Free vibration analysis of size-dependent cracked microbeam based on the modified couple stress theory

Sourki, Reza; Hoseini, S. A. H.

doi:10.1007/s00339-016-9961-6

Cited by 40 publications

(14 citation statements)

References 44 publications

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“…However, it is known that the classical continuum mechanics cannot predict and explain the sizedependent behavior of nanostructures. Therefore, in order to incorporate the size effects in continuum mechanics, there are several higher-order continuum theories, such as the couple stress theory [34], strain gradient theory [10], nonlocal elasticity theory [11], micropolar theory [12] and surface elasticity [13]. But, among all of these theories, the nonlocal elasticity of Eringen [11] is proved to be capable for different analyses on nanostructures.…”

Section: Introductionmentioning

confidence: 98%

“…This model comprises a Winkler-type elastic spring besides the transverse shear stress as a result of the shear deformation in the medium, while the Winkler model incorporates the normal pressure from surrounding medium [30,31]. A few investigations have been carried out in the open literature dealing with the elastic medium in dynamic analysis of nanostructures such as [15,18,[32][33][34].…”

Section: Introductionmentioning

confidence: 99%

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Thermo-electro-mechanical vibration analysis of size-dependent nanobeam resting on elastic medium under axial preload in presence of surface effect

2016

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In the present manuscript, a nonclassical beam theory is developed to analyze free vibration of piezoelectric nanobeam by considering surface effects resting on Winkler-Pasternak elastic medium and thermal loading with axial preload. The nonclassical Eringen theory is utilized to incorporate the length-scale parameter to account for the small-scale effect, while the Gurtin-Murdoch model is employed to inject the surface effects including surface elasticity, surface stress and surface density. The governing equations are derived using Hamilton's principle in the framework of Euler-Bernoulli beam theory. The governing partial differential equations of motions of system are reduced to a set of algebraic equations with the help of differential transformation method as a semi-analytical-numerical. The mathematical derivations and numerical results are presented in detail for various boundary conditions. Some numerical examples are illustrated in order to investigate the effect of several parameters such as the nonlocal parameter, piezoelectric voltage, surface effects, temperature change, axial preload and elastic medium parameters. Moreover, it is also indicated that the numerical results have good agreement with previous studies.

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Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Thermo-electro-mechanical vibration analysis of size-dependent nanobeam resting on elastic medium under axial preload in presence of surface effect

2016

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“…Loya [16] investigated free vibration of cracked Euler-Bernoulli nanobeams using nonlocal elasticity model. Sourki and Hoseini [17] investigated vibration of a cracked nanobeam based on the modified couple stress theory within the framework of Euler-Bernoulli beam theory. Also, they simulated a cracked nanobeam with the nonlocal modified couple stress theory and investigated the mechanical parameters with analytical method in [18].…”

Section: Introductionmentioning

confidence: 99%

Vibrations Analysis of Cracked Nanobeams Using Quadrature Technique

Elkhalek¹,

Osman²,

Matbuly³

2019

ENGMATH

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This work concerns with free vibration analysis of cracked nanobeam problems. Based on Eringen's nonlocal elasticity theory, the governing equation of Euler-Bernoulli and Timoshenko nanobeams, are derived. It is assumed that strain at a certain point is a function of the strains at all points within the influence domain. The cracked beam is modeled as multisegments connected by a rotational spring located at the cracked sections. This model promotes discontinuities in rotational displacement due to bending which is proportional to bending moment transmitted by the cracked section. Polynomial based differential quadrature method is employed to solve the problem. Derivatives of the field quantities are approximated as a weighted linear sum of the nodal values. For different supporting cases, the boundary conditions are directly substituted in the equation of motion, such that the problem is reduced to that of linear homogeneous algebraic system. This suggested numerical scheme accurately determined angular frequencies of the problem. A comparative study is tabulated to compare the obtained results with the previous ones. Further, a parametric study is introduced to investigate the influence of crack locations, crack severity and the nonlocal scale parameter on the obtained results. The obtained results recorded that frequency values decrease with the increasing of both of crack severity and the nonlocal scale parameter. The results of the proposed scheme may be applied for structural health monitoring.

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“…The local and nonlocal solutions were evaluated for wave velocity. Sourki and Hoseini (2016) developed modified couple stress theory to an Euler–Bernoulli beam for vibration analysis of a cracked microbeam. The cracked beam was modeled by dividing the beam into two segments connected by a rotational spring located at the cracked section.…”

Section: Introductionmentioning

confidence: 99%

Size-dependent electro-elastic analysis of a sandwich microbeam based on higher-order sinusoidal shear deformation theory and strain gradient theory

Arefi

Zenkour

2017

Journal of Intelligent Material Systems and Structures

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The governing equations of bending analysis of a sandwich microbeam are derived in this article. The sandwich microbeam includes an elastic micro-core and two piezoelectric micro face-sheets. The microbeam is subjected to transverse loads and two-dimensional electric potential. Higher-order sinusoidal shear deformation beam theory is used for description of displacement field. To account for size dependency in governing equations of bending, strain gradient theory is used to mention higher-order stress and strains. An analytical approach for simply supported sandwich microbeam with short-circuited electric potential is proposed. The numerical results indicate that various types of parameters such as foundation, material and loads parameters have significant effect on the bending results. Comparison of valid references is performed to validate our numerical results. The numerical results indicate that maximum displacement and electric potential are approximately insensitive to applied voltage unlike to beam rotation and beam higher-order rotation of sandwich microbeam that are changed with applied voltage.

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Free vibration analysis of size-dependent cracked microbeam based on the modified couple stress theory

Cited by 40 publications

References 44 publications

Thermo-electro-mechanical vibration analysis of size-dependent nanobeam resting on elastic medium under axial preload in presence of surface effect

Thermo-electro-mechanical vibration analysis of size-dependent nanobeam resting on elastic medium under axial preload in presence of surface effect

Vibrations Analysis of Cracked Nanobeams Using Quadrature Technique

Size-dependent electro-elastic analysis of a sandwich microbeam based on higher-order sinusoidal shear deformation theory and strain gradient theory

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