The dynamic behaviour of stiffened strings

Summary The small oscillation of a stiffened string about its static equilibrium configuration is studied. The solution requires both the static and dynamic shape of the rod to be determined and since the governing equations do not lend themselves to an analytical solution a Runge-Kutta integration technique was used. Experimental results for the natural frequencies are compared to the numerical solution for a particular stiffened string.

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Übersicht Es werden die kleinen Schwingungen eines versteiften Bandes um die statische Gleichgewichtslage untersucht. Dabei muß sowohl die statische wie auch die dynamische Form des Bandes bestimmt werden. Da eine analytische Lösung der Bewegungsgleichungen nicht möglich ist, wurde numerisch nach Runge-Kutta integriert. Für verschieden versteifte Bänder werden Versuchsergebnisse für die Eigenfrequenzen mit numerischen Lösungen verglichen.

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The authors would like to acknowledge the work of David Stredulinsky in the initial stages of this project and to thank the National Research Council for support under operating grant NRC A7514 (Faulkner).     

The influence of tyres on the dynamic behaviour of a lawn mower

Agricultural tractors are used for on-road and off-road transport purposes, for supplying the necessary power during field operations and for controlling the mounted implements. Unfortunately, soil undulations induce tractor and machine vibrations, reducing driver's comfort and their capability of controlling the linked machinery. In this introductory study, the effect of some characteristics parameters, such as tyre pressure, and herewith related tyre stiffness, and mass addition on the dynamic behaviour and, more specifically, on the resonance frequencies of a lawn mower, are analysed by experimental modal analysis. After adapting the modal model, field unevenness instead of disturbance forces could be introduced as excitation inputs. A final validation of the adapted modal models shows good agreement with measured lawn mower vibrations.     

On the dynamic behaviour of axially excited helical springs

Summary In this paper we have used Wittrick's theory on the propagation of deformation waves in a coiled wire — taking only into account the coupling between the displacements of the wire cross-section along the tangent and along the binormal of the average helix — in oder to show how the natural frequencies of the axial and rotational modes of a cylindrical helical spring vary according to a non-linear function of the wave number. Moreover it is here demonstrated that the natural frequencies resulting from the proposed theory for the natural modes to which correspond wave lengths greater than two coils do not differ much from those which can be calculated by considering the spring as a periodic discrete system. Theoretical results are finally tested by an appropriate experimental investigation.

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Sommario Viene utilizzata la teoria proposta dal Wittrick sulla propagazione delle onde di deformazione in un filo avvolto ad elica, tenendo conto del solo accoppiamento tra gli spostamenti delle sezioni del filo lungo la tangente e lungo la binormale all'elica media, per mettere in evidenza come le pulsazioni naturali dei modi assiali e rotazionali di una molla ad elica cilindrica varino secondo una funzione non lineare del numero d'onda. Si dimostra che le pulsazioni naturali che si ottengono dalla teoria proposta, per modi di vibrare cui corrispondono lunghezze d'onda maggiori di due spire, sono poco discoste da quelle prevedibili considerando la molla come sistema discreto periodico. I risultati della teoria surriportata vengono infine controllati a mezzo di una opportuna indagine sperimentale.

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Research supported by the Ministero della Pubblica Istruzione, Italy.     

A laboratory investigation of the flow in the left ventricle of a human heart with prosthetic, tilting-disk valves

The understanding of the phenomena involved in ventricular flow is becoming more and more important because of two main reasons: the continuous improvements in the field of diagnostic techniques and the increasing popularity of prosthetic devices. On one hand, more accurate investigation techniques gives the chance to better diagnose diseases before they become dangerous to the health of the patient. On the other hand, the diffusion of prosthetic devices requires very detailed assessment of the modifications that they introduce in the functioning of the heart. The present work is focussed on the experimental investigation of the flow in the left ventricle of the human heart with the presence of a tilting-disk valve in the mitral position, as this kind of valve is known to change deeply the structure of such a flow. A laboratory model has been built up, which consists of a cavity able to change its volume, representing the ventricle, on which two prosthetic valves are mounted. The facility is designed to be able to reproduce any arbitrarily assigned law of variation of the ventricular volume with time. In the present experiment, a physiologically shaped curve has been used. Velocity was measured using a feature-tracking (FT) algorithm; as a consequence, the particle trajectories are known. The flow has been studied by changing both the beat rate and the stroke volume. The flow was studied both kinematically, examining velocity and vorticity fields, and dynamically, evaluating turbulent and viscous shear stresses, and inertial forces exerted on fluid elements. The analysis of the results allows the identification of the main features of the ventricular flow, generated by a mitral, tilting-disk valve, during the whole cardiac cycle and its dependence on the frequency and the stroke volume.     

The role of radial motion in the dynamic plasticity of rods

For a radial shear wave generated by a dispersive, incident plastic wave that impinges upon a silicone lubricated, infinitesimally elastic interface, experimental data introduced here reveal that there is an equipartition of energy between the longitudinal and radial components of the incident wave. The former reflects from a quasi-fixed boundary and, because of the lubrication, the latter reflects from a free surface.     

Effect of trabeculae and papillary muscles on the hemodynamics of the left ventricle

The impact of surface trabeculae and papillary muscles on the hemodynamics of the left ventricle (LV) is investigated using numerical simulations. Simulations of ventricular flow are conducted for two different models of the LV derived from high-resolution cardiac computed tomography (CT) scans using an immersed boundary method-based flow solver. One model comprises a trabeculated left ventricle (TLV) that includes both trabeculae and papillary muscles, while the second model has a smooth left ventricle that is devoid of any of these surface features. Results indicate that the trabeculae and papillary muscles significantly disrupt the vortices that develop during early filling in the TLV model. Large recirculation zones are found to form in the wake of the papillary muscles; these zones enhance the blockage provided by the papillary muscles and create a path for the mitral jet to penetrate deeper into the ventricular apex during diastole. During systole, the trabeculae enhance the apical washout by ‘squeezing’ the flow from the apical region. Finally, the trabeculae enhance viscous dissipation rate of the ventricular flow, but this effect is not significant in the overall power budget.     

Static and dynamic behaviour of a rigid rotor on journal bearings

This experimental investigation concerns the static and dynamic behaviour of a rigid balanced rotor on journal bearings. Running conditions were chosen in order to obtain relatively high eccentricity ratios near the instability threshold speeds.The results, compared also with the theoretical predictions of some authors, have substantially shown the importance of examining the static behaviour near the instability threshold speed to allow a correct interpretation of some aspects of the dynamic behaviour.In order to clarify the discrepancies between the observed and the theoretically predicted dynamic behaviour, some further tests have been carried out.

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Sommario E' stato esaminato sperimentalmente sia il comportamento statico che quello dinamico di un rotore rigido e bilanciato sostenuto da cuscinetti cilindrici lubrificati.Le condizioni di funzionamento sono state scelte in modo tale che, in prossimità della soglia di instabilità, il valore del rapporto di eccentricità risultasse relativamente grande.I risultati, confrontati anche con le indicazioni teoriche di altri autori, hanno sostanzialmente evidenziato l'importanza dell'esame del comportamento statico in prossimità della soglia di instabilità al fine di interpretare correttamente alcuni aspetti del fenomeno dell'instabilità.Sono state inoltre effettuate una serie di ulteriori indagini con lo scopo di chiarire le discordanze fra il comportamento dinamico osservato e quello previsto dalla teoria.

     

Non-linear dynamic behaviour of multi-folding microstructure systems based on origami skill

This paper presents the theoretical basis for both static and dynamic numerical approaches to the elastic stability and elasto-plastic stability of a folding multi-layered truss. Both analyses are based on bifurcation theory and include geometrical non-linearity. The dynamic analysis includes an allowance for contact between nodes. Comparisons are made between elastic behaviour and elasto-plastic behaviour obtained from both numerical dynamic methods in which bifurcations are demonstrated as a theoretically elastic analysis. Our analysis reveals that several folding behaviours in the pantographic truss are identified during the elastic and elasto-plastic instabilities, where the folding behaviour of the truss is shown to be a function of the initial geometry and velocity of the dynamic loading. The authors suggest that understanding this behaviour will be very useful for developing light-weight structures subject to dynamic loading based on static bifurcation analysis and dynamic analysis.     

Effect of accelerometer mass on the flexural motion of plates

When the flexural acceleration of a plate is measured by an accelerometer, the mass of the accelerometer tends to reduce the magnitude of the acceleration.This study establishes a simple analytical relation between the accelerometer mass and the corresponding reduction of acceleration. This has been done by studying an idealized diffraction problem for the plate flexural waves.The complex frequency response depends upon the accelerometer mass, the frequency of the flexural wave, the plate thickness and the material parameters of the plate.A numerical filtering method is used to bring an experimental result and a corresponding numerical prediction closer together.     

The effect of bonding layer properties on the dynamic behaviour of surface-bonded piezoelectric sensors

The dynamic behaviour of piezoelectric sensors depends on the bonding condition along the interface between the sensors and the host structure. This paper provides a comprehensive theoretical study of the effect of the bonding layer on the coupled electromechanical characteristics of a piezoelectric sensor bonded to an elastic substrate, which is subjected to a high frequency elastic wave. A sensor model with a viscoelastic bonding layer, which undergoes a shear deformation, is proposed to simulate the two dimensional electromechanical behaviour of the integrated system. Analytical solution of the problem is provided by using Fourier transform and solving the resulting integral equations in terms of the interfacial stress. Numerical simulation is conducted to study the effect of the bonding layer upon the dynamic response of the sensor under different loading frequencies. The results indicate that the modulus and the thickness of the bonding layer have significant effects on sensor response, but the viscosity of the bonding layer is relatively less important.     

Sample size effect on the dynamic torsional behaviour of the 2A12 aluminium alloy

In order to investigate the effect of sample size on the dynamic torsional behaviour of the 2A12 aluminium alloy. In this paper, torsional split Hopkinson bar tests are conducted on this alloy with different sample dimensions. It is found that with the decreasing gauge length and thickness, the tested yield strength increases. However, the sample inner/outer diameter has little effect on the dynamic torsional behaviour.Based on the finite element method, the stress states in the alloy with different sample sizes are analysed.Due to the effect of stress concentration zone(SCZ), the shorter sample has a higher yield stress.Furthermore, the stress distributes more uniformly in the thinner sample, which leads to the higher tested yield stress. According to the experimental and simulation analysis, some suggestions on choosing the sample size are given as well.     

The dynamic equations of motion for a two-component system

The motion of solid particles in a fluid flow is represented as a random process with independent increments. The resulting kinetic equation for the particle distribution has the form previously proposed [1]. The solution to this equation provides a system of equations for the hydrodynamics of the assembly of solid particles. These equations differ from ones previously proposed [2, 3] in having additional terms related to relative motion of the components, whose presence is due to anisotropy in the distribution of the normal stresses in the pseudogas.I am indebted to V. G. Levich for valuable discussions and for constant interest in the work.     

An interpretation of the yield behaviour of polymers in terms of correlated motion

An interpretation of yield behaviour in polymers is given in terms of the stress-activated flow of structural units over an energy barrier together with an additional correlated component to the motion. This correlated contribution takes account, in the simplest way possible, of the state of other conformations, and it is shown to lead to an effective activation-energy barrier which depends in part on the strain present at any time in the material. In this manner, the present work relates to previous work by M.G. Brereton, S.G. Croll, R.A. Duckett and I.M. Ward (1974), who, on purely phenomenological grounds, proposed a relation between stress and strain which had the form of a feedback equation. Specifically, the strain resulting from an applied stress was assumed to modify the material in a way which reduced its resistance to stress. The basic equation obtained here is non-linear and shows a yield-like behaviour resulting from a dynamical (as opposed to a geometrical) instability. Furthermore, it indicates a consistent relation between yield in creep tests and in constant strain-rate tests.     

On the dynamic behaviour of a beam with an accelerating mass

Summary The dynamic behaviour of an Euler beam traversed by a moving concentrated mass, is analyzed for the general case of a mass moving with a varying speed. The equation of motion in a matrix form is formulated using the Lagrangian approach and the assumed mode method. The dimensionless form of the equation enables the numerical results to be applicable for a wide range of system parameters. The possibility of the mass separating from the beam is analyzed by examining the contact forces between the mass and the beam during the motion.