Coupled flexural,longitudinal and shear wave motion in two- and three-layered damped beams

The purpose of this paper is to show how a ceramic layer attached to a two-layered (elastic/viscoelastic) beam alters the wave propagation mechanism in the beam. The ceramic layer is assumed to possess mass but not longitudinal stiffness. Shear deformation, rotatory, longitudinal and transverse inertia forces are all included in the analysis. The equations of motion of the layered beam are derived by using the virtual work principle. Relevant dispersion curves for an infinite beam are presented and discussed, and are compared with dispersion curves obtained from a number of simplified theories. The influence of the inertia coupling between different wave types, caused by the ceramic layer, has been examined. The loss factors of the different waves are found to be critically dependent upon the inertia coupling and wave-number in particular wave-number regions. This occurs when uncoupled waves of different types have close wave-speeds. Under these circumstances a coupled wave can exist which has much less damping than any of its constituent uncoupled waves.     

Vibration characteristics of piezoelectric torsional transducers

The vibrational characteristics of Langevin-type torsional transducers, which consist of two piezoelectric torsional disks and two elastic blocks, are studied theoretically and experimentally in this paper. The differential equations of piezoelectric torsional motions are derived in terms of the circumferential displacement and the electric potential. Solutions of the boundary-value problem yield the natural frequencies and mode shapes of the transducers, and the natural frequencies are verified by comparing the numerical results with the experimental ones. The theoretical results enable one to quantitatively predict the effect of the elastic blocks on the reduction of the natural frequencies of a Langevin-type torsional transducer.     

矩形扭转压电换能器的研制

本文从压电和机械振动等基本理论出发，首次较系统地建立了矩形扭转压电换能器的理论，推导出频率方程，并通过实验进行了验证。     

Equations of motion for rotational motion in liquids

The equations of motion corresponding to master equations describing rotational relaxation in liquids are shown to be purely deterministic and, in general, nonlocal in time.     

Transverse oscillations for tissue motion estimation

This paper gives an overview of the methods developed for tissue motion estimation using transverse oscillation images (TO). TO images are specific radiofrequency ultrasound images featuring oscillations in both spatial directions. The initial studies on TO were published in the late 1990s. This paper reviews the main ideas and applications behind this motion estimation approach. First the origin and motivation of TO is briefly reviewed. Then the beamforming methods that lead to TO images are given, detailing the receive-only approach and the transmit-and-receive approach using synthetic aperture data. The different medical applications where TO has been used are discussed (blood flow, elastography and echocardiography), showing how it can improve motion estimation. Finally, the future perspectives of TO are outlined.     

Study of the sandwiched piezoelectric ultrasonic torsional transducer

The sandwiched piezoelectric ultrasonic torsional transducer was studied. The transducer consists of front and back metal cylinders, and coaxially segmented, tangentially polarized, piezoelectric ceramic tubes. The torsional vibration of the tangentially polarized piezoelectric ceramic slender tube was studied first and its electromechanical equivalent circuit was derived. Based on the network theory and the electromechanical equivalent circuit, the torsional vibration of the piezoelectric ceramic cylinder, formed by stacking a number of identical short piezoelectric ceramic rings, was analysed and the electromechanical equivalent circuit of the piezoelectric ceramic stack in torsional vibration was developed. Finally, the sandwiched ultrasonic torsional transducer was studied and resonance frequency equations were derived which can be used to design and calculate the torsional transducers for different applications.     

Phenomenological theory of damped and undamped intensity oscillations in lasers

The usual phenomenological laser rate equations for the population inversion and the light intensity (Statz-deMars equations) are generalized to take into account intensity-dependent losses and Einstein coefficients. Sufficient conditions are given for these generalized equations in order to have only physically admissible solutions. The solutions either tend towards an equilibrium value in an aperiodic or oscillatory way or display an undamped periodic behavior. The theory is applied to the three-level laser and the four-level laser, without and with a saturable absorber asQ-switch. The applicability of the theory to various problems is discussed.     

Electrical equivalent circuit for the modes of oscillations of piezo-electric bars

The equivalent circuits for odd and even longitudinal, flexural and torsional vibrations of piezo-electric bars were calculated by means of series development for various ways of excitation. The effect of coupling due to internal frictions was neglected.In Conclusion I would like to thank Prof. Dr. V. Petrílka, corresponding member of the Czechoslovak Academy of Sciences, for his tireless interest and help in this work. At the same time I would like to thank all my friends who in any way contributed, particularly Dr. J. Tichy and Dr. A. Apfelbeck.     

Trap-recharging waves versus damped,forced charge-density oscillations in hexagonal silicon carbide

The structural parameters and hydrostatic pressure coefficients of CdS_xTe_1-x in the two phases, namely zinc-blende and NaCl as well as the transition pressures from zinc-blende to NaCl structures at various S concentrations are presented. The calculations are performed using the full potential linearized augmented plane wave (FP-LAPW) method within the density functional theory (DFT) in the local density approximation (LDA), and two developed refinements, namely the generalized gradient approximation (GGA) of Perdew et al. for the structural properties and Engel-Vosko for the band structure calculations. Detailed comparisons are made with published experimental and theoretical data and show generally good agreement. The present results regarding the studied quantities for compositions x in the 0–1 range (0 < x < 1) and for the NaCl phase are predictions and may serve as a reference for experimental work.     

Equations of motion for continuum systems

We construct equations of motion for anN-component continuum. The basic assumption is that the dynamical vector field is the sum of two terms: a conservative term, being a Hamiltonian vector field associated with the energy function of the system; and a dissipative term, being a gradient vector field associated with a family of functions. The resulting equations satisfy the usual conservation laws for continuum systems, and, moreover, reduce to the standard fluid equations when the continuum is a fluid.     

Damping of longitudinal plasma oscillations

Attenuation of electron oscillations in a fully ionized plasma is investigated by solving linearized kinetic equation without external fields. The general dispersion relation for longitudinal plasma oscillations is obtained using the BGK model. Damping due to electron ion collisions is obtained with a correction term. It is also observed that damping rate decreases ask increases, which is in agreement with McBride.     

The internal friction of torsional oscillations in ferromagnetic materials

The paper is a continuation of the first part [1] and deals with the internal friction of torsional oscillations of ferromagnetic materials in a static and an alternating magnetic field. The calculation differs considerably from the case of longitudinal oscillations, particularly in the following points. In the first place, the internal friction of torsional oscillations depends quite differently on the dimensions of the sample, and the continuous distribution of magnetic domains and Bloch walls cannot be so easily defined. Secondly, a magnetic field created as a result of eddy currents during torsional oscillations does not penetrate the surroundings, so that the internal friction in an electrically conducting medium is the same as in vacuum. Thirdly, the deformation here is an antisymmetrical function of the field, so that the coefficient is an even function while with longitudinal oscillations it was expressed by an odd function. Despite these different conditions the results are very similar to those with longitudinal oscillations and agree well with experiment. In an alternating magnetic field the internal friction of torsional oscillations has a sharp maximum atH=0.64H _S whereH _S is the saturated value of the field for which magnetoelastic effects disappear.

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[1] . , , . . -, , , , , , . , , , . , , , . , H=0,64H _S, H _S , .

     

Nonlinear nonuniform torsional vibrations of bars by the boundary element method

In this paper a boundary element method is developed for the nonuniform torsional vibration problem of bars of arbitrary doubly symmetric constant cross-section taking into account the effect of geometrical nonlinearity. The bar is subjected to arbitrarily distributed or concentrated conservative dynamic twisting and warping moments along its length, while its edges are supported by the most general torsional boundary conditions. The transverse displacement components are expressed so as to be valid for large twisting rotations (finite displacement-small strain theory), thus the arising governing differential equations and boundary conditions are in general nonlinear. The resulting coupling effect between twisting and axial displacement components is considered and torsional vibration analysis is performed in both the torsional pre- or post-buckled state. A distributed mass model system is employed, taking into account the warping, rotatory and axial inertia, leading to the formulation of a coupled nonlinear initial boundary value problem with respect to the variable along the bar angle of twist and to an “average” axial displacement of the cross-section of the bar. The numerical solution of the aforementioned initial boundary value problem is performed using the analog equation method, a BEM based method, leading to a system of nonlinear differential-algebraic equations (DAE), which is solved using an efficient time discretization scheme. Additionally, for the free vibrations case, a nonlinear generalized eigenvalue problem is formulated with respect to the fundamental mode shape at the points of reversal of motion after ignoring the axial inertia to verify the accuracy of the proposed method. The problem is solved using the direct iteration technique (DIT), with a geometrically linear fundamental mode shape as a starting vector. The validity of negligible axial inertia assumption is examined for the problem at hand.     

Snap loads and torsional oscillations of the original Tacoma Narrows Bridge

In 1940, the original Tacoma Narrows Bridge was completed on June 10 and opened to traffic on July 1. On November 7, the deck collapsed. Before that day, significant vertical oscillations had occurred, but no torsion. The bridge as built was stable with respect to torsional motion under the winds of November 7 and previous winds with higher speeds. However, snap loads in the diagonal ties attached to the north midspan cable band helped to loosen the band, and the frictional resistance between the band and the north suspension cable passing through it was overcome. The cable began to slip through the band. For this new structural system, with longitudinal motion of the north cable, the wind speed was higher than the critical speed for torsional flutter, and torsional motion was initiated. Approximately 700 cycles of torsional oscillations occurred during the hour prior to the collapse. In the present study, the snap loads on the cable band are discussed first. Then a continuum model of the central span (deck, cables, and hangers) is formulated. The longitudinal motions of the cables are included, so that the slippage can be incorporated. Known information from the observed steady-state torsional motion is utilized with assumed forms of the vertical cable displacements, and the governing equations provide the horizontal cable displacements, the dynamic tensions in the cables, the vertical and torsional motions of the deck, and the resultant lift force and pitching moment (including damping) acting on the deck during its final hour.     

Nonlinear longitudinal oscillations of relativistic plasma

The investigation has been made of nonlinear forced longitudinal oscillations of a relativistic plasma. It was demonstrated that: a) the nonlinear terms (v▽)p arising in the equations of motion do not restrict the electron oscillation amplitude increase in the region of plasma resonance; b) the nonlinear terms due to the relativistic nature of oscillations, firstly, limit the oscillation amplitude in the resonance region and, secondly, lead to the development of a parametric instability. The harmonic, sub- and ultraharmonic oscillations turned out to be unstable. The conditions for the instability as well as expressions for the growth rates of unstable oscillations were obtained.     

非简谐阻尼振动与匀加速直线运动合成实验

分析了小球在斜槽内横向作非简谐阻尼振动同时又在其纵向作匀加速直线运动的轨迹的理论公式.让粘满碳粉的小球在铺有坐标纸的斜槽内运动,记录真实运动轨迹,从实验图像中可以看出振幅越来越小、波长越来越长,这与理论分析相符.