Nonlocal integral approach to the dynamical response of nanobeams

Eptaimeros, K.G.; Koutsoumaris, C. Chr.; Tsamasphyros, G.

doi:10.1016/j.ijmecsci.2016.06.013

Cited by 86 publications

(28 citation statements)

References 63 publications

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“…In this respect, several papers have been recently published using the two-phase theory to study static bending [43,44] and buckling [45] of Euler-Bernoulli nanobeams. The bending vibration of Euler-Bernoulli nanobeams has been also studied using the Finite Element (F E) approach [46]. We refer to the recent paper by Fernández-Sáez and Zaera [47] for an analytical study of the free axial and bending vibration of a uniform beam modelled within the two-phase nonlocal elasticity theory.…”

Section: The Nonlocal Continuum Mechanics Theories Initiated Bymentioning

confidence: 99%

Mass detection in nanobeams from bending resonant frequency shifts

Dilena

Dell’Oste

Fernández-Sáez

et al. 2019

Mechanical Systems and Signal Processing

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Nanobeams are frequently used as vibration based-sensors to detect mass changes caused, for instance, by attachment of foreign atoms/molecules or chemical/molecular absorption. This paper deals with the bending vibration of a uniform nanobeam carrying a single point mass (direct problem) as well as the identification of the attached mass (inverse problem). The nanobeam is described using the modified strain energy theory adapted to the Euler-Bernoulli beam model, and the natural vibration frequencies have been obtained. Under the assumption of small intensity of the concentrated mass, a solution of the inverse problem based on the measurement of the mass-induced shifts in the first two eigenfrequencies is proposed. Both the cases of simply supported and cantilever end conditions are discussed in detail. The theoretical method is verified by numerical simulation and numerical tests agree well with analytical results.

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Section: The Nonlocal Continuum Mechanics Theories Initiated Bymentioning

confidence: 99%

Mass detection in nanobeams from bending resonant frequency shifts

Dilena

Dell’Oste

Fernández-Sáez

et al. 2019

Mechanical Systems and Signal Processing

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“…Hence, one needs to split the boundary conditions and assign the two main conditions for y m0 , with the additional ones used to determine y mk for k ≥ 1 and the constants a k1 , a k2 appearing in (42). To this purpose, we substitute (36), (37) and (42) into the boundary conditions and, taking into account the asymptotic estimates (40), impose the following conditions:…”

Section: Asymptotic Solutions (Tpnm)mentioning

confidence: 99%

Free vibrations of nonlocally elastic rods

Mikhasev

Avdeichik

Приказчиков

2018

Mathematics and Mechanics of Solids

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Several of the Eringen's nonlocal stress models, including two-phase and purely nonlocal integral models, along with the simplified differential model, are studied in case of free longitudinal vibrations of a nanorod, for various types of boundary conditions. Assuming the exponential attenuation kernel in the nonlocal integral models, the integro-differential equation corresponding to the two-phase nonlocal model is reduced to a fourth order differential equation with additional boundary conditions taking into account nonlocal effects in the neighbourhood of the rod ends. Exact analytical and asymptotic solutions of boundary-value problems are constructed. Formulas for natural frequencies and associated modes found in the framework of the purely nonlocal model and its "equivalent" differential analogue are also compared. A detailed analysis of solutions suggests that the purely nonlocal and differential models lead to ill-posed problems.

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“…A large number of studies related to vibration characteristics of intact and cracked FG uniform beams are available [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Furthermore the studies have been extended in mechanical analysis of small-sized structures [23][24][25][26][27][28][29][30][31]. Studies on non-uniform FG beams can also be found in literature [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47], while studies on non-uniform FG beams with an imperfection are scarce.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of cracked functionally graded non-uniform beams

Shabani

Cunedioĝlu

2020

Mater. Res. Express

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This paper presents the free vibration analysis of an edge cracked non-uniform symmetric beam made of functionally graded material. The Timoshenko beam theory is used for the finite element analysis of the multi-layered sandwich beam and the cantilever beam is modeled by 50 layers of material. The material properties vary continuously along the thickness direction according to the exponential and power laws. A MATLAB code is used to find the natural frequencies of two types of non-uniform beams, having a constant height but an exponential or linear width variation along the length of the beam. The natural frequencies of the beam are verified with ANSYS software as well as with available literature and good agreement is found. In the study, the effects of different parameters such as crack location, crack depth, power-law index, geometric index and taper ratio on natural frequencies are analyzed in detail.

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Nonlocal integral approach to the dynamical response of nanobeams

Cited by 86 publications

References 63 publications

Mass detection in nanobeams from bending resonant frequency shifts

Mass detection in nanobeams from bending resonant frequency shifts

Free vibrations of nonlocally elastic rods

Free vibration analysis of cracked functionally graded non-uniform beams

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