Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory

Şi̇mşek, Mesut; Reddy, J. N.

doi:10.1016/j.ijengsci.2012.12.002

Cited by 440 publications

(74 citation statements)

References 48 publications

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“…They concluded that employing the modified couple stress theory leads to a stiffer beam rather than old theories. Simsek and Reddy [9] presented bending and free vibration analyses of FG microbeams based on the modified couple stress theory and some higher-order beam theories. They used the couple stress theory to account the effect of material length scale parameters, different material compositions, and shear deformations on the responses of the system.…”

Section: Introductionmentioning

confidence: 99%

Transient analysis of a three-layer microbeam subjected to electric potential

Arefi

Zenkour

2017

International Journal of Smart and Nano Materials

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In this paper, free vibration, wave propagation, and bending analyses of a sandwich microbeam integrated with piezoelectric face-sheets resting on Pasternak foundation under electric potential are presented based on the strain gradient theory and Euler-Bernoulli beam theory. The material properties of core are assumed variable along the thickness direction and piezoelectric face-sheets are assumed homogeneous piezoelectric materials. A two-dimensional electric potential distribution along the axial and transverse direction is applied on the face-sheets of microbeam. Hamilton principal is used to derive governing differential equations of motion. Three behaviors of sandwich microbeam including free vibration, wave propagation, and bending analyses are studied in this paper. Some numerical results are presented to capture the effect of important parameters of the problem such as in-homogeneous index, applied voltage, parameters of foundation, and material length scales. The numerical results indicate that the effect of electric potential along the axial direction is very small rather than one along the transverse direction where initial voltage is applied. ARTICLE HISTORY

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Section: Introductionmentioning

confidence: 99%

Transient analysis of a three-layer microbeam subjected to electric potential

Arefi

Zenkour

2017

International Journal of Smart and Nano Materials

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“…Akgöz and Civalek [36] presented a new non-classical sinusoidal plate model on the basis of modified strain gradient theory to investigate bending, buckling and vibration behavior. In addition to the above studies, the modified couple stress theory is also used to study the behavior of microbeams and microplates made of composite materials [37][38][39][40][41][42][43][44][45][46][47][48][49].…”

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confidence: 99%

Size-dependent vibration of a microplate under the action of a moving load based on the modified couple stress theory

et al. 2015

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This study deals with forced vibration analysis of a microplate subjected to a moving load. The formulation is developed based on the modified couple stress theory in conjunction with Kirchhoff-Love plate theory. The equations of motion of the problem are derived using Lagrange's equations. In order to obtain the response of the microplate, the trial function for the dynamic deflection is expressed in the polynomial form. The equations of motion are solved by using the implicit time integration Newmark-β method, and then displacements, velocities and accelerations of the microplate at the considered point and time are determined. Five different sets of boundary condition are considered. For this purpose, boundary conditions are satisfied by adding some auxiliary functions to the trial functions. A parametric study is conducted to study the effects of the material length scale parameter, plate aspect ratio, boundary conditions and the moving load velocity on the dynamic response of the microplate. Also, in order to validate the present formulation and solution method, some comparisons with those available in the literature are performed. Good agreement is found. The results show that the dynamic deflections are significantly affected by the scale parameter and the load velocity.

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“…In this context, the strain gradient theory and the modified couple stress theory are capable of incorporating the stiffness enhancement [21][22][23][24][25][26][27][28][29][30]. As seen from the previous discussion, the nonlocal elasticity theory and the strain gradient theory handle the different aspects of size-dependent mechanical behavior of micro and nanostructures.…”

Section: Introductionmentioning

confidence: 99%

Yerel Olmayan Şekil Değiştirme Gradyanı Teorisi Kullanılarak Elastik Zemine Gömülü Nano Çubuğun Eksenel Titreşim Analizi

Şi̇mşek¹

2016

Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi

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Size-dependent axial vibration of a nanorod embedded in elastic medium is studied for the first time in this paper within the framework of the nonlocal strain gradient theory. The governing equation of motion of the problem is derived using the equilibrium condition and it is solved analytically to obtain the exact expression of vibration frequency for a fixed-fixed nanorod. The influences of the nonlocal parameter, the material length scale parameter and the elastic medium coefficient on the free vibration frequencies are investigated in detail. The results show that free vibration frequencies are significantly dependent on the size effects, and the size effects gain more importance at higher modes. Therefore, the classical continuum theory is inappropriate to investigate the mechanical behavior of nanostructures.Keywords: Nanotechnology, Vibration, Nonlocal elasticity theory, Strain gradient theory, Nanorod Yerel Olmayan Şekil Değiştirme Gradyanı Teorisi Kullanılarak Elastik Zemine Gömülü Nano Çubuğun Eksenel Titreşim Analizi ÖzetElastik zemine gömülü bir nano çubuğun boyut etkisine bağlı eksenel titreşimi yerel olmayan şekil değiştirme gradyanı teorisi çerçevesinde ilk olarak bu çalışmada incelenmiştir. Probleme ait yönetici hareket denklemi denge şartı kullanılarak çıkarılmış, iki ucu ankastre nano çubuğun serbest titreşim frekansına ait kesin ifadeyi elde etmek için yönetici denklem analitik olarak çözülmüştür. Yerel olmayan parametre, malzeme uzunluk ölçek parametresi ve elastik zemin parametresinin serbest titreşim frekansları üzerindeki etkisi detaylı olarak incelenmiştir. Elde edilen sayısal sonuçlar göstermiştir ki; serbest titreşim frekansları boyut etkisine önemli derecede bağlıdır ve boyut etkisi yüksek modlarda daha çok önem kazanmaktadır. Bu nedenlerden dolayı, klasik sürekli ortamlar mekaniği nano ölçekteki yapıların analizi için uygun değildir.

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Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory

Cited by 440 publications

References 48 publications

Transient analysis of a three-layer microbeam subjected to electric potential

Transient analysis of a three-layer microbeam subjected to electric potential

Size-dependent vibration of a microplate under the action of a moving load based on the modified couple stress theory

Yerel Olmayan Şekil Değiştirme Gradyanı Teorisi Kullanılarak Elastik Zemine Gömülü Nano Çubuğun Eksenel Titreşim Analizi

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