Thermal and magnetic effects on the vibration of a cracked nanobeam embedded in an elastic medium

Karličić, Danilo; Jovanović, Dragan; Kozić, Predrag; Cajić, Milan

doi:10.2140/jomms.2015.10.43

Cited by 18 publications

(9 citation statements)

References 55 publications

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“…Karlicić et al [45] studied vibration of a cracked nanobeam in an elastic Winklertype medium with an account of the effects of longitudinal magnetic field and temperature change. The considerations were based on the Euler-Bernoulli beam theory and the nonlocal elasticity as well as on the Maxwell classical equation.…”

Section: Magnetic Fieldmentioning

confidence: 99%

Nanostructural Members in Various Fields: A Literature Review

Awrejcewicz

Krysko

Zhigalov

et al. 2020

Advanced Structured Materials

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Guo and Zhao [1] developed a theoretical background aimed at a study of the sizedependent bending elastic properties of nanobeams with surface effects.Lim and Wang [2] employed the exact variational nonlocal stress modelling with asymptotic higher order strain gradients for nanobeams.Wang et al.[3] analysed vibrations of initially stressed micro-and nanobeams. Challamel and Wang [4] solved a paradox associated with the small-scale effect for a nonlocal cantilever beam. Lim et al. [5] illustrated the stiffness strengthening effects of nonlocal stress and axial tension on free vibration of cantilever nanobeams.Aydogdu [6] proposed a general nonlocal beam theory to analyse bending, buckling and free vibration of nanobeams based on the classical Euler-Bernoulli, Timoshenko, Reddy and Levinson theories.Zhang et al.[7] analysed bending and vibration of hybrid nonlocal beams. Murmu and Adhikari [8] studied nonlocal transverse vibration of doublenanobeam systems within the framework of Eringen's nonlocal elasticity theory. The following results were reported: nonlocal natural frequencies are smaller than the corresponding local frequencies, small-scale effects are higher with increasing values of nonlocal parameter, whereas increase of stiffness of coupling springs reduces the nonlocal effects.Li et al.[9] derived a sixth-order PDE governing dynamics of simply supported nanobeams under initial axial force based on nonlocal elasticity theory. The effects of the nonlocal nanoscale and dimensionless axial force on the first twice mode frequencies were presented and discussed.Hosseini-Hashemi et al.[10] investigated the surface effects (elasticity, stress and density) of free vibrations of the Euler-Bernoulli and Timoshenko nanobeams employing the nonlocal elasticity theory. The governing PDEs were studied with regard to three different boundary conditions, i.e. simple-simple, clamped-simple and clamped-clamped. In particular, it was shown that rotary inertia and shear deformation had more effects on the surface than the nonlocal parameter.Simsek [11] proposed a novel size-dependent beam model for nonlinear free vibration of a functionally graded nanobeam by matching the nonlocal strain gradient theory and the Euler-Bernoulli beam theory with an account of the von Kármán's nonlinearity. Hamilton's principle yielded the governing PDEs and boundary conditions. A few case studies were supplemented pointing out the important features of the strain gradient length scale, the nonlocal parameters, vibration amplitude and various material compositions.Hashemi and Khaniki [12] studied free vibrations of a Timoshenko nanobeam with variable cross section in frame of the nonlocal elasticity theory. The smallscale effects were modelled by Eringen's nonlocal elasticity theory. They derived an analytical solution with regard to the Timoshenko nanobeams for three different

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Section: Magnetic Fieldmentioning

confidence: 99%

Nanostructural Members in Various Fields: A Literature Review

Awrejcewicz

Krysko

Zhigalov

et al. 2020

Advanced Structured Materials

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“…Based on the transfer matrix method, Ma and Chen [10] calculated the natural frequencies of the variable cross-section beam with multiple cracks under different temperatures, and the accuracy of this method was verified by the finite element method. Considering the influence of the temperature variation, Karličić et al [11] developed analytical model to investigate the free vibration of the cracked nanoscale beams. Literatures above discussed the influence of the high temperature on the natural frequency of the cracked beam, without consideration of the temperature load generated by the temperature variation.…”

Section: Shock and Vibrationmentioning

confidence: 99%

Modal Analysis of a Simply Supported Steel Beam with Cracks under Temperature Load

Yan¹,

Chen²,

Yang³

2017

Shock and Vibration

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Based on the transfer matrix method, an analytical method is proposed to conduct the modal analysis of the simply supported steel beam with multiple transverse open cracks under different temperatures. The open cracks are replaced with torsion springs without mass, and local flexibility caused by each crack can be derived; the temperature module is introduced by the mechanical properties variation of the structural material, and the temperature load is caused by the temperature variation, which can be transformed to the axial force on the cross-section. The transfer matrix of the whole beam with the temperature and geometric parameters of cracks can be obtained. According to boundary conditions of the simply supported beam, natural frequencies of the beam can be calculated, which are compared with the finite element results. Results indicate that the analytical method proposed has a high accuracy; the natural frequencies of the simply supported steel beam are mostly affected by the temperature load, which cannot be ignored.

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“…12,13,20,24,27,31,33,35,[39][40][41] In Hedrih (Stevanovi c) and Simonovi c [42][43][44][45][46][47][48][49][50][51] published in period in 2008-2013, and late published Simonovi c [52][53][54] as well as in monographs published by Kluwer and Springer and other contributions of author and coauthors to linear and nonlinear dynamics of deformable bodies (rods, beams, plates, moving strips) can be classified as systems of coupled subsystems and deformable bodies. [55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73] After the first published scientific papers by Hedrih (Stevanovi c) K.R. in the newly opened field of coupled deformable bodies and the dynamics of hybrid systems of complex structures, Hedrih (Stevanovi c) K.R.…”

Section: Introductionmentioning

confidence: 99%

Linear and nonlinear dynamics of hybrid systems

Hedrih

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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Discrete continuum method for investigation of linear and nonlinear dynamics of hybrid systems containing coupled multi deformable bodies is presented. By use coupled rods, beams, strings, plates and membranes by discrete continuum mass less layers as well as layers with translator and rotator inertia properties into series of hybrid system dynamics are investigated and phenomenological mappings in dynamics of these different real systems are identified. Expressions of generalized forces of subsystem interactions in hybrid system are presented by component mechanical energies and functions of energy dissipations. A model of dynamical dislocations with inertia properties in plate is presented. Transfer energy between subsystems is investigated. Constitutive relation of standard elements of discrete continuum coupling layers with translator and rolling inertia properties, nonlinear elastic and fractional order properties are presented. Interaction between two coupled linear and nonlinear system, each with one degree of freedom as well as dynamics of discrete no homogeneous chain are considered in the light of mathematical analogy for obtaining eigen time functions of solutions of component deformable body displacements in hybrid system dynamics. For pointing out the major contributions outlined in the manuscript it is necessary to add: The manuscript contains reviews on results obtained of a few scientific problems of nonlinear dynamics, namely, for stochastic stability of vibration modes of a parametrically excited sandwich beam, transversal vibrations of axially moving double belt system, multi deformable bodies coupled by standard light fractional type discrete continuum layers. New model of dynamical dislocation in continuum is proposed and analyzed Series of the original results of author’s doctorates supervised is listed.

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Thermal and magnetic effects on the vibration of a cracked nanobeam embedded in an elastic medium

Cited by 18 publications

References 55 publications

Nanostructural Members in Various Fields: A Literature Review

Nanostructural Members in Various Fields: A Literature Review

Modal Analysis of a Simply Supported Steel Beam with Cracks under Temperature Load

Linear and nonlinear dynamics of hybrid systems

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