Nonlinear Free and Forced Vibrations of a Hyperelastic Micro/Nanobeam Considering Strain Stiffening Effect
In recent years, the static and dynamic response of micro/nanobeams made of hyperelasticity materials received great attention. In the majority of studies in this area, the strain-stiffing effect that plays a major role in many hyperelastic materials has not been investigated deeply. Moreover, the i...
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| Format: | Article |
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MDPI AG
2021-11-01
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| Series: | Nanomaterials |
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| Online Access: | https://www.mdpi.com/2079-4991/11/11/3066 |
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| author | Amin Alibakhshi Shahriar Dastjerdi Mohammad Malikan Victor A. Eremeyev |
| author_facet | Amin Alibakhshi Shahriar Dastjerdi Mohammad Malikan Victor A. Eremeyev |
| author_sort | Amin Alibakhshi |
| collection | DOAJ |
| description | In recent years, the static and dynamic response of micro/nanobeams made of hyperelasticity materials received great attention. In the majority of studies in this area, the strain-stiffing effect that plays a major role in many hyperelastic materials has not been investigated deeply. Moreover, the influence of the size effect and large rotation for such a beam that is important for the large deformation was not addressed. This paper attempts to explore the free and forced vibrations of a micro/nanobeam made of a hyperelastic material incorporating strain-stiffening, size effect, and moderate rotation. The beam is modelled based on the Euler–Bernoulli beam theory, and strains are obtained via an extended von Kármán theory. Boundary conditions and governing equations are derived by way of Hamilton’s principle. The multiple scales method is applied to obtain the frequency response equation, and Hamilton’s technique is utilized to obtain the free undamped nonlinear frequency. The influence of important system parameters such as the stiffening parameter, damping coefficient, length of the beam, length-scale parameter, and forcing amplitude on the frequency response, force response, and nonlinear frequency is analyzed. Results show that the hyperelastic microbeam shows a nonlinear hardening behavior, which this type of nonlinearity gets stronger by increasing the strain-stiffening effect. Conversely, as the strain-stiffening effect is decreased, the nonlinear frequency is decreased accordingly. The evidence from this study suggests that incorporating strain-stiffening in hyperelastic beams could improve their vibrational performance. The model proposed in this paper is mathematically simple and can be utilized for other kinds of micro/nanobeams with different boundary conditions. |
| first_indexed | 2024-03-10T05:12:57Z |
| format | Article |
| id | doaj.art-7c5cdca67701463f94d369bf4a9c0483 |
| institution | Directory Open Access Journal |
| issn | 2079-4991 |
| language | English |
| last_indexed | 2024-03-10T05:12:57Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Nanomaterials |
| spelling | doaj.art-7c5cdca67701463f94d369bf4a9c04832023-11-23T00:42:40ZengMDPI AGNanomaterials2079-49912021-11-011111306610.3390/nano11113066Nonlinear Free and Forced Vibrations of a Hyperelastic Micro/Nanobeam Considering Strain Stiffening EffectAmin Alibakhshi0Shahriar Dastjerdi1Mohammad Malikan2Victor A. Eremeyev3Department of Mechanical Engineering, Science and Research Branch, Islamic Azad University, Tehran 1477893855, IranCivil Engineering Department, Division of Mechanics, Akdeniz University, Antalya 07058, TurkeyDepartment of Mechanics of Materials and Structures, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, 80-233 Gdansk, PolandDepartment of Mechanics of Materials and Structures, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, 80-233 Gdansk, PolandIn recent years, the static and dynamic response of micro/nanobeams made of hyperelasticity materials received great attention. In the majority of studies in this area, the strain-stiffing effect that plays a major role in many hyperelastic materials has not been investigated deeply. Moreover, the influence of the size effect and large rotation for such a beam that is important for the large deformation was not addressed. This paper attempts to explore the free and forced vibrations of a micro/nanobeam made of a hyperelastic material incorporating strain-stiffening, size effect, and moderate rotation. The beam is modelled based on the Euler–Bernoulli beam theory, and strains are obtained via an extended von Kármán theory. Boundary conditions and governing equations are derived by way of Hamilton’s principle. The multiple scales method is applied to obtain the frequency response equation, and Hamilton’s technique is utilized to obtain the free undamped nonlinear frequency. The influence of important system parameters such as the stiffening parameter, damping coefficient, length of the beam, length-scale parameter, and forcing amplitude on the frequency response, force response, and nonlinear frequency is analyzed. Results show that the hyperelastic microbeam shows a nonlinear hardening behavior, which this type of nonlinearity gets stronger by increasing the strain-stiffening effect. Conversely, as the strain-stiffening effect is decreased, the nonlinear frequency is decreased accordingly. The evidence from this study suggests that incorporating strain-stiffening in hyperelastic beams could improve their vibrational performance. The model proposed in this paper is mathematically simple and can be utilized for other kinds of micro/nanobeams with different boundary conditions.https://www.mdpi.com/2079-4991/11/11/3066hyperelastic micro/nanobeamextended modified couple stress theorystrain-stiffening effectnonlinear frequency response |
| spellingShingle | Amin Alibakhshi Shahriar Dastjerdi Mohammad Malikan Victor A. Eremeyev Nonlinear Free and Forced Vibrations of a Hyperelastic Micro/Nanobeam Considering Strain Stiffening Effect Nanomaterials hyperelastic micro/nanobeam extended modified couple stress theory strain-stiffening effect nonlinear frequency response |
| title | Nonlinear Free and Forced Vibrations of a Hyperelastic Micro/Nanobeam Considering Strain Stiffening Effect |
| title_full | Nonlinear Free and Forced Vibrations of a Hyperelastic Micro/Nanobeam Considering Strain Stiffening Effect |
| title_fullStr | Nonlinear Free and Forced Vibrations of a Hyperelastic Micro/Nanobeam Considering Strain Stiffening Effect |
| title_full_unstemmed | Nonlinear Free and Forced Vibrations of a Hyperelastic Micro/Nanobeam Considering Strain Stiffening Effect |
| title_short | Nonlinear Free and Forced Vibrations of a Hyperelastic Micro/Nanobeam Considering Strain Stiffening Effect |
| title_sort | nonlinear free and forced vibrations of a hyperelastic micro nanobeam considering strain stiffening effect |
| topic | hyperelastic micro/nanobeam extended modified couple stress theory strain-stiffening effect nonlinear frequency response |
| url | https://www.mdpi.com/2079-4991/11/11/3066 |
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