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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Autores principales:	Amin Alibakhshi, Shahriar Dastjerdi, Mohammad Malikan, Victor A. Eremeyev
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	hyperelastic micro/nanobeam extended modified couple stress theory strain-stiffening effect nonlinear frequency response Chemistry QD1-999
Acceso en línea:	https://doaj.org/article/7c5cdca67701463f94d369bf4a9c0483
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spelling	oai:doaj.org-article:7c5cdca67701463f94d369bf4a9c04832021-11-25T18:32:11ZNonlinear Free and Forced Vibrations of a Hyperelastic Micro/Nanobeam Considering Strain Stiffening Effect10.3390/nano111130662079-4991https://doaj.org/article/7c5cdca67701463f94d369bf4a9c04832021-11-01T00:00:00Zhttps://www.mdpi.com/2079-4991/11/11/3066https://doaj.org/toc/2079-4991In 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.Amin AlibakhshiShahriar DastjerdiMohammad MalikanVictor A. EremeyevMDPI AGarticlehyperelastic micro/nanobeamextended modified couple stress theorystrain-stiffening effectnonlinear frequency responseChemistryQD1-999ENNanomaterials, Vol 11, Iss 3066, p 3066 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	hyperelastic micro/nanobeam extended modified couple stress theory strain-stiffening effect nonlinear frequency response Chemistry QD1-999
spellingShingle	hyperelastic micro/nanobeam extended modified couple stress theory strain-stiffening effect nonlinear frequency response Chemistry QD1-999 Amin Alibakhshi Shahriar Dastjerdi Mohammad Malikan Victor A. Eremeyev Nonlinear Free and Forced Vibrations of a Hyperelastic Micro/Nanobeam Considering Strain Stiffening Effect
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.
format	article
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
title	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_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_sort	nonlinear free and forced vibrations of a hyperelastic micro/nanobeam considering strain stiffening effect
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/7c5cdca67701463f94d369bf4a9c0483
work_keys_str_mv	AT aminalibakhshi nonlinearfreeandforcedvibrationsofahyperelasticmicronanobeamconsideringstrainstiffeningeffect AT shahriardastjerdi nonlinearfreeandforcedvibrationsofahyperelasticmicronanobeamconsideringstrainstiffeningeffect AT mohammadmalikan nonlinearfreeandforcedvibrationsofahyperelasticmicronanobeamconsideringstrainstiffeningeffect AT victoraeremeyev nonlinearfreeandforcedvibrationsofahyperelasticmicronanobeamconsideringstrainstiffeningeffect
_version_	1718411026875023360

Nonlinear Free and Forced Vibrations of a Hyperelastic Micro/Nanobeam Considering Strain Stiffening Effect

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