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Bifurcation and hysteresis analysis of the non-degenerate Euler beam problem

Yıl 2024, Cilt: 4 Sayı: 5-Special Issue: ICAME'24, 79 - 93, 31.12.2024

Atia Afroz , Mohammad Sahadet Hossain , Shad Dhewan Shopnil , Md. Tamim

https://doi.org/10.53391/mmnsa.1523578
Cited By: 1

Öz

In this work, the bifurcation and hysteresis phenomena of the Euler beam problem are focused on from the singularity theory viewpoint. Confirming the continuity of the problem is a necessary condition for performing a bifurcation and hysteresis analysis. A bifurcation problem is transformed from an infinite dimension to a finite dimension by applying the Lyapunov equations. A suitable central force minimizes our considered model and makes the problem stable. Moreover, we perform numerical investigations and interpret the results obtained from the bifurcation and hysteresis analysis geometrically with suitable values of the new unfolding parameters and with different lengths.

Anahtar Kelimeler

Bifurcation non-degeneracy Euler beam hysteresis

Teşekkür

Thanks to North South University, Bangladesh, for their support.

Kaynakça

  • [1] Golubitsky, M. and Schaeffer, D. A theory for imperfect bifurcation via singularity theory. Communications on Pure and Applied Mathematics, 32(1), 21-98, (1979).
  • [2] Golubitsky, M., Stewart, I. and Schaeffer, D.G. Further Examples of Hopf Bifurcation with Symmetry. In Singularities and Groups in Bifurcation Theory Vol.2, (pp. 363-411). New York, NY: Springer, (1988).
  • [3] Golubitsky, M. and Schaeffer, D. A theory for imperfect bifurcation via singularity theory. Communications on Pure and Applied Mathematics, 32(1), 21-98, (1979).
  • [4] Afroz, A. Bifurcation Analysis of Euler Buckling Problem from the viewpoint of Singularity Theory. Ph.D. Thesis, Department of Mathematics, Saitama University, (2019). [https://sucra.repo.nii.ac.jp/records/19055]
  • [5] Afroz, A. and Fukui, T. Bifurcation of Euler buckling problem, revisited. Hokkaido Mathematical Journal, 50(1), 111-150, (2021).
  • [6] Ioffe, A.D. Variational Analysis of Regular Mapping. Springer: Cham, (2017).
  • [7] Ambrosetti, A. and Álvarez, D.A. An Introduction to Nonlinear Functional Analysis and Eliptic Problems (Vol. 82). Springer Science & Business Media: Berlin, (2011).
  • [8] Brezis, H. Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer: New York, (2011).
  • [9] Sofonea, M., Han, W. and Shillor, M. Analysis and Approximation of Contact Problems with Adhesion or Damage. Chapman and Hall/CRC: New York, (2005).
  • [10] Hamilton, R.S. The inverse function theorem of Nash and Moser. Bulletin of the American Mathematical Society, 7(1), 65-222, (1982).
  • [11] Abraham, R., Marsden, J.E. and Ratiu, T. Manifolds, Tensor Analysis, and Applications (Vol. 75). Springer Science & Business Media: New York, (2012).
  • [12] Han, S.M., Benaroya, H. and Wei, T. Dynamics of transversely vibrating beams using four engineering theories. Journal of Sound and Vibration, 225(5), 935-988, (1999).
  • [13] Marsden, J.E. and Hughes, T.J. Mathematical Foundations of Elasticity. Dover Publications: New York, (1994).
  • [14] Kielhöfer, H. Bifurcation Theory. Springer: New York, (2012).

Yıl 2024, Cilt: 4 Sayı: 5-Special Issue: ICAME'24, 79 - 93, 31.12.2024

Atia Afroz , Mohammad Sahadet Hossain , Shad Dhewan Shopnil , Md. Tamim

https://doi.org/10.53391/mmnsa.1523578
Cited By: 1

Öz

Kaynakça

  • [1] Golubitsky, M. and Schaeffer, D. A theory for imperfect bifurcation via singularity theory. Communications on Pure and Applied Mathematics, 32(1), 21-98, (1979).
  • [2] Golubitsky, M., Stewart, I. and Schaeffer, D.G. Further Examples of Hopf Bifurcation with Symmetry. In Singularities and Groups in Bifurcation Theory Vol.2, (pp. 363-411). New York, NY: Springer, (1988).
  • [3] Golubitsky, M. and Schaeffer, D. A theory for imperfect bifurcation via singularity theory. Communications on Pure and Applied Mathematics, 32(1), 21-98, (1979).
  • [4] Afroz, A. Bifurcation Analysis of Euler Buckling Problem from the viewpoint of Singularity Theory. Ph.D. Thesis, Department of Mathematics, Saitama University, (2019). [https://sucra.repo.nii.ac.jp/records/19055]
  • [5] Afroz, A. and Fukui, T. Bifurcation of Euler buckling problem, revisited. Hokkaido Mathematical Journal, 50(1), 111-150, (2021).
  • [6] Ioffe, A.D. Variational Analysis of Regular Mapping. Springer: Cham, (2017).
  • [7] Ambrosetti, A. and Álvarez, D.A. An Introduction to Nonlinear Functional Analysis and Eliptic Problems (Vol. 82). Springer Science & Business Media: Berlin, (2011).
  • [8] Brezis, H. Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer: New York, (2011).
  • [9] Sofonea, M., Han, W. and Shillor, M. Analysis and Approximation of Contact Problems with Adhesion or Damage. Chapman and Hall/CRC: New York, (2005).
  • [10] Hamilton, R.S. The inverse function theorem of Nash and Moser. Bulletin of the American Mathematical Society, 7(1), 65-222, (1982).
  • [11] Abraham, R., Marsden, J.E. and Ratiu, T. Manifolds, Tensor Analysis, and Applications (Vol. 75). Springer Science & Business Media: New York, (2012).
  • [12] Han, S.M., Benaroya, H. and Wei, T. Dynamics of transversely vibrating beams using four engineering theories. Journal of Sound and Vibration, 225(5), 935-988, (1999).
  • [13] Marsden, J.E. and Hughes, T.J. Mathematical Foundations of Elasticity. Dover Publications: New York, (1994).
  • [14] Kielhöfer, H. Bifurcation Theory. Springer: New York, (2012).
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematikte Optimizasyon, Teorik ve Uygulamalı Mekanik Matematiği, Uygulamalarda Dinamik Sistemler
Bölüm Araştırma Makalesi
Yazarlar

Atia Afroz 0000-0001-6708-3486

Mohammad Sahadet Hossain 0000-0002-7953-1351

Shad Dhewan Shopnil 0009-0001-3070-2893

Md. Tamim 0009-0003-9547-2720

Yayımlanma Tarihi 31 Aralık 2024
Gönderilme Tarihi 28 Temmuz 2024
Kabul Tarihi 15 Aralık 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 4 Sayı: 5-Special Issue: ICAME'24

Kaynak Göster

APA Afroz, A., Hossain, M. S., Shopnil, S. D., Tamim, M. (2024). Bifurcation and hysteresis analysis of the non-degenerate Euler beam problem. Mathematical Modelling and Numerical Simulation With Applications, 4(5-Special Issue: ICAME’24), 79-93. https://doi.org/10.53391/mmnsa.1523578

Cited By

Advanced computational methods and innovative applications in science and engineering
Mathematical Modelling and Numerical Simulation with Applications
https://doi.org/10.53391/mmnsa.1611132


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