OPTIMAL BOUNDARY CONTROL FOR A SECOND STRAIN GRADIENT THEORY-BASED BEAM MODEL

Seda Göktepe Körpeoğlu; Ismail Kucuk; Kenan Yıldırım

OPTIMAL BOUNDARY CONTROL FOR A SECOND STRAIN GRADIENT THEORY-BASED BEAM MODEL

Abstract

The second strain gradient theory is a non-classical continuum theory that captures the behavior of micrometer and nanometer sized beam structures. Timoshenko and Euler-Bernoulli theories are classical beam models that neglect the effects of small size structures when compared to the second strain gradient theory-based beam model. In this study, an optimal boundary control problem is formulated for the second strain gradient theory-based beam model to control free vibrations in the system. A quadratic performance index expressing the dynamic response of the system is to be minimized while an affordable control is in use. An indirect method based on Pontryagin’s maximum principle is used to derive a necessary condition analytically for optimal control. Then, the problem is transformed into a system of partial differential equations consisting of state and costate (adjoint) variables together. The solution of the control problem is carried out using the computer codes produced in MATLAB©. The effectiveness and competence of the introduced optimal boundary control are presented in numerical simulations.

Keywords

References

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Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Seda Göktepe Körpeoğlu This is me
0000-0001-7146-0846
Türkiye

Ismail Kucuk This is me
0000-0003-3071-0612
Türkiye

Kenan Yıldırım This is me
0000-0002-4471-3964
Türkiye

Publication Date

December 1, 2019

Submission Date

February 25, 2018

Acceptance Date

September 12, 2019

Published in Issue

Year 2019 Volume: 37 Number: 4

IZ

https://izlik.org/JA34ZT67WN

Cite

RIS / Bibtex

APA

Göktepe Körpeoğlu, S., Kucuk, I., & Yıldırım, K. (2019). OPTIMAL BOUNDARY CONTROL FOR A SECOND STRAIN GRADIENT THEORY-BASED BEAM MODEL. Sigma Journal of Engineering and Natural Sciences, 37(4), 1280-1292. https://izlik.org/JA34ZT67WN

AMA

1.Göktepe Körpeoğlu S, Kucuk I, Yıldırım K. OPTIMAL BOUNDARY CONTROL FOR A SECOND STRAIN GRADIENT THEORY-BASED BEAM MODEL. SIGMA. 2019;37(4):1280-1292. https://izlik.org/JA34ZT67WN

Chicago

Göktepe Körpeoğlu, Seda, Ismail Kucuk, and Kenan Yıldırım. 2019. “OPTIMAL BOUNDARY CONTROL FOR A SECOND STRAIN GRADIENT THEORY-BASED BEAM MODEL”. Sigma Journal of Engineering and Natural Sciences 37 (4): 1280-92. https://izlik.org/JA34ZT67WN.

EndNote

Göktepe Körpeoğlu S, Kucuk I, Yıldırım K (December 1, 2019) OPTIMAL BOUNDARY CONTROL FOR A SECOND STRAIN GRADIENT THEORY-BASED BEAM MODEL. Sigma Journal of Engineering and Natural Sciences 37 4 1280–1292.

IEEE

[1]S. Göktepe Körpeoğlu, I. Kucuk, and K. Yıldırım, “OPTIMAL BOUNDARY CONTROL FOR A SECOND STRAIN GRADIENT THEORY-BASED BEAM MODEL”, SIGMA, vol. 37, no. 4, pp. 1280–1292, Dec. 2019, [Online]. Available: https://izlik.org/JA34ZT67WN

ISNAD

Göktepe Körpeoğlu, Seda - Kucuk, Ismail - Yıldırım, Kenan. “OPTIMAL BOUNDARY CONTROL FOR A SECOND STRAIN GRADIENT THEORY-BASED BEAM MODEL”. Sigma Journal of Engineering and Natural Sciences 37/4 (December 1, 2019): 1280-1292. https://izlik.org/JA34ZT67WN.

JAMA

1.Göktepe Körpeoğlu S, Kucuk I, Yıldırım K. OPTIMAL BOUNDARY CONTROL FOR A SECOND STRAIN GRADIENT THEORY-BASED BEAM MODEL. SIGMA. 2019;37:1280–1292.

MLA

Göktepe Körpeoğlu, Seda, et al. “OPTIMAL BOUNDARY CONTROL FOR A SECOND STRAIN GRADIENT THEORY-BASED BEAM MODEL”. Sigma Journal of Engineering and Natural Sciences, vol. 37, no. 4, Dec. 2019, pp. 1280-92, https://izlik.org/JA34ZT67WN.

Vancouver

1.Seda Göktepe Körpeoğlu, Ismail Kucuk, Kenan Yıldırım. OPTIMAL BOUNDARY CONTROL FOR A SECOND STRAIN GRADIENT THEORY-BASED BEAM MODEL. SIGMA [Internet]. 2019 Dec. 1;37(4):1280-92. Available from: https://izlik.org/JA34ZT67WN