Free and forced vibrations of nanowires on elastic substrates

Li, Yingxu; Li, Xiangyu; Müller, Ralf

doi:10.1016/j.ijmecsci.2018.01.039

Cited by 12 publications

(10 citation statements)

References 33 publications

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“…The deformations of bulk materials are described using the Timoshenko beam model. The displacement components in the x − and z − directions read (Su et al, 2018)…”

Section: Basic Equationsmentioning

confidence: 99%

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Steady-state forced vibrations of magneto-electro-elastic Timoshenko nanobeams

Wang

et al. 2022

Journal of Intelligent Material Systems and Structures

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This paper aims to investigate forced vibrations of Timoshenko nanobeam, which is under axially loaded. The material is assumed to be magneto-electro-elastic coupling and surface effect is considered. The governing equations and the corresponding boundary conditions are derived, with the Hamilton principle. For steady-state forced vibrations, the variable separation and the Laplace transform methods are employed to obtain the Green’s function, for three typical kinds of beams, namely Hinged-Hinged, Clamped-Clamped, and Clamped-Free. Numerical examples are performed to check the validity of the present solutions and to evaluate the influence of magneto-electric coupling and surface effect on the forced vibration of the beams.

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“…The deformations of bulk materials are described using the Timoshenko beam model. The displacement components in the x − and z − directions read (Su et al, 2018)…”

Section: Basic Equationsmentioning

confidence: 99%

“…For the surface layer-bulk material nanobeam system, the kinetic energy includes the kinetic energy of the bulk material (denoted by T 1 ) and that of the surface layer (denoted by T 2 ). Within the time interval [0,T], the first-order variation of the total kinetic energy reads (Su et al, 2018)…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Steady-state forced vibrations of magneto-electro-elastic Timoshenko nanobeams

Wang

et al. 2022

Journal of Intelligent Material Systems and Structures

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“…The Winkler model as an external force makes a thermodynamic work calculated as [48][49] (14) where kw demonstrates the value of springiness in the foundation.…”

Section: The External Forcementioning

confidence: 99%

“…The governing equations were derived regarding a surface elasticity and solved respecting to various boundary conditions. Su et al [14] addressed small scale effects for considering mechanically transverse response of several nanostructures with one-dimension like nanoropes and nanowires. They presented the strain gradient model to examine small size influences and obtained constitutive equations on the basis of classical beam theory.…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

Vibro-Electrical Behavior of a Viscoelastic Piezo-Nanowire in an Elastic Substrate Considering Stress Nonlocality and Microstructural Size-Dependent Effects

Malikan

2019

International Journal of Engineering and Applied Sciences

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This research deals with dynamic response of a Polymer/BaTiO3 nanowire including viscosity influences. The wire is also impressed by a longitudinal electric field. Hamilton's principle, Lagrangian strains and a refined higher-order beam theory are combined together in order to derive equations of motion. By combining nonlocality and small size effects of a unique model into the derived equations, the couple relations which describe nanosize behavior in a small scale are presented. By employing an analytical approach, the fundamental natural frequencies are calculated numerically. The important results display that the effect of internal viscosity and nonlocality whenever the nanowire is very large are pointless.

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“…Zhao et al (2016) provided the explicit expressions of the steady-state responses of a cracked Euler–Bernoulli beam excited by a harmonic force and investigated the influences of crack geometry on the mechanical behavior of beam. Su et al (2018) derived the exact solutions for the free and forced vibrations of nanowires on elastic substrates.…”

Section: Introductionmentioning

confidence: 99%

Closed-form solutions for vibrations of a magneto-electro-elastic beam with variable cross section by means of Green’s functions

Zhang

Chen

Yang

et al. 2018

Journal of Intelligent Material Systems and Structures

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In this article, closed-form solutions are obtained for vibrations of a magneto-electro-elastic beam with variable cross section. Based on Timoshenko beam assumptions, governing equation for the non-uniform beam with exponentially varying width is obtained. Laplace transform approach applied to the governing equation results in the corresponding Green’s functions for the beams with various boundary conditions. The equations, which are solved to obtain Green’s functions, are degenerated for the analyses of the characters of free vibration. For free vibrations of the beams under different mechanical boundary conditions, the effects of the non-uniformly cross-sectional parameters and magneto-electric boundary conditions on the dynamic characters are studied. In addition, the magneto-electric potential modal variables’ distributions through the thickness are presented. In the discussions of forced vibration, two points in the beam are selected to investigate frequency responses in terms of displacement and magneto-electric potential. Moreover, the influences of excitation frequency and cross-sectional parameter on through-the-thickness distributions of electric potentials are investigated.

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Free and forced vibrations of nanowires on elastic substrates

Cited by 12 publications

References 33 publications

Steady-state forced vibrations of magneto-electro-elastic Timoshenko nanobeams

Steady-state forced vibrations of magneto-electro-elastic Timoshenko nanobeams

Vibro-Electrical Behavior of a Viscoelastic Piezo-Nanowire in an Elastic Substrate Considering Stress Nonlocality and Microstructural Size-Dependent Effects

Closed-form solutions for vibrations of a magneto-electro-elastic beam with variable cross section by means of Green’s functions

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