E. A. Ivanova

Method of Determining the Eigenfrequencies of an Ordered System of Nanoobjects

A method is proposed to determine the eigenfrequencies of nanostructures (nanotubes and nanocrystals) by measuring the eigenfrequencies of a “large system” that comprises an array of vertically oriented similar nanotubes or nanocrystals equidistantly grown on a substrate. It is shown that the eigenfrequencies of a single nanoobject can be derived from the eigenfrequency spectra of the large (array-substrate) system and of the substrate. In other words, using experimental data for large systems, one can determine the eigenfrequencies of single nanoobjects, which are difficult to determine otherwise. By way of example, the eigenfrequencies of an array of zinc oxide micro-or nanocrystals on a sapphire substrate are calculated.

On the determination of eigenfrequencies for nanometer-size objects

At present, the problem of the experimental determination of mechanical characteristics for nanometersize objects (nanoobjects) is urgent. One of the most efficient methods for the determination of elastic-moduli is based on the measurement of the eigenfrequencies of objects under study. However, the measurement of nanoobject frequencies, in particular, on the basis of optical methods turns out to be problematic [1]. The main, though not exclusive, limitation upon the application of optical methods is the fact that the laser-beam cross section is not a point ...

Inclusion of the Moment Interaction in the Calculation of the Flexural Rigidity of Nanostructures

In recent years, in addition to the investigation of the electronic and optical properties of nanostructures [1], the study of their mechanical properties has become particularly important. Many works have been devoted to the production of nanotubes and investigation of their properties [2–8]. According to the data obtained in [4], nanotubes can retain their elastic properties under significant strains. The stress–strain state of nanotubes is usually calculated in the theory of elastic shells [9]. In this case, the elastic moduli are determined in discrete models, where only the force interaction between atoms forming a nanotube is taken into account. However, the existence of monolayer nanotubes [5–8] makes it necessary to consider also the moment interaction between atoms. Otherwise, the atomic layer forming the nanotube would have zero flexural rigidity, so that such a nanotube would be unstable.

The Spectrum of Natural Oscillations of an Array of Micro- or Nanospheres on an Elastic Substrate

EREMEYEV et al. elastic shells of thickness h and radius R are attached (Fig. 1). We assume that the shells are attached to the plate (substrate) at the points x= xk, y= yk (k= 1, 2,... n). The spherical shells are considered as membranes loaded by a uniform internal hydrostatic pressure p. In the equilibrium state, the force resultants acting on the shell surface is everywhere the same: N1= N2= N= pR/2. This N value is in fact the surface tension, and the whole membrane can be considered as a spherical shell of equal ...

Natural Vibrations of Nanotubes

431 Nanoobjects exhibit anomalous properties that are very attractive for applications and generally do not correlate with the properties of the macroscopic samples [1‐4]. For this reason, one of the key problems of nanomechanics is the determination of the mechanical and physical characteristics of nanoobjects. One of the most efficient methods for determining elastic moduli used in the mechanics of macroobjects is based on measurement of natural frequencies. A method for determining the natural frequencies of some nanostructures (nanotubes and nanocrystals) was proposed in [5, 6] on the basis of the measurement of natural frequencies of an “extended system” consisting of a highly oriented array (lattice) of identical nanotubes or nanocrystals, which are grown on a macroscopic substrate and are perpendicular to the substrate, and a single substrate. According to [5, 6], the spectrum of the natural frequencies of the large system can be separated into two components. One component of the system spectrum corresponds to the natural frequencies of single nanoobjects. The substrate remains almost static upon vibrations with these frequencies. The other component of the system spectrum is the spectrum of natural frequencies close to the natural frequencies of the substrate without nanoobjects. At these frequencies, the amplitude of the vibrations of the nanoobjects is much smaller than the amplitude of the substrate vibrations. Two modifications of the experimental procedure for determining the natural frequencies can be proposed in developing the method proposed in [5, 6]. Modification 1. Measure the natural frequencies of the nanotube lattice‐substrate or nanocrystal lattice‐ substrate. Measure the natural frequencies of the same substrate without nanoobjects. Compare the two spectra obtained. The frequencies in the system spectrum that have no correspondence among the frequencies in the substrate spectrum are the frequencies of the nanoobjects. Modification 2. Measure the natural frequencies of the system by detecting both the electromagnetic radiation of the nanoobjects, many of which are piezoelectric materials, and the substrate vibration amplitude. The resonant frequencies at which the substrate vibration amplitude is equal to zero are the natural frequencies of the nanoobjects.

On the Determination of Rigidity Parameters for Nanoobjects

569 The goal of the present study is to develop theoretical principles for experimentally determining the rigidity parameters of nanometer-size objects (nanoobjects). It is well known that one of the most efficient methods for the determination of elastic moduli used in macroscopic mechanics is based on measurements of the eigenfrequencies of objects under investigation. In this paper, we discuss subtle features arising when such a method is applied in studying nanoobjects. We propose a method for experimentally determining their rigidity parameters, which is based on the phenomenon of the dynamical quenching of so-called “antiresonance” vibrations. The advantage of this method is the possibility to isolate eigenfrequencies of a nanoobject under study from the entire spectrum of a nanoobject‐cantilever system of an atomic-force microscope (AFM).

A New Approach to the Solution of some Problems of Rigid Body Dynamics

A representation of the turn-tensor of an axisymmetrical rigid body by using the moment of momentum vector is proposed. It is proved that for certain external moments the motion of an axisymmetrical rigid body differs from the motion of the spherical rigid body only by the additional rotation around its axis of symmetry. Analogy between the problems of the rotation of an axisgmmetrical rigid body under the action of the moment, directed along the axis of symmetry of the body and under the action of the constantly directed moment, is exposed. Exact solution of the problem of free rotation of an axisymmetrical rigid body, taking account of a linear viscous friction, is constructed.