Natural vibrations in a system of nanotubes

Minimization of Shear Energy in Two Dimensional Continua with Two Orthogonal Families of Inextensible Fibers: The Case of Standard Bias Extension Test

“…The interest of results presented here could go far beyond the context considered up to now: (i) electrospinning (see, e.g., [50]) opens unexpected possibilities to the constructions of fabrics whose lower length-scale could go up to the nanometers (the most recent formulations of the theory of nearly-inextensible nano-fibers and nano-beams can be found in [12,24,25,75]; (ii) the most recent investigations have shown that many biological tissues incorporate nearly-inextensible fibers and consequently many models have been presented in different papers to account for their presence [28-30, 33, 34, 76]. Therefore, the insight gained in the present study may produce some impact in other fields of application: (i) biological systems have been optimized by natural selection to resist externally applied loads with a minimum expense of material; hence they have the same mechanical properties as composite reinforcements, (ii) reinforcements fabrics are more and more often woven at nanoscale; while the inextensibility constraint still plays a relevant role, it is not clear what are the limits of applicability of classical mechanics in this case (see, e.g., [12]), (iii) the microstructure of fabrics does allow for instability phenomena at microlevel which may initiate related instabilities at macro-level.…”

A new method for evaluating the natural frequency in radial breathing like mode vibration of double‐walled carbon nanotubes

“…But their relationship with the tube radii is still an open question, which is the most important for understanding the experimental RBLMs. Eremeyev et al studied free vibrations of some elastic structures and compared the spectrum of eigenfrequencies of these structures with the spectra of nanoobject and substrate [18,19]. Ghavanloo and Fazelzadeh studied the RBLMs of DWCNTs with arbitrary chirality are investigated by a simple analytical model [12].…”

Mechanically stable nanostructures with desirable characteristic field enhancement factors: a response from scale invariance in electrostatics

“…In fact, the issue of mechanical stability requires a solution for the degradation and failure of nanostructures that occurs during field electron emission at or near the substrate emitter contact [2] and for the self-mechanical oscillations that occur during field electron emission measurements [3,4] or from electrostatic interactions [5]. In particular, a method to study the self-oscillations of a nanostructure mounted on a macroscopic frame requires using a laser beam to excite the sample; subsequently, a second laser beam is then used to register the amplitude of vibrations at a certain point from the object [6].Applications of these nanostructures mounted on tip devices include carbon nanotubes (CNTs) mounted on a support tip, which can be used as an electron source in a high-resolution electron beam. The latter acquires properties such as a stable emitted current and high brightness [7].…”