RADIAL VIBRATION CHARACTERISTICS OF SPHERICAL NANOPARTICLES IMMERSED IN FLUID MEDIUM

2013 ◽  
Vol 27 (26) ◽  
pp. 1350186 ◽  
Author(s):  
S. AHMAD FAZELZADEH ◽  
ESMAEAL GHAVANLOO
Keyword(s):  
Bessel Functions ◽  
Nonlocal Elasticity Theory ◽  
Frequency Equation ◽  
Small Scale ◽  
Complex Frequency ◽  
Radial Vibration ◽  
Radial Vibrations ◽  
Fluid Medium ◽  
Nanoparticle Radius ◽  
New Formulation

The vibrational properties of nanoparticles coupled with surrounding media are of recent interest. These nanostructures can be modeled as nanoscale spherical solids. In this paper, new formulation based on the nonlocal elasticity theory is proposed to investigate radial vibrations of the nanoparticles immersed in fluid medium. The nanoparticles with size ranging from 1 nm to 10 nm are discussed. The nanoparticles are considered elastic, homogeneous and anisotropic. Along the contact surface between the nanoparticle and the fluid, the compatibility requirement is applied and the Bessel functions are used to obtain the complex frequency equation. Numerical results are evaluated, and their comparisons are performed to confirm the validity and accuracy of the proposed method. Furthermore, the model is used to elucidate the effect of small scale on the vibration of several nanoparticles. Our results show that the small scale is essential for the radial vibration of nanoparticles when the nanoparticle radius is smaller than 2 nm.

scholarly journals Flutter and Divergence Instability of Axially-Moving Nanoplates Resting on a Viscoelastic Foundation

2019 ◽  
Vol 9 (6) ◽  
pp. 1097 ◽  
Author(s):  
Jingbo Duan ◽  
Dapeng Zhang ◽  
Wenjie Wang
Keyword(s):  
Graphene Nanosheets ◽  
Viscoelastic Behavior ◽  
Nonlocal Elasticity Theory ◽  
Small Scale ◽  
Complex Frequency ◽  
Viscoelastic Foundation ◽  
Viscoelastic Parameters ◽  
Axial Forces ◽  
Divergence Instability ◽  
Axially Moving

Moving nanosystems often rest on a medium exhibiting viscoelastic behavior in engineering applications. The moving velocity and viscoelastic parameters of the medium usually have an interacting impact on the mechanical properties of nanostructures. This paper investigates the dynamic stability of an axially-moving nanoplate resting on a viscoelastic foundation based on the nonlocal elasticity theory. Firstly, the governing partial equations subject to appropriate boundary conditions are derived through utilizing the Hamilton’s principle with the axial velocity, viscoelastic foundation, nonlocal effect and biaxial loadings taken into consideration. Subsequently, the characteristic equation describing the dynamic characteristics is obtained by employing the Galerkin strip distributed transfer function method. Then, complex frequency curves for the nanoplate are displayed graphically and the effects of viscoelastic foundation parameters, small-scale parameters and axial forces on divergence instability and coupled-mode flutter are analyzed, which show that these parameters play a crucial role in affecting nanostructural instability. The presented results benefit the designation of axially-moving graphene nanosheets or other plate-like nanostructures resting on a viscoelastic foundation.

scholarly journals Double mode model of size-dependent chaotic vibrations of nanoplates based on the nonlocal elasticity theory

2021 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Grzegorz Kudra ◽  
Olga Mazur
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Scale Effects ◽  
Plate Theory ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Phase Portraits ◽  
Small Scale ◽  
Governing System ◽  
Account Due

AbstractIn this paper vibrations of the isotropic micro/nanoplates subjected to transverse and in-plane excitation are investigated. The governing equations of the problem are based on the von Kármán plate theory and Kirchhoff–Love hypothesis. The small-size effect is taken into account due to the nonlocal elasticity theory. The formulation of the problem is mixed and employs the Airy stress function. The two-mode approximation of the deflection and application of the Bubnov–Galerkin method reduces the governing system of equations to the system of ordinary differential equations. Varying the load parameters and the nonlocal parameter, the bifurcation analysis is performed. The bifurcations diagrams, the maximum Lyapunov exponents, phase portraits as well as Poincare maps are constructed based on the numerical simulations. It is shown that for some excitation conditions the chaotic motion may occur in the system. Also, the small-scale effects on the character of vibrating regimes are illustrated and discussed.

scholarly journals Nonlinear magneto-thermo-elastic vibration of mass sensor armchair carbon nanotube resting on an elastic substrate

2020 ◽  
Vol 7 (1) ◽  
pp. 153-165
Author(s):  
Rajendran Selvamani ◽  
M. Mahaveer Sree Jayan ◽  
Rossana Dimitri ◽  
Francesco Tornabene ◽  
Farzad Ebrahimi
Keyword(s):  
Carbon Nanotube ◽  
Mechanical Response ◽  
Scale Effects ◽  
Nonlocal Elasticity Theory ◽  
Wave Dispersion ◽  
Elastic Vibration ◽  
Ultrasonic Waves ◽  
Small Scale ◽  
Dimensionless Frequency ◽  
Mass Sensors

AbstractThe present paper aims at studying the nonlinear ultrasonic waves in a magneto-thermo-elastic armchair single-walled (SW) carbon nanotube (CNT) with mass sensors resting on a polymer substrate. The analytical formulation accounts for small scale effects based on the Eringen’s nonlocal elasticity theory. The mathematical model and its differential equations are solved theoretically in terms of dimensionless frequencies while assuming a nonlinear Winkler-Pasternak-type foundation. The solution is obtained by means of ultrasonic wave dispersion relations. A parametric work is carried out to check for the effect of the nonlocal scaling parameter, together with the magneto-mechanical loadings, the foundation parameters, the attached mass, boundary conditions and geometries, on the dimensionless frequency of nanotubes. The sensitivity of the mechanical response of nanotubes investigated herein, could be of great interest for design purposes in nano-engineering systems and devices.

scholarly journals Parametric vibrations of graphene sheets based on the double mode model and the nonlocal elasticity theory

2021 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Grzegorz Kudra ◽  
Olga Mazur
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Nonlinear Oscillations ◽  
Scale Effects ◽  
Equations Of Motion ◽  
Nonlocal Elasticity Theory ◽  
Small Scale ◽  
Largest Lyapunov Exponent ◽  
Graphene Sheets ◽  
Parametric Vibrations

AbstractParametric vibrations of the single-layered graphene sheet (SLGS) are studied in the presented work. The equations of motion govern geometrically nonlinear oscillations. The appearance of small effects is analysed due to the application of the nonlocal elasticity theory. The approach is developed for rectangular simply supported small-scale plate and it employs the Bubnov–Galerkin method with a double mode model, which reduces the problem to investigation of the system of the second-order ordinary differential equations (ODEs). The dynamic behaviour of the micro/nanoplate with varying excitation parameter is analysed to determine the chaotic regimes. As well the influence of small-scale effects to change the nature of vibrations is studied. The bifurcation diagrams, phase plots, Poincaré sections and the largest Lyapunov exponent are constructed and analysed. It is established that the use of nonlocal equations in the dynamic analysis of graphene sheets leads to a significant alteration in the character of oscillations, including the appearance of chaotic attractors.

Effects of DNA Encapsulation on Buckling Instability of Carbon Nanotube Based on Nonlocal Elasticity Theory

2014 ◽  
Author(s):  
Jacob Rafati ◽  
Mohsen Asghari ◽  
Sachin Goyal
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Scale Effects ◽  
Nonlocal Elasticity Theory ◽  
Van Der Waals Interactions ◽  
Small Scale ◽  
Elastic Rod ◽  
Nano Structure ◽  
Buckling Instability ◽  
Nano Structures

Carbon nanotubes (CNTs) are capable to absorb and encapsulate some molecules to create new hybrid nano-structures providing a variety of functionally useful properties. CNTs functionalized by encapsulaitng single-stranded deoxy-ribonucleic acid (ssDNA) promise great potentials for applications in nanotechnology and nano-biotechnology. In this paper, buckling instability of ssDNA@CNT i.e. hybrid nano-structure composed of ssDNA encapsulated inside CNT has been investigated using the nonlocal elasticity theory. The nonlocal elasticity theory is capable to capture the small scale effects due to the discontinuity of nano-structures at atomic scales. The nonlocal elastic rod and shell equations are derived for modeling ssDNA and CNT respectively. Providing numerical examples, it is predicted that, ssDNA@(10,10) CNT is more resistant than the pristine (10,10) CNT against the buckling instability under radial pressure due to the inter-atomic van der Waals interactions between DNA and CNT. Furthermore, nonlocal elasticity theory predicts lower critical buckling pressure than does the local elasticity theory.

Micro Cantilever Beam Theory for Transverse Dynamics Using a Continuum Mechanics Model

2011 ◽  
Vol 415-417 ◽  
pp. 760-763
Author(s):  
Cheng Li ◽  
Wei Guo Huang ◽  
Lin Quan Yao
Keyword(s):  
Scale Parameter ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Small Scale ◽  
Beam Model ◽  
Cantilever Beams ◽  
Mechanics Model ◽  
Axial Tension ◽  
Vibrational Characteristics ◽  
Micro Cantilever

The vibrational characteristics of cantilever beams with initial axial tension were studied using a nonlocal continuum Euler-Bernoulli beam model. Small size effects are essential to nanotechnology and it can not be ignored in micro or nano scale. Nonlocal elasticity theory has been proved to work well in nanomechanics and it is considered into the governing equation which can be transformed into a fourth-order ordinary differential equation together with a dispersion relation. Boundary conditions are applied so as to determine the analytical solutions of vibrational mode shape and transverse deformation through a numerical method. Relations between natural frequency and the small scale parameter are obtained, including the fundamental and the second order frequencies. It is found that both the small scale parameter and dimensionless initial axial tension play remarkable roles in dynamic behaviors of micro cantilever beams and their effects are analyzed and discussed in detail.

A comparison of phase inversion and traveltime tomography for processing near-surface refraction traveltimes

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCB11-WCB24 ◽  
Author(s):  
Karl J. Ellefsen
Keyword(s):  
Standard Deviation ◽  
Phase Inversion ◽  
Small Scale ◽  
Complex Frequency ◽  
S Wave ◽  
Near Surface ◽  
Residual Standard Deviation ◽  
Wave Refraction ◽  
Traveltime Tomography ◽  
The Difference

With phase inversion, one can estimate subsurface velocities using the phases of first-arriving waves, which are the frequency-domain equivalents of the traveltimes. Phase inversion is modified to make it suitable for processing traveltimes from near-surface refraction surveys. The modifications include parameterizing the model, correcting the observed phases, and selecting the complex frequency. This modified phase inversion is compared to traveltime tomography. For two comparisons using computer-simulated traveltimes, the difference between the estimated and correct models, the residual mean, and the residual standard deviation are smaller for the phase inversion than they are for the traveltime tomography. For a comparison using field data from an S-wave refraction survey, both methods estimate models that are consistent with the known geology. Nonetheless, the phase-inversion model includes small-scale features in the bedrock that are geologically plausible; the residual mean and the residual standard deviation are smaller for the phase inversion than they are for the traveltime tomography.

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