Dynamic structure factor of vibrating fractals

Motivated by novel experimental work and the lack of an adequate theory, we study the dynamic structure factor S(k,t) of large vibrating fractal networks at large wave numbers k. We show that the decay of S(k,t) is dominated by the spatially averaged mean square displacement of a network node, which evolves subdiffusively in time, ((u[over →](i)(t)-u[over →](i)(0))(2))～t(ν), where ν depends on the spectral dimension d(s) and fractal dimension d(f). As a result, S(k,t) decays as a stretched exponential S(k,t)≈S(k)e(-(Γ(k)t)(ν)) with Γ(k)～k(2/ν). Applications to a variety of fractal-like systems are elucidated.     

The response of a vibrating structure as a function of structural parameters—application and experiment

The theory used for examining the response of a structure subject to an external oscillatory force when certain structural parameters are changed is applied to the mathematical model of a pilot's seat structure. The results are discussed with a view to assessing those parts of the structure that are most effective in minimizing the response. Also, a laboratory experiment is described in which the basic circular response locus is verified, and doubts about the assumptions made in mathematical modelling resolved.     

Experimental validations of the HELS method for reconstructing acoustic radiation from a complex vibrating structure

This paper presents experimental validations of the Helmholtz Equation Least Squares (HELS) method [Wang and Wu, J. Acoust. Soc. Am. 102, 2020-2032 (1997); Wu and Wang, U.S. Patent Number 5712805 (1998); Wu, J. Acoust. Soc. Am. 107, 2511-2522 (2000)] on reconstruction of the radiated acoustic pressures from a complex vibrating structure. The structure under consideration has geometry and dimensions similar to those of a real passenger vehicle front end. To simulate noise radiation from a vehicle, a high fidelity loudspeaker installed inside the structure at the location of the engine is employed to generate both random and harmonic acoustic excitations. The radiated acoustic pressures are measured over a finite planar surface above the structure by a microphone. The measured data are taken as input to the HELS formulation to reconstruct the acoustic pressures on the top surface of the structure as well as in the field. The reconstructed acoustic pressures are then compared with measured ones at the same locations. Also shown are comparisons of the reconstructed and measured acoustic pressure spectra at various locations on the surface. Results show that satisfactory reconstruction can be obtained on the top surface of the structure subject to both random and harmonic excitations. Moreover, the more measurements and the closer their distances to the source surface, the more accurate the reconstruction. The efficiency of the HELS method may decrease with increasing of the excitation frequency. This high frequency difficulty is inherent in all expansion theories.     

A pendulum on a rotating and vibrating foundation

The motion of a pendulum is investigated in a uniform gravity field. The foundation of the pendulum is assumed to rotate around the vertical simultaneously accomplishing harmonic vibrations along it with a high frequency and small amplitude. With use of the classical perturbation theory and modern methods of analysis of nonlinear dynamical sets, the problem on the existence and stability of periodic motions of a pendulum with the period equal to that of the vibrations of the foundation is solved.     

Coalescence of spreading droplets on a wettable substrate

We investigate experimentally and theoretically the coalescence dynamics of two spreading droplets on a highly wettable substrate. Upon contact, surface tension drives a rapid motion perpendicular to the line of centers that joins the drops and lowers the total surface area. We find that the width of the growing meniscus bridge between the two droplets exhibits power-law behavior, growing at early times as t1/2. Moreover, the growth rate is highly sensitive to both the radii and heights of the droplets at contact, scaling as ho3/2/Ro. This size dependence differs significantly from the behavior of freely suspended droplets, in which the coalescence growth rate depends only weakly on the droplet size. We demonstrate that the scaling behavior is consistent with a model in which the growth of the meniscus bridge is governed by the viscously hindered flux from the droplets.     

Acoustic flows in a fluid layer on a vibrating substrate

The field of radiation forces in a fluid layer on a solid substrate is calculated. This field is formed during propagation of surface capillary wave along a free surface. The wave is excited by substrate vibrations as a result of instability development. The structure of acoustic flows is studied. Their effect on small-size particles and the possibilities of generating ordered structures from these particles are discussed.     

Hybrid tool for quickly estimating the radiated acoustic power from a vibrating structure in a multiple-source environment

This paper presents a new hybrid method for predicting overestimating and underestimating indicators of the acoustic power radiated by a vibrating surface even in the presence of other surrounding acoustic sources. This method is applicable to plates or low curvature surfaces radiating in open acoustic fields. The method is hybrid in the sense that the vibration field is measured and the parietal pressure field is predicted considering two extreme academic cases "baffled" and "unbaffled." Many simplifications are made and justified in order to save running time. The method is successfully validated in comparison with experimental results on both laboratory and real life structures. This method has led to a quick tool, allowing one to obtain a good approximation of the radiated power in a few minutes. It provides a natural extension of a classical analyzer for vibroacoustics engineering.     

Optimization of a universal matchbox on an ultrasonic vibrating system

The main scope of the article is to investigate the effect of ferrite cores gap in a universal matchbox on an ultrasonic vibrating system. A gapped transformer mechanism in a universal matchbox has been thoroughly studied. Characteristics of an ultrasonic vibrating system have been recorded such as mechanical vibrations, inductance, resonant frequencies, current and voltage levels as the gap of ferrite cores gradually increases. In addition, the phase difference between the supplied voltage and the current is also computed and displayed in a Lissajous curve in order to determine the optimal gap between two ferrite cores in the universal matchbox. Explanations supplement the experiment results.     

Rebound behaviors of droplets impacting on a superhydrophobic surface

The rebound behaviors of droplets impacting on a self-fabricated superhydrophobic brass surface (WCA=164.5°) were observed and studied by using high-speed-camera. In accordance with energy conversion, theoretical analysis of different behaviors and rebound mechanism were given. At lower velocities, three behaviors in different velocity ranges were observed: partial rebounding, entire rebounding and ejecting during rebounding. At higher velocities, such two behaviors as rebound after splashing and rebound, ejecting after splashing, occurred alternately and exhibited certain periodicity. A function to predict the critical impact velocity is derived from energy conservation condition, and the prediction values tally with the experimental values, with the maximum relative error about 14%.     

The apparent state of droplets on a rough surface

The factors influencing the state and wetting transition of droplets on a rough surface are both complex and obscure. The change in wetting is directly reflected by changes under the contact condition of the droplets with the surface. The recent study about the wettability of the superhydrophobic surface under the condensing condition arouses the new understanding about the apparent state of droplets on a rough surface. In this work, to validate the existence of droplets in an intermediate state, a microscale pillar topological polydimethylsiloxane (PDMS) surface was manufactured and its wettability under various conditions was studied. According to the experimental data, it is proposed that the wetting state of a rough surface may be embodied using the contact area ratio of a solid/liquid/gas droplet with the projective plane. A general calculation model for the apparent contact angle of droplets is given and expressed diagrammatically. It is found that the measured apparent contact angles of droplets at different states on the surface falls within the range predicted by our proposed equation. Supported by the National Natural Science Foundation of China (Grant No. 50606025)     

Heat transfer from a vibrating cylinder

This paper is concerned with the stability of vibration of parametrically excited systems. A simple approximate procedure is proposed for determining the characteristic exponents of a set of linear differential equations with periodically varying coefficients.     

完全非弹性蹦球的动力学行为

对振动台面上的完全非弹性球的蹦跳行为进行了初步分析.受约化振动加速度的控制，球的运动可以表现出一系列倍周期分岔过程.对几种典型的倍周期运动及分岔情况进行了讨论. 关键词： 蹦球 倍周期分岔 混沌 颗粒物质     

Scattering of a sound wave by a vibrating surface

We report an experimental study of the scattering of a sound wave of frequency f by a surface vibrating at frequency F. Both the Doppler shift at the vibrating surface and acoustic nonlinearities in the bulk of the fluid, generate the frequencies f±nF (n integer) in the spectrum of the scattered wave. We show that these two contributions can be separated because they scale differently with respect to the vibration frequency and to the distance between the vibrating scatterer and the detector. We determine the parameter ranges in which one or the other mechanism dominates and present quantitative studies of these two regimes. Received 2 December 2002 / Received in final form 27 March 2003 Published online 4 June 2003 RID="a" ID="a"e-mail: fauve@physique.ens.fr RID="b" ID="b"UMR 8550     

Scanning mirror on a vibrating membrane for dynamic optical trapping

A study of the variation of the spectral shape and the harmonic distribution of the high-order harmonics generated from silver plasma on the frequency chirp of the driving laser radiation (793 nm 48 fs) is reported. The results of the systematic study of the harmonic generation from the 21st order up to the 61st order (λ=13 nm) are presented. A tuning of the harmonic wavelength up to 0.8 nm can be accomplished by variation of the laser chirp. PACS 42.65.Ky; 42.79.Nv; 52.38.Mf     

Mechanical impedance gauge based on measurement of strains on a vibrating rod

An impedance gauge based on measurement of strains at two different cross-sections of a vibrating rod is analyzed and tested. The gauge rod, which may have variable characteristic impedance, is in contact with the object at one end and is driven by a harmonic vibrator at the other end. For conical and cylindrical rods explicit relations between point impedance and measured strains are derived. For a cylindrical gauge rod of steel with length 800 mm, diameter 10 mm, and distance between strain gauges 250 mm a fair agreement was generally obtained between experimental and theoretical point impedances of cylindrical test objects in the frequency range 50 Hz to 1·7 kHz. Significant improvements in accuracy over that of the tested prototype are expected to be feasible.