Free oscillation of a curvilinear rod

A method and finite-element algorithm are presented for determining the frequencies and form of free oscillations of elastic curvilinear rods with finite rigidity under deflection. Numerical examples are introduced in order to investigate the dependence of the precision of the calculated frequencies and the form of the oscillations on the method of division into finite elements.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 29, pp. 72–76, 1989.     

Application of amplitude–frequency formulation to nonlinear oscillation system of the motion of a rigid rod rocking back

The scope of this paper is evaluating an oscillation system with nonlinearities, using a periodic solution called amplitude–frequency formulation, such as the motion of a rigid rod rocking back. The approach proposes a choice to overcome the difficulty of computing the periodic behavior of the oscillation problems in engineering. We are to compare the solutions results of this method with the exact ones in order to validate the approach and assess the accuracy of the solutions. This method has a distinguished feature, which makes it simple to use and agree with the exact solutions for various parameters. Moreover, it is perceived that with one‐step iteration high accuracy of the solution will be achieved. We may apply the results of the solution to explain some of the practical physical problems. Copyright © 2009 John Wiley & Sons, Ltd.     

Effect of loading frequency on the fatigue strength of glass plastics

A method of fatigue-testing glass-plastics in the frequency range 1000–6000 Hz is presented together with some typical results. On the basis of the experimental results it is recommended that fatigue tests on glass plastics of the technological sample type should be carried out at high frequencies.     

Modelling and nanoscale force spectroscopy of frequency modulation atomic force microscopy

In this paper, a simulation model for frequency modulation atomic force microscopy (FM-AFM) operating in constant amplitude dynamic mode is presented. The model is based on the slow time varying function theory. The mathematical principles to derive the dynamical equations for the amplitude and phase of the FM-AFM cantilever-tip motion are explained and the stability and performance of its closed-loop controller to keep the amplitude at constant value and phase at 90° is analysed. Then, the performance of the theoretical model is supported by comparison of numerical simulations and experiments. Furthermore, the transient behaviour of amplitude, phase and frequency shift of FM-AFM is investigated and the effect of controller gains on the transient motion is analysed. Finally, the derived FM-AFM model is used to simulate the single molecule/nanoscale force spectroscopy and study the effect of sample viscosity, stiffness and Hamaker constant on the response of FM-AFM.     

Experimental studies of self-starting passive mode locking Er3+ -doped fiber ring soliton laser

The mechanism of femtosecond optical pulse generation in a self-starting Er³⁺-doped fiber ring soliton laser and experimental research results are discussed. Using the nonlinear polarization rotation effect of the fiber for sat-urable absorbers (and then self-amplitude modulation) which acts as the mode locking mechanism in an Er³⁺-doped fiber ring cavity laser, stable self-starting mode locking pulses have been generated. The shortest output pulse is 269 fs, with the central wavelength of 1,531 pm at the repetition rate of 21.37 MHz. The average output powen of the two terminators of the laser are 0.25 mW and 0.08 mW respectively. The threshold pump power which sustains the mode locking is 15 mW. Under high pump power, the laser works in a high order harmonic mode locking state. The mode locking pulse durations vs different cavity lengths are also studied. Project supported by Major Project of Chines: Academy of Sciences (No. KJ952-J1-705).     

Some effects of the equilibrium position and cyclic oscillation frequency of a solid body in a liquid

The problem concerning rotational oscillations of a heterogeneous solid body having an arbitrary “smooth” shape in an ideal liquid in the presence of gravity force is considered in the paper. New hydromechanical effects are discovered: a stable equilibrium position of the body changes due to the redistribution of the body mass, while the cyclic oscillation frequency remains constant; and, vice versa, the cyclic oscillation frequency of the body changes, while the stable equilibrium position remains constant.     

A comprehensive study on the oscillation frequency of spherical fullerenes in carbon nanotubes under different system parameters

Amongst possible new nanomechanical devices created based on carbon nanostructures, high-frequency nanoscale oscillators, or the so-called gigahertz oscillators have attracted much attention. In this paper, the oscillatory behavior of spherical fullerenes inside carbon nanotubes is thoroughly investigated. To this end, the continuum approximation together with Lennard-Jones potential is used to evaluate the van der Waals potential energy and interaction force. The equation of motion is directly solved based on the actual force distribution between the two nanostructures, without any simplifying assumption. A semi-analytical expression is obtained for the oscillation frequency into which the effect of initial conditions is incorporated. Thereafter, this newly derived expression is utilized in order to present a comprehensive study on the effects of different system variables such as geometrical parameters and initial conditions on the oscillation frequency. Based upon these studies, some new features of such oscillations have been revealed.     

Influence of oscillation localization on film detachment from a substrate

In modern constructions, thin-layer coats are often used as protecting or strengthening elements. Deformations of such constructions may cause significant stresses on the interface between the base and the coat because of the difference in their physical-mechanical properties, which leads to the destruction or detachment of the cover. Of special interest is strength analysis under dynamical or vibrational impacts because of the possibility of localizing oscillations in a neighborhood of the initial inhomogeneities (such as inclusions, defects, construction elements, etc.). In this paper, on the example of the detachment of a string from an elastic substrate, the possibility of localizing oscillations on a detachment defect is demonstrated and the effect of this localization on the growth of the detachment zone is analyzed. A simplified setting of the problem is considered. The possibility of localizing oscillations on a detachment defect is demonstrated and an approximate analytical solution is constructed, which takes into account only the first symmetric form of oscillations describing the development of the initial detachment. A numerical modeling of the problem is performed, and the results of modeling are compared with the approximate analytical solution.     

Stability and bifurcation for periodic perturbations of the equilibrium of an oscillator with infinite or infinitesimal oscillation frequency

We consider small perturbations periodic in time of an oscillator whose restoring force has a leading term with exponent 3 or 1/3. The first case corresponds to oscillations with infinitesimal frequency and the second case to oscillations with infinite frequency. The smallness of the perturbation is determined both by the smallness of the considered neighborhood of the equilibrium point and by a small nonnegative parameter ε. For ε=0, the stability of the equilibrium point is studied. For ε>0, we find conditions for an invariant two-dimensional torus to branch off with “soft” or “rigid” loss of stability with loss index 1/2. Translated fromMatematicheskie Zametki, Vol. 65, No. 3, pp. 323–335, March, 1999.     

Stability condition for vertical oscillation of 3-dim heavy spring elastic pendulum

Equations of motion for 3-dim heavy spring elastic pendulum are derived and rescaled to contain a single parameter. Condition for the stability of vertical large amplitude oscillations is derived analytically relating the parameter of the system and the amplitude of the vertical oscillation. Numerical continuation is used to find the border of the stability region in parameter space with high precision. The stability condition is approximated by a simple formula valid for a large range of the parameter and of the amplitude of oscillation. The bifurcation responsible for the loss of stability is identified.      

On the derivation of nonlinear rod theories from three-dimensional elasticity

Summary Nonlinear elastic constitutive laws for slender rods are derived from three-dimensional elasticity, using an asymptotic analysis in appropriate scaled material coordinates. Although the strain is everywhere small, displacements and rotations may be large and the elastic behaviour is nonlinear. In the lowest-order rod theory, the couple-resultant and tensile load are expressed as derivatives of a cross-sectional energy. The equations of this theory are similar to those in a director theory of Green and Laws. An iterative procedure for the generation of higher order rod theories is outlined.

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Sommario A partire dell'elasticità tridimensionale, si dedottono le leggi costituive non-lineare elastiche per verghe sottile, utilizzando un metodo asintotico in coordinate materiau delle scale opportune. Benchè la deformazione sia piccolò, i dislocamenti e le rotazioni possono essere grandi ed il comportamento elastico è non-lineare. Nella teoria delle verghe del ordine molto basso, la coppiarisultanta ed il carico tensile si esprimono come derivate di una energia trasversale. Le equazioni di questa teoria sono analoghe di quelle nella teoria direttiva di Green & Laws. Un procedimento iterativo è delineato per la generazione delle teorie delle verghe di ordini superiori.

     

Glass transition and crystallization process of hard magnetic bulk Nd60Al10Fe20Co10 metallic glass

Glass transition and crystallization process of bulk Nd60Al10Fe20Co10 metallic glass were investigated by means of dynamic mechanical thermal analysis (DMTA), differential scanning calorimetry (DSC), X-ray diffraction (XRD) and scanning electronic microscopy (SEM). It is shown that the glass transition and onset crystallization temperature determined by DMTA at a heating rate of 0.167 K/s are 480 and 588 K respectively. The crystallization process of the metallic glass is concluded as follows: amorphous α→α′＋metastable FeNdAl novel phase →α′＋primary δ phase→primary δ phase＋eutectic δ phase Nd3Al phase＋Nd3Co phase. The appearance of hard magnetism in this alloy is ascribed to the presence of amorphous phase with highly relaxed structure. The hard magnetism disappeared after the eutectic crystallization of amorphous phase.     

Sharp estimate of electric field from a conductive rod and application

We are concerned with the quantitative study of the electric field perturbation due to the presence of an inhomogeneous conductive rod embedded in a homogenous conductivity. We sharply quantify the dependence of the perturbed electric field on the geometry of the conductive rod. In particular, we accurately characterize the localization of the gradient field (i.e., the electric current) near the boundary of the rod where the curvature is sufficiently large. We develop layer‐potential techniques in deriving the quantitative estimates and the major difficulty comes from the anisotropic geometry of the rod. The result complements and sharpens several existing studies in the literature. It also generates an interesting application in EIT (electrical impedance tomography) in determining the conductive rod by a single measurement, which is also known as the Calderón's inverse inclusion problem in the literature.     

Interlaminar fracture of multidirectional glass/epoxy laminates under mixed-mode I + II loading

The mixed-mode I + II interlaminar fracture of multidirectional glass/epoxy laminates is investigated. Mixed-mode bending (MMB) tests were performed on specimens with delaminations in 0/θ-type interfaces, with θ varying from 0 to 90°. Preliminary three-dimensional finite-element analyses validated the beam theory model (BTM) used for analysing experimental data. The compliances measured are in a good agreement with BTM predictions. The total critical energy release rate G_c varies linearly with the mode II ratio G_II/G, although some discrepancies are observed in the high-mode II results for the 0/45 and 0/90 specimens. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 3, pp. 349–366, May–June, 2007.     

Experimental studies of high order soliton compression effect and gain characteristics in femtosecond laser pulses E3+r-doped fiber amplifier

Seed laser pulses with average power of 146 μW and pulse duration of 480 fs were amplified to 14.5 mW. The pulse duration was compressed to 260 fs using 6 m high concentration E3+r-doped fiber under forward pumping. The amplified signal pulse energy was 0.691 nJ (corresponding to a peak power of 2 657.7 W) and the repetition rate was 20.84 MHz. Spectrum breakup was observed simultaneously. The spectrum of pulses amplified by 3 m E3+r-doped fiber remains a single peak under different pump power. The amplified pulse duration was compressed abnormally with the increasing pump power using the backward pumping; that is, the amplified pulses were compressed with the increasing pump power under low pump power. When the pump power reached 38 mW, the shortest amplified pulse duration was 309 fs. With further increase in pump power, the amplified pulses began broadening, accompanied by a single peak spectrum under different pump power.     

Experimental studies of high order soliton compression effect and gain characteristics in femtosecond laser pulses Er 3+-doped fiber amplifier

Seed laser pulses with average power of 146 μW and pulse duration of 480 fs were amplified to 14.5 mW. The pulse duration was compressed to 260 fs using 6 m high concentration E³⁺ _r -doped fiber under forward pumping. The amplified signal pulse energy was 0.691 nJ (corresponding to a peak power of 2 657.7 W) and the repetition rate was 20.84 MHz. Spectrum breakup was observed simultaneously. The spectrum of pulses amplified by 3 m E³⁺ _r -doped fiber remains a single peak under different pump power. The amplified pulse duration was compressed abnormally with the increasing pump power using the backward pumping; that is, the amplified pulses were compressed with the increasing pump power under low pump power. When the pump power reached 38 mW, the shortest amplified pulse duration was 309 fs. With further increase in pump power, the amplified pulses began broadening, accompanied by a single peak spectrum under different pump power.