimization Theory Using the Homogenization Method). Series C, 9 (562), 1730-1736.
[5]	Tenek, L. H. & Hagiwara, I. (1993). Static and Vibrational Shape and Topology Optimization Using Homogenization and Mathematical Programming. Comput. Method sin Appl. Mech. Energy, 109, 143-154.
[6]	Tenek, L. H. & Hagiwara, I. (1994). Eigenfrequency Maximization of Plates by Optimization of Topology Using Homogenization and Mathematical Programming. JSME International Journal Series C, 37 (4), 667-677.
[7]	Ma, Z. D., Kikuchi, N., Hagiwara, I. and Torigaki, T., Development of Structural Optimization Method for Vibration Reduction, (2nd Report, An Improved Algorithm for the Optimization Problem), JSME Series C, Vol. 60, No. 577 (1994-9), pp. 3018-3024 (in Japanese).
[8]	Torigaki, T., Hagiwara, I., Kitagawa, Y., Ueda, M., Ma, Z. D. and Kikuchi, N., Development and Application of a Shape-Topology Optimization System Using a Homogenization Method, SAE International Congress and Exposition. (1994-3).
[9]	Tenek, L. H. and Hagiwara, I., Optimal Plate and Shell Topologies Using Thickness Distribution or Homogenization, Comput. Methods in Appl. Mech. Engrg. Vol. 115 (1994-7) Nos. 1 & 2, pp. 111-124.
[10]	Tenek, L. H. and Hagiwara, I., A Substructure Method Incorporating Homogenization for Finding Optimum Vehicle Body Panel Topologies JSME International Journal Series I, Vol. 38, No. 1 (1995-1), pp. 44-51.
[11]	Ma, Z. D., Kikuchi, N., Cheng, H. C. and Hagiwara, I., Topological Optimization Technique for Free Vibration Problems, ASME Journal of Applied Mechanics, Vol. 62 (1995-3), pp. 201-207.
[12]	Hagiwara, I. and Tenek, L. H., Development of Topology Optimization Method for Control of Plural Eigenvalues Simultaneously with a Laminated Composite Plate, Transaction JSME, Series C, Vol. 61, No. 587 (1995-7), pp. 2675-2682. (in Japanese).
[13]	Kozukue, W. and Hagiwara, I., Topology optimization analysis for vehicle interior noise reduction using homogenization and integral sensitivity, Transaction JSME, Series C, Vol. 61, No. 587 (1995-7), pp. 2746-2752. (in Japanese).
[14]	Mike, J. D. and Powell, A direct search optimization method that models the objective and constraint functions by linear interpolation”, Proc. Sixth Workshop on Optimization and Numerical Analysis, Vol. 275, pp. 5167, Kluwer Academic Publishers, Dordrecht, NL, 1994.
[15]	COMSOL Multiphysics® v. 5.5. www.comsol.com. COMSOL AB, Stockholm, Sweden (2019).
[16]	Hagiwara, I., Global Optimization Method to Multiple Local Optimals with the Surface Approximation Methodology and Its Application for Industry Problems [Online First], DOI: 10.5772/intechopen.98907. (2021-9), pp. 1-41.

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APA Style

Toshie Sasaki, Yang Yang, Ichiro Hagiwara. (2022). Proposition of a New High Speed and High Efficiency Control Method for Plural Eigen Frequencies by Changing Topology. International Journal of Mechanical Engineering and Applications, 10(6), 135-143. https://doi.org/10.11648/j.ijmea.20221006.12

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ACS Style

Toshie Sasaki; Yang Yang; Ichiro Hagiwara. Proposition of a New High Speed and High Efficiency Control Method for Plural Eigen Frequencies by Changing Topology. Int. J. Mech. Eng. Appl. 2022, 10(6), 135-143. doi: 10.11648/j.ijmea.20221006.12

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AMA Style

Toshie Sasaki, Yang Yang, Ichiro Hagiwara. Proposition of a New High Speed and High Efficiency Control Method for Plural Eigen Frequencies by Changing Topology. Int J Mech Eng Appl. 2022;10(6):135-143. doi: 10.11648/j.ijmea.20221006.12

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@article{10.11648/j.ijmea.20221006.12,
  author = {Toshie Sasaki and Yang Yang and Ichiro Hagiwara},
  title = {Proposition of a New High Speed and High Efficiency Control Method for Plural Eigen Frequencies by Changing Topology},
  journal = {International Journal of Mechanical Engineering and Applications},
  volume = {10},
  number = {6},
  pages = {135-143},
  doi = {10.11648/j.ijmea.20221006.12},
  url = {https://doi.org/10.11648/j.ijmea.20221006.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmea.20221006.12},
  abstract = {We have developed many types of transport boxes by origami-operation and space filling operation. But it has not been solved that the fruits, vegetables, strawberries, cells, blood and a bottle of liquor are damaged, broken during transportation. It is the greatest factor in this situation that there is a danger vibration frequency band where these are easy to scratch and are prone to death. If there are eigen frequencies within this danger frequency band, it needs that those eigen frequencies within this danger frequency band are moved out of the band. But it is difficult to apply the existing topology optimization methods using homogenization method or density method to control plural eigen frequencies for two reasons. One reason is that even if homogenization method or density method is used, finally after convergence, holes are made on finite elements of which the size of the homogenizing element or the thickness is smaller than the threshold by keeping the rest the original size. In such processing, there is a possibility that the converged solution again deviates from the convergence value. Another reason is that it is difficult to control plural eigen frequencies simultaneously because some eigen frequencies go up and some ones go down no matter where it is reinforced although displacement at any point goes down in static problem. Although in such way, it is very difficult to control plural eigen frequencies, here we propose a new high precision and high efficiency method for controlling plural eigen frequencies simultaneously using the kinetic energy density and the strain energy density.},
 year = {2022}
}

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TY  - JOUR
T1  - Proposition of a New High Speed and High Efficiency Control Method for Plural Eigen Frequencies by Changing Topology
AU  - Toshie Sasaki
AU  - Yang Yang
AU  - Ichiro Hagiwara
Y1  - 2022/11/29
PY  - 2022
N1  - https://doi.org/10.11648/j.ijmea.20221006.12
DO  - 10.11648/j.ijmea.20221006.12
T2  - International Journal of Mechanical Engineering and Applications
JF  - International Journal of Mechanical Engineering and Applications
JO  - International Journal of Mechanical Engineering and Applications
SP  - 135
EP  - 143
PB  - Science Publishing Group
SN  - 2330-0248
UR  - https://doi.org/10.11648/j.ijmea.20221006.12
AB  - We have developed many types of transport boxes by origami-operation and space filling operation. But it has not been solved that the fruits, vegetables, strawberries, cells, blood and a bottle of liquor are damaged, broken during transportation. It is the greatest factor in this situation that there is a danger vibration frequency band where these are easy to scratch and are prone to death. If there are eigen frequencies within this danger frequency band, it needs that those eigen frequencies within this danger frequency band are moved out of the band. But it is difficult to apply the existing topology optimization methods using homogenization method or density method to control plural eigen frequencies for two reasons. One reason is that even if homogenization method or density method is used, finally after convergence, holes are made on finite elements of which the size of the homogenizing element or the thickness is smaller than the threshold by keeping the rest the original size. In such processing, there is a possibility that the converged solution again deviates from the convergence value. Another reason is that it is difficult to control plural eigen frequencies simultaneously because some eigen frequencies go up and some ones go down no matter where it is reinforced although displacement at any point goes down in static problem. Although in such way, it is very difficult to control plural eigen frequencies, here we propose a new high precision and high efficiency method for controlling plural eigen frequencies simultaneously using the kinetic energy density and the strain energy density.
VL  - 10
IS  - 6
ER  -

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Author Information

Toshie Sasaki

Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Tokyo, Japan
Yang Yang

Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Tokyo, Japan
Ichiro Hagiwara

Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Tokyo, Japan

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Plain Text BibTeX RIS

APA Style

Toshie Sasaki, Yang Yang, Ichiro Hagiwara. (2022). Proposition of a New High Speed and High Efficiency Control Method for Plural Eigen Frequencies by Changing Topology. International Journal of Mechanical Engineering and Applications, 10(6), 135-143. https://doi.org/10.11648/j.ijmea.20221006.12

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ACS Style

Toshie Sasaki; Yang Yang; Ichiro Hagiwara. Proposition of a New High Speed and High Efficiency Control Method for Plural Eigen Frequencies by Changing Topology. Int. J. Mech. Eng. Appl. 2022, 10(6), 135-143. doi: 10.11648/j.ijmea.20221006.12

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AMA Style

Toshie Sasaki, Yang Yang, Ichiro Hagiwara. Proposition of a New High Speed and High Efficiency Control Method for Plural Eigen Frequencies by Changing Topology. Int J Mech Eng Appl. 2022;10(6):135-143. doi: 10.11648/j.ijmea.20221006.12

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@article{10.11648/j.ijmea.20221006.12,
  author = {Toshie Sasaki and Yang Yang and Ichiro Hagiwara},
  title = {Proposition of a New High Speed and High Efficiency Control Method for Plural Eigen Frequencies by Changing Topology},
  journal = {International Journal of Mechanical Engineering and Applications},
  volume = {10},
  number = {6},
  pages = {135-143},
  doi = {10.11648/j.ijmea.20221006.12},
  url = {https://doi.org/10.11648/j.ijmea.20221006.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmea.20221006.12},
  abstract = {We have developed many types of transport boxes by origami-operation and space filling operation. But it has not been solved that the fruits, vegetables, strawberries, cells, blood and a bottle of liquor are damaged, broken during transportation. It is the greatest factor in this situation that there is a danger vibration frequency band where these are easy to scratch and are prone to death. If there are eigen frequencies within this danger frequency band, it needs that those eigen frequencies within this danger frequency band are moved out of the band. But it is difficult to apply the existing topology optimization methods using homogenization method or density method to control plural eigen frequencies for two reasons. One reason is that even if homogenization method or density method is used, finally after convergence, holes are made on finite elements of which the size of the homogenizing element or the thickness is smaller than the threshold by keeping the rest the original size. In such processing, there is a possibility that the converged solution again deviates from the convergence value. Another reason is that it is difficult to control plural eigen frequencies simultaneously because some eigen frequencies go up and some ones go down no matter where it is reinforced although displacement at any point goes down in static problem. Although in such way, it is very difficult to control plural eigen frequencies, here we propose a new high precision and high efficiency method for controlling plural eigen frequencies simultaneously using the kinetic energy density and the strain energy density.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Proposition of a New High Speed and High Efficiency Control Method for Plural Eigen Frequencies by Changing Topology
AU  - Toshie Sasaki
AU  - Yang Yang
AU  - Ichiro Hagiwara
Y1  - 2022/11/29
PY  - 2022
N1  - https://doi.org/10.11648/j.ijmea.20221006.12
DO  - 10.11648/j.ijmea.20221006.12
T2  - International Journal of Mechanical Engineering and Applications
JF  - International Journal of Mechanical Engineering and Applications
JO  - International Journal of Mechanical Engineering and Applications
SP  - 135
EP  - 143
PB  - Science Publishing Group
SN  - 2330-0248
UR  - https://doi.org/10.11648/j.ijmea.20221006.12
AB  - We have developed many types of transport boxes by origami-operation and space filling operation. But it has not been solved that the fruits, vegetables, strawberries, cells, blood and a bottle of liquor are damaged, broken during transportation. It is the greatest factor in this situation that there is a danger vibration frequency band where these are easy to scratch and are prone to death. If there are eigen frequencies within this danger frequency band, it needs that those eigen frequencies within this danger frequency band are moved out of the band. But it is difficult to apply the existing topology optimization methods using homogenization method or density method to control plural eigen frequencies for two reasons. One reason is that even if homogenization method or density method is used, finally after convergence, holes are made on finite elements of which the size of the homogenizing element or the thickness is smaller than the threshold by keeping the rest the original size. In such processing, there is a possibility that the converged solution again deviates from the convergence value. Another reason is that it is difficult to control plural eigen frequencies simultaneously because some eigen frequencies go up and some ones go down no matter where it is reinforced although displacement at any point goes down in static problem. Although in such way, it is very difficult to control plural eigen frequencies, here we propose a new high precision and high efficiency method for controlling plural eigen frequencies simultaneously using the kinetic energy density and the strain energy density.
VL  - 10
IS  - 6
ER  -

Copy | Download