Nonlocal effects in modal analysis of forced responses with single carbon nanotubes

Claeyssen, Julio Cesar Ruiz; Tsukazan, Teresa; Coppeti, Rosemaira D.

doi:10.1016/j.ymssp.2013.01.014

Cited by 17 publications

(5 citation statements)

References 46 publications

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“…However, this is not the case when dealing with non-classical boundary conditions or with beams made of new materials that are used to improve and optimize its properties and subjected to internal and external damping [16][17][18].…”

Section: Waves With Exponential Profilementioning

confidence: 99%

Matrix basis for plane and modal waves in a Timoshenko beam

2016

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Plane waves and modal waves of the Timoshenko beam model are characterized in closed form by introducing robust matrix basis that behave according to the nature of frequency and wave or modal numbers. These new characterizations are given in terms of a finite number of coupling matrices and closed form generating scalar functions. Through Liouville’s technique, these latter are well behaved at critical or static situations. Eigenanalysis is formulated for exponential and modal waves. Modal waves are superposition of four plane waves, but there are plane waves that cannot be modal waves. Reflected and transmitted waves at an interface point are formulated in matrix terms, regardless of having a conservative or a dissipative situation. The matrix representation of modal waves is used in a crack problem for determining the reflected and transmitted matrices. Their euclidean norms are seen to be dominated by certain components at low and high frequencies. The matrix basis technique is also used with a non-local Timoshenko model and with the wave interaction with a boundary. The matrix basis allows to characterize reflected and transmitted waves in spectral and non-spectral form.

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Section: Waves With Exponential Profilementioning

confidence: 99%

Matrix basis for plane and modal waves in a Timoshenko beam

2016

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“…The Navier-type solution method was used for simply supported nanoplates where forced vibration response was obtained in the analytical form. Claeyssen et al [2013] explored the forced response of a single carbon nanotube modeled via the nonlocal Euler-Bernoulli beam theory. Forced responses were determined for different external loads and boundary conditions using the Galerkin method.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal forced vibration of a double single-walled carbon nanotube system under the influence of an axial magnetic field

Stamenković

Karličić

Janevski

et al. 2016

J. Mech. Mater. Struct.

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The influence of various physical phenomena on the dynamic behavior of nanostructures has been attracting more and more attention of the scientific community. This paper discusses the effects of the axial magnetic field on the externally excited double single-walled carbon nanotube (DSWCNT) coupled by a Winkler elastic medium. It is assumed that both carbon nanotubes are identical and under the influence of compressive axial load with simply supported ends. Based on the Eringen nonlocal elasticity and Euler-Bernoulli beam theory, the system of two coupled nonhomogeneous partial differential equations of motion is derived, where the effects of the Lorentz magnetic force are obtained via a Maxwell relation. The dynamic responses of the DSWCNT system for four different cases of external transversal load are considered. The closed form solutions for the transversal displacements are obtained by applying the Bernoulli-Fourier method of particular integrals on the system of nonhomogeneous partial differential equations of motion. Also, analytical expressions of the amplitude ratio for forced vibration are derived and then validated with existing results. Moreover, the obtained analytical results for fundamental natural frequency are validated with results obtained by molecular dynamics (MD) simulation and show fine agreements. The effects of compressive axial load, nonlocal parameter, axial magnetic field and stiffness coefficient of the elastic medium on the forced dynamic behavior of DSWCNT are considered through numerical examples. From numerical results we can conclude that the dynamical behavior of DSWCNT is greatly influenced by the magnetic field and nonlocal parameter. Furthermore, by selecting the intensity of the axial magnetic field in a certain range, it is possible to adjust the stiffness of the system without changing the material and geometric parameters. This effect implies a change in the natural frequencies of the system.

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“…For example, if the nanotubes are to be used as nano mechanical resonators, the oscillation frequency is a key property of the resonator. Moreover, the e ective elastic modulus of a nanotube may be indirectly determined from its measured natural frequencies or mode shapes if a su ciently accurate theoretical model is used [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear free and forced vibrations of curved single walled carbon nanotube on a Pasternak elastic foundation

2016

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Based on elastic continuum mechanics, the nonlinear free and forced vibrations of an embedded single-walled carbon nanotube with waviness along its axis were analyzed. The single-walled carbon nanotube was embedded in a Pasternak elastic foundation. Two analytical approaches were utilized to obtain the frequency-amplitude relationship of the free vibrational model, and one other analytical approach was used to obtain the forced vibrations of the curved single-walled carbon nanotube on the Pasternak elastic foundation. Subsequently, a parametric study was performed to study the importance of di erent parameters, such as the amplitude of oscillation and the curvature radius, on the nonlinear behavior of the system. Also, a numerical simulation was carried out to obtain the results and investigate the accuracy of the analytical solution methods. Comparison of the results obtained by the proposed methods shows excellent agreement with those obtained by the numerical solution.

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Nonlocal effects in modal analysis of forced responses with single carbon nanotubes

Cited by 17 publications

References 46 publications

Matrix basis for plane and modal waves in a Timoshenko beam

Matrix basis for plane and modal waves in a Timoshenko beam

Nonlocal forced vibration of a double single-walled carbon nanotube system under the influence of an axial magnetic field

Nonlinear free and forced vibrations of curved single walled carbon nanotube on a Pasternak elastic foundation

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