Genetic algorithm shape optimization to manipulate the nonlinear response of a clamped-clamped beam
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 or...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2022-11-01
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| Series: | Heliyon |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844022031218 |
| _version_ | 1811190933939552256 |
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| author | Tushar Mollik Ying Geng Md Raf E Ul Shougat Timothy Fitzgerald Edmon Perkins |
| author_facet | Tushar Mollik Ying Geng Md Raf E Ul Shougat Timothy Fitzgerald Edmon Perkins |
| author_sort | Tushar Mollik |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T14:58:39Z |
| format | Article |
| id | doaj.art-bc9953233a1a4334841f00db9954a21c |
| institution | Directory Open Access Journal |
| issn | 2405-8440 |
| language | English |
| last_indexed | 2024-04-11T14:58:39Z |
| publishDate | 2022-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj.art-bc9953233a1a4334841f00db9954a21c2022-12-22T04:17:06ZengElsevierHeliyon2405-84402022-11-01811e11833Genetic algorithm shape optimization to manipulate the nonlinear response of a clamped-clamped beamTushar Mollik0Ying Geng1Md Raf E Ul Shougat2Timothy Fitzgerald3Edmon Perkins4LAB2701, Department of Mechanical & Aerospace Engineering, North Carolina State University, Raleigh, NC 27695, United States of AmericaLAB2701, Atwood, OK 74827, United States of AmericaLAB2701, Department of Mechanical & Aerospace Engineering, North Carolina State University, Raleigh, NC 27695, United States of AmericaDepartment of Mechanical Engineering, Gonzaga University, Spokane, WA 99258, United States of AmericaLAB2701, Department of Mechanical & Aerospace Engineering, North Carolina State University, Raleigh, NC 27695, United States of America; Corresponding author.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.http://www.sciencedirect.com/science/article/pii/S2405844022031218Shape optimizationNonlinear oscillatorsBeamsDuffing oscillator |
| spellingShingle | Tushar Mollik Ying Geng Md Raf E Ul Shougat Timothy Fitzgerald Edmon Perkins Genetic algorithm shape optimization to manipulate the nonlinear response of a clamped-clamped beam Heliyon Shape optimization Nonlinear oscillators Beams Duffing oscillator |
| title | Genetic algorithm shape optimization to manipulate the nonlinear response of a clamped-clamped beam |
| title_full | Genetic algorithm shape optimization to manipulate the nonlinear response of a clamped-clamped beam |
| title_fullStr | Genetic algorithm shape optimization to manipulate the nonlinear response of a clamped-clamped beam |
| title_full_unstemmed | Genetic algorithm shape optimization to manipulate the nonlinear response of a clamped-clamped beam |
| title_short | Genetic algorithm shape optimization to manipulate the nonlinear response of a clamped-clamped beam |
| title_sort | genetic algorithm shape optimization to manipulate the nonlinear response of a clamped clamped beam |
| topic | Shape optimization Nonlinear oscillators Beams Duffing oscillator |
| url | http://www.sciencedirect.com/science/article/pii/S2405844022031218 |
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