Document Type
Article
Publication Title
Heliyon
Abstract
Dynamical systems, which are described by differential equations, can have an enhanced response because of their nonlinearity. As one example, the Duffing oscillator can exhibit multiple stable vibratory states for some external forcing frequencies. Although discrete systems that are described by ordinary differential equations have helped to build fundamental groundwork, further efforts are needed in order to tailor nonlinearity into distributed parameter, continuous systems, which are described by partial differential equations. To modify the nonlinear response of continuous systems, topology optimization can be used to change the shape of the mechanical system. While topology optimization is well-developed for linear systems, less work has been pursued to optimize the nonlinear vibratory response of continuous systems. In this paper, a genetic algorithm implementation of shape optimization for continuous systems is described. The method is very general, with flexible objective functions and very few assumptions; it is applicable to any continuous system. As a case study, a clamped-clamped beam is optimized to have a more nonlinear or less nonlinear vibratory response. This genetic algorithm implementation of shape optimization could provide a tool to improve the performance of many continuous structures, including MEMS sensors, actuators, and macroscale civil structures.
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DOI
https://doi.org/10.1016/j.heliyon.2022.e11833
Volume
8
Issue
11
Publication Date
11-2022
Keywords
Shape optimization, Nonlinear oscillators, Beams, Duffing oscillator
Disciplines
Mechanical Engineering
ISSN
2405-8440
Recommended Citation
Mollik, Tushar; Geng, Ying; Ul Shougat, Md Raf E.; Fitzgerald, Timothy; and Perkins, Edmon, "Genetic Algorithm Shape Optimization To Manipulate the Nonlinear Response of a Clamped-Clamped Beam" (2022). Mechanical Engineering Faculty Scholarship. 3.
https://repository.gonzaga.edu/mechengschol/3
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This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Comments
This version has been reformatted for accessibility. Please see the Supplemental Documents section at the bottom of the page or visit the journal website via the citation below for the Version of Record:
Mollik, T., Geng, Y., Shougat, M. R. E. U., Fitzgerald, T., & Perkins, E.. (2022). Genetic algorithm shape optimization to manipulate the nonlinear response of a clamped-clamped beam. Heliyon, 8, e11833. https://doi.org/10.1016/j.heliyon.2022.e11833.