Stationary Vibration Research Articles

418 鉄道車両の車体振動特性測定試験 : 構体への各種部材取付けによる車体振動特性の変化

Experimental result of a series of stationary vibration test for a real railway vehicle is presented in this report. In the vibration test, excitation force is added by using electrodynamic exciter, and response acceleration of the floor, roof and side panel is measured to determine the vibration characteristics of the carbody as three-dimensional structure. The series of the measurement test is carried out with three steps (for body shell only, body shell with inner panel supporting member, complete carbody) to study the effect of sub-structure members on the vibration of carbody. From the measured acceleration data, frequency response function (FRF) is calculated and loss factor and modal characteristics (natural frequency and mode shape) are also determined.

SUPPRESSION OF RANDOM VIBRATION IN PLATES USING VIBRATION ABSORBERS

In the work presented here, a method to predict the effectiveness of application of damped dynamic vibration absorbers to suppress stationary random vibration of rectangular simply supported plates is given. Numerical examples of two different spatial distributions of the random-in-time forcing function are explored and optimal absorber parameters are presented.

A two-dimensional model for extensional motion of a pre-stressed incompressible elastic layer near cut-off frequencies

A two-dimensional model for extensional motion of a pre-stressed incompressible elastic layer near its cut-ofi frequencies is derived. Leading order solutions for dis- placement and pressure are obtained in terms of the long wave amplitude by direct asymptotic integration. A governing equation, together with corrections for displace- ment and pressure, is derived from the second order problem. A novel feature of this (two-dimensional) hyperbolic governing equation is that, for certain pre-stressed states, time and one of the two (in-plane) spatial variables can change roles. Although whenever this phenomenon occurs the equation still remains hyperbolic, it is clearly not wave-like. The second order solution is completed by deriving a reflned governing equation from the third order problem. Asymptotic consistency, in the sense that the dispersion relation associated with the two-dimensional model concurs with the ap- propriate order expansion of the three-dimensional relation at each order, is verifled. The model has particular application to stationary thickness vibration of, or transient response to high frequency shock loading in, thin walled bodies.

Highly sensitive and direct detection of DNA fragments using a laser-induced capillary vibration effect.

A pulsed laser-induced stationary wave capillary vibration detection method was applied to the sensitive detection of capillary gel electrophoresis, and the direct detection of non-labeled nucleic acids, such as DNA sequencing products, was demonstrated. An excimer laser operating at 248 nm was used as a CVL excitation source, and polynucleotides were sensitively detected without derivatization. From an investigation on the endurance of several matrixes to pulsed laser irradiation, a polyacrylamide without a cross-linker (0%C) was found to have adequate endurance, and it exhibited no serious damage during an analysis. A cytosine-terminated sequence reaction product was detected with a sensitivity close to that of laser-induced fluorometry (LIF). These results suggest the feasibility of the highly sensitive detection of ultramicro amounts of biological materials without a pre- or post-column derivatization, which has usually been required in sensitive detection procedures, such as LIF. Furthermore, the feasibility of a novel DNA sequencing method is also suggested.

Stationary Stressed State of a Multiply Connected Rectangular Isotropic Cylinder

The theory of complex variables is used to construct an approximate solution for the stationary vibrations of an isotropic rectangular cylinder with longitudinal curvilinear cavities. Numerical calculations are presented for a cylinder with one elliptical cavity.

Viscoelastic vibrations of a triangular plates

The problem of stationary vibrations of a viscoelastic equilateral triangular plate is treated. The vibrations are caused by the action of a uniformly distributed load which varies harmonically and by the motion of the simply supported boundary of the plate as a rigid body which vibrates at the same frequency. The level lines of the vibration amplitude are studied and the graphs of the amplitude distribution along the height of the triangle are given.

Flexural Vibrations of a Piezoelectric Bimorph with a Cut Internal Electrode

Stationary vibrations of a bimorph plate composed of two piezoelectric layers of equal thickness are studied. There is an infinitely thin cut electrode between the layers. A model of flexural vibrations of the bimorph that is based on the variational equation generalizing the Hamilton principle in electroelasticity is proposed. For the plane problem, a system of equations of motion is derived and the boundary conditions and the conjugate conditions at the interface of the regions of the cut electrode are formulated. For the TsTS–19 piezoceramics, resonance and antiresonance frequencies are calculated. The values obtained are compared with the calculation results obtained with the use of the Kirchhoff model and the finite–element method. It is shown that the use of a plate with a cut electrode allows one to increase the efficiency of vibration excitation compared to the case of a continuous internal electrode.

Computer simulation of structural random loading identification

Loading identification has long been a difficult problem for multi-input–multi-output stationary random vibration problems. In this paper, the inverse pseudo-excitation method is developed for dealing with such identification problems. Numerical simulations are used to reveal the difficulties in such problems, and some numerical analysis measurements are suggested, which may be very useful in the setting up and processing of experimental data so as to obtain reasonable predictions of the input loading from selected structural responses, e.g. a few structural displacements or strains, or a combination of them. It is shown that computer simulation is a very cheap way of overcoming the problem of which responses to measure on real structures in order to identify the power spectral density matrix of the applied forces.

Bounded parametric control of random vibrations

The dynamic programming approach is used to study a feedback control problem for a randomly excited single–degree–of–freedom system. The available actuator for control can provide temporal stiffness variations for the system, which are of a bounded magnitude. An analytical solution is obtained for the corresponding Hamilton–Jacobi–Bellman equation for the expected response energy, which should be minimized according to the integral cost criterion. While this solution is valid within some parts of the phase plane only, it extends to the whole phase plane with increasing time–interval of control. Thus the exact explicit expression for the optimal control law is obtained for the case where steady–state response is to be controlled. This law requires feedback–controlled switching stiffness between the given bounds. Stationary random vibration of the system with this control law is studied then, by a direct energy balance approach and by a stochastic averaging method. The latter of these provides a more extensive description of the response, which may provide reliability estimates for the controlled system, but this asymptotic approach is valid for the limiting case of a weak control only. The direct energy balance predicts only the expected response energy, or the mean square displacement. However, its range of applicability is expected to be less restrictive with respect to the maximal magnitude of the system9s stiffness variations: the non–dimensional variations may not be much smaller than unity. The analytical studies are extended to the case of a controlled system with a nonlinear restoring force.

Forced stationary vibrations of flexible plates induced by random narrow-band excitations

We consider some problems related to the analysis of the modes of forced vibrations of elastic plates induced by random narrow-band excitations. The investigation of nonlinear vibrations of a plate is performed within the framework of a reduced discrete model constructed by using the Hamilton variational principle, finite-element methods, and generalized coordinates. To study the dynamical state of the analyzed structure, we perform numerical simulation of the vibrations induced by a particular realization of narrow-band excitations. Each realization of random narrow-band excitations is obtained with the help of a shaping filter of the second order and describes harmonic oscillations with slowly varying amplitude and phase. We also consider the scenarios of transitions between different modes of vibrations of the plate and estimate the time of its residence in different dynamical states.

プレート状模型交差部における曲げ波・縦波・横波による固体音の統計的エネルギー解析に関する研究 : 結合構造における固体音の統計的エネルギー解析に関する研究 その2

Statistical Energy Analysis (SEA) method is utilized to investigate the vibration energy of structure-borne sound. This method analyses the complex connected structures with many vibration modes received stationary random vibration in broad-band excitation, if the natural frequencies within the frequency bandwidth are statistically distributed. The present paper describes equations of power balances and coupling loss factors between coupled systems from theoretical perspective. The paper also discusses the diffuse vibration field of plates and the transmission efficiency of junctions in detail. Moreover, the author calculated the "average" transmission efficiency using reciprocity relations by three incident bending, longitudinal, transverse waves. A series of experimental investigation was conducted by using the "average" transmission efficiency.

Pecularities of acoustic phonon scattering from a planar crystal defect and pseudosurface phonons (Resonant scattering of transverse phonons from a thin defect layer)

A scattering of acoustical phonons from a planar crystal defect is studied. A resonance reflection of the transverse phonons from the planar defect is discovered and conditions of such a reflection are investigated. It is shown that the resonance conditions are connected with existence of longitudinal phonons localized at the planar defect and travelling along it. The problem is analyzed basing both on the lattice dynamics and on the theory of elasticity. A non-symmetrical stationary solution which consists of (1) a homogeneous transverse wave propagating only in one elastic semispace and (2) longitudinal localized waves in the both elastic semispaces is found. The condition of the resonance reflection of the transverse phonons from the defect layer coincides with a condition under which the non-symmetrical stationary vibration exists. The influence of properties of the models considered on the resonance frequencies is discussed.

STATE–SPACE IDENTIFICATION OF VIBRATING SYSTEMS FROM MULTI-OUTPUT MEASUREMENTS

A time series model procedure for the synthesis of multivariate stationary time series random vibrations is shown. The vibrations are assumed to be the outputs of a regularly sampled, random noise excited, differential equation model of a vibration system. The matrix block Hankel stochastic realisation method is used to determine the system matrices and modal parameters. The problem of the minimal representation is discussed and a new test for determining the number of states in the model is derived. This test is based in the estimation of the coefficients in a particular column of the observability matrix and has a χ2distribution. A numerical example illustrates the procedure for identifying the order, parameters and spectrum of a noisy process.

Study on Optimum Tuning of Viscoelastic Dynamic Absorber. Analysis by Fractional Differential Voigt Model.

Dynamic model of viscoelastic material may be described by fractional differential Voigt model. Free vibration and forced vibration of a single-DOP (single degree of freedom) system with viscoelastic material have been described by the equations of motion with fractional differential term. This paper deals with bibration reduction of a single-DOF mechanical system with viscoelastic DA (dynamic absorber). Property of stationary vibration response of a 2-DOF viscous camping system has been fully known, yet a 2-DOF viscoelastic damping system is still unknown. Here, the responses of the 2-DOF system with the viscoelastic DA are analyzed and compared with those with the viscous DA.

Pulsed UV Laser-Induced Stationary Capillary Vibration for Highly Sensitive and Direct Detection of Capillary Electrophoresis

A stationary wave of the capillary vibration effect was successfully induced by a series of short laser pulses. This wave could be applied to highly sensitive detection of capillary electrophoresis as well as the already reported capillary vibration induced by an intensity-modulated CW laser (CVL effect). Generally, pulses with much shorter width than the period of the natural frequency of the vibrating system cannot induce a standing vibration. However, utilizing the time constant of CVL determined by heat dissipation time, we found conditions which could induce a stable stationary wave of the capillary by a series of nanosecond light pulses. We used the KrF excimer laser operated at 248 nm with a pulse width of 60 ns and output of ∼10 μJ/pulse as the CVL excitation source and applied it to highly sensitive detection of nonderivatized amino acids at the femtomole level. The sensitivity was at least 2 orders of magnitude superior to that of a commercially available UV absorbance detector. This technique extends the CVL's spectral regions. For example, in the UV region, where many biological materials have significant absorption bands, this technique will extend analytical applications in capillary electrophoresis by eliminating the need for a derivatization process.

Construction of the solutions of the equations of vibration of the classical theory of plates with parameters periodic on one coordinate

The system of classical equations of transverse vibrations of plates that are inhomogeneous on one coordinate and have exponential dependence of the solution on the other coordinate and time are presented in the canonical Hamiltonian form with suitably chosen canonical variables. For periodically varying parameters we use the general properties of periodic Hamiltonian systems to study the structure of the solutions of boundary-value problems for stationary vibrations of plates.

Control of a multidegree of freedom standing wave ultrasonic motor driven precise positioning system

A newly developed positioning system incorporating a multidegree of freedom standing wave ultrasonic motor (SWUM) is presented and its advantageous features, operating principles, and some experimental results are described. The principle of motorization is based on the conversion, through frictional contact, of a stationary bending vibration sustained in a slotted metallic resonator, into rigid body displacements. A small autonomous multidegree of freedom nanopositioner using a SWUM motor is presented for fine positioning in scanning tunneling microscopy. The positioning system is achieved via the simultaneous operation of two identical pulse width modulation servo-control systems, each having a laser vibrometer position feedback loop. The closed loop position schemes are theoretically considered and their results are demonstrated and evaluated in practice. Evaluations of experimental tests indicate that a positioning resolution less than 100 nm are successfully achieved for an unlimited X−Y travel range with linear speeds between 1 mm s−1 and few cm s−1.

Active and Reactive Structural Energy Flow

Vibration of linear structures having internal material damping is considered. Energy supplied to such structures by external dynamic loads and mechanical energy flow inside these structures are investigated. The paper aims at presenting and discussing relations which are useful when studying energy transmission through mechanical systems. Special attention is paid to the case of stationary harmonic vibration, but general stationary vibration is also discussed. Continuity equations for the active and reactive mechanical intensities are derived for a solid continuum model. Limits for the active and reactive power supplied to a structure in terms of structural and loading properties are also established. Numerical examples with discrete, continuous and discretized structures demonstrate the results obtained.

Active Vibration Control of Stationary Vibration. Effect of Number and Location of Control Forces.

Recently, active vibration control has been applied to some bridges and buildings. However, the control has only been used to reduce vibration of lower modes. Control methods and spillover problems have also been discussed, but little has been done in terms of analysis of the number and location of actuators. For reduction of the vibration of higher modes, it is necessary to use many actuators. In terms of industrial application, it is important to know the necessary number and optimum location of actuators in order to obtain the required vibration reduction. In this report, we discuss the relationship between the number and location of actuators and vibration reduction for stationary vibration of a simple supported uniform beam. The following results were obtained. First, vibration reduction is strongly affected by the location of the actuators. Second, vibration reduction varies according to the distribution pattern of forces. Based on the findings, an estimation technique for the vibration reduction was proposed.

Nonstationary Random Nature of Local Vibration Induced on Elastic Tube Wall Downstream of Stenosis with Pulsatile Flow.

According to previous experimental study, local vibration that forms natural mode (wave number 2) around reattachment point was observed on elastic tube wall downstream of stenosis. A peak exists in the frequency spectrum of this stationary random vibration. This peak is attributable to natural frequency of local vibration on the elastic tube, so the peak frequency depends on transmural pressure, and the power depends on Reynolds number. In biological blood flow both transmural pressure and Reynolds number are pulsatile, but flow in the tube was steady in that previous study. In this research, experimental observation was made on pulsatile flow. It was found that the vibration acts quasi-stationary random nature at least 1 Hz. And relation between the vibration and murmurs contained in Korotkov sound was a little discussed.