沉痛悼念许兵先生

通过对胞壁随机移除的蜂窝结构动态变形过程的有限元模拟,分析了随机缺陷对蜂窝 结构变形模式的影响,得到蜂窝结构在两个加载方向上的变形模式图及不同模式间转换的临 界速度. 对含缺陷蜂窝结构平台应力的研究发现,当变形模式为过渡模式或动态模式时结构 平台应力与冲击速度的平方成线性关系. 相同密度下,低缺陷蜂窝结构的平台应力在由过渡 模式向动态模式转变的临界速度附近高于规则蜂窝结构,较高的随机缺陷则使蜂窝结构的平 台应力在由准静态模式向过渡模式转变的临界速度附近显著下降. 关键词：多孔材料,蜂窝,缺陷,平台应力,有限元分析     

The study on the chaotic motion of a nonlinear dynamic system

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The dynamic coupling of left ventricle and systemic arteries

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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.     

Swelling effect on the dynamic behaviour of composite cylindrical shells conveying fluid

This paper presents a semi‐analytical investigation of a fluid–structure system. Both isotropic and composite cylindrical shells filled with or subjected to a flowing fluid have been considered in this study. The structure may be uniform or non‐uniform in the circumferential direction. The hybrid finite element approach, shearable shell theory and velocity potential flow theory have been combined to establish the dynamic equations of the coupled system. The set of matrices describing their relative contributions to equilibrium is determined by exact analytical integration of the equilibrium equations. The linear potential flow theory is applied to describe the fluid effects that lead to the inertial, centrifugal and Coriolis forces. The axisymmetric, beam‐like and shell modes of vibrations in both cases of uniform and non‐uniform cylindrical shells are investigated. Fluid elastic stability of a structure subjected to a flowing fluid is also studied. This theory yields the high and the low eigenvalues and eigenmodes with comparably high accuracy. Reasonable agreement is found with other theories and experiments. Copyright © 2005 John Wiley & Sons, Ltd.     

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.     

含裂纹梁非线性静动力特性及简化动力学建模Static and dynamic behaviour of cracked beam and simplified dynamic model

主要研究裂纹对梁结构动力特性的影响规律,进而为含裂纹梁结构状态监测提供理论依据。首先,对裂纹影响区域进行分析,建立含裂纹梁二维接触非线性有限元模型,阐明含裂纹梁具有拉压不同刚度的静力特性;其次,通过对机理模型的分析,指出拉压不同刚度会引起轴向与弯曲的耦合振动;然后,通过非线性动力学分析方法研究其动力特性,观察到含裂纹梁在冲击荷载下会产生轴向与弯曲的耦合振动现象,并指出这种轴向与弯曲耦合振动的一个重要特征是轴向振动频谱图中含有弯曲振动基频的两倍频成分;最后,通过引入非线性弹簧建立一种新颖的含裂纹梁简化动力学模型,通过与精细有限元分析对比,验证了模型的合理性。该简化动力学模型将接触非线性问题转换为材料非线性问题,避免了费时的接触非线性动力学求解过程。     

作大范围运动矩形板的动力学建模理论研究

研究了初应力法的作大范围运动矩形板的建模理论。根据连续介质理论,考虑应变-位移中的非线性项,用一致质量有限元法对柔性板进行离散,基于Jourdain速度变分原理导出定轴转动下大范围运动为自由的柔性板刚-柔耦合动力学方程。从其刚柔耦合动力学方程出发,考虑在大范围运动已知情况下的结构动力学方程。通过引入准静态概念,把其结构动力学方程转化为准静态方程。对纵向和横向变形节点坐标进行坐标分离,解出与纵向变形相关的准静态方程,得到准静态时的纵向应力表达式,从而获得附加刚度项;并对此非惯性系下作大范围运动柔性板的结构动力学方程进行数值仿真,验证了采用初应力法柔性板的动力学建模方法来计算经历大范围运动的不规则柔性板的动力学响应是可行的,体现了初应力法对柔性板建模的优越性。     

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.     

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.     

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.

     

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.     

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.     

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.     

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.