Optimum synthesis of spatial function generator mechanisms

In this study a numerical method for optimum synthesis of spatial function generator four-bar linkages is presented. The key features of the method are: the embedding of the assembly criterion and of the transmission ratio in the penalty function; the non-derivative minimization procedure; the parametric variation of the first-guess mechanism. The effectiveness of the method is illustrated by means of examples of optimum design. In some examples articulated mechanisms, which can replace cam systems in automatic machinery, are synthesized.

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Sommario In questo studio si presenta un metodo per la sintesi ottimale di quadrilateri articolati spaziali generatori di funzione. Le principali caratteristiche del metodo proposto sono: l'inclusione del criterio di assemblabilità e dell'angolo di pressione nella funzione penalità; l'utilizzazione di un algoritmo di minimizzazione non derivativo; la variazione parametrica del meccanismo di primo tentativo. L'efficacia del metodo è messa in luce tramite una serie di esempi di progetto ottimale; in alcuni di essi sono stati sintetizzati dei quadrilateri spaziali in grado di sostituire i sistemi a camma spaziale nelle macchine automatiche.

     

Vibration and stability of an axially moving viscoelastic beam with hybrid supports

Vibration and stability are investigated for an axially moving beam constrained by simple supports with torsion springs. A scheme is proposed to derive natural frequencies and modal functions from given boundary conditions of an elastic beam moving at a constant speed. For a beam constituted by the Kelvin model, effects of viscoelasticity on the free vibration are analyzed via the method of multiple scales and demonstrated via numerical simulations. When the axial speed is characterized as a simple harmonic variation about the constant mean speed, the instability conditions are presented for axially accelerating viscoelastic beams in parametric resonance. Numerical examples show the effects of the constraint stiffness, the mean axial speed, and the viscoelasticity.     

Kinematic analysis of a novel pin-wheel joint

In this paper an innovative joint for the transmission of motion between parallel and incident axes is presented. It is made up of two frontal pin-wheels with cylindrical pins. The kinematics in case of parallel axes is discussed in detail. It is shown that, quite surprisingly, it may behave in many different ways, depending on the value of the center distance between the two axes. A systematic way to analyze the joint kinematics is provided.     

Dynamic instability of axially loaded shafts in the Mathieu map

It is shown that the Mathieu eigenvalues can be straightforwardly utilized to study the instability regions of an axially loaded simply supported shaft, the shaft being modeled as a continuous rotating beam. When a harmonic axial load is taken into account, the equation of motion of the system, here written according to the Lagrangian formulation of continuous systems, proves to be the Mathieu equation. It follows that the conditions for the stable or unstable motion of the shaft can be graphically investigated once the operation line corresponding to an actual rotating shaft is drawn in the Mathieu map.     

Vibration of an atomising disc subjected to a growing distributed mass

Centrifugal atomisation using a spinning disc is an effective means of producing high quality metal powder. The atomising disc frequently experiences severe vibration and produces noise. The vibration adversely affects the production of metal powder. This paper presents the first study of the dynamics of atomising discs. The disc is modelled as a plate under the excitation of a growing mass, which represents the metal stream flowing down to and spreading out on the disc. The influence of the rotating speed of the disc and the growing mass on the dynamics of the disc is investigated. It is found that the disc vibration is non-stationary with multiple frequencies that vary with time and its magnitude increases with mass flow rate of the model metal and decreases with the disc speed. One interesting finding is that the disc vibration grows like flutter in the period before the metal flow on the disc becomes steady, due to the radially growing mass.     

Cycle-to-cycle oscillations of heat release in a spark ignition engine

Fluctuations of combustion were studied using experimental time series of internal pressure in one of four cylinders in a spark ignition engine. Employing standard statistical methods like histograms and return maps, cycle-to-cycle variations of heat release were analyzed. A substantial difference in system behavior corresponding to quality of combustion was observed with a changing spark advance angle. Examining recurrence plots for a higher spark advance angle formation of specific patterns of vertical lines characteristic to intermittent behavior was found.     

Dynamic Response of a Piezoelectric Material with a Conducting Rigid Inclusion

The problem of a conducting rigid inclusion embedded in an infinite piezoelectric matrix is considered under the action of combined electromechanical impact loads. By using integral transform techniques, the mixed initial-boundary value problem for the case of anti-plane shear load and in-plane electric field is transformed into two systems of dual integral equations, the solutions of which give the singularity coefficients of electroelastic field near the inclusion tips in closed-form in the Laplace transform domain. Numerical results for the stress singularity coefficient in the physical space are presented graphically by numerically solving the resulting Fredholm integral equation and carrying out the numerical inversion of Laplace transform for a PZT-5H material with a conducting rigid line inclusion.     

Dynamic model and performance analysis of landing buffer for bionic locust mechanism

The landing buffer is an important problem in the research on bionic locust jumping robots, and the differ-ent modes of landing and buffering can affect the dynamic performance of the buffering process significantly. Based on an experimental observation, the different modes of landing and buffering are determined, which include the different numbers of landing legs and different motion modes of legs in the buffering process. Then a bionic locust mechanism is established, and the springs are used to replace the leg muscles to achieve a buffering effect. To reveal the dynamic performance in the buffering process of the bionic locust mechanism, a dynamic model is established with different modes of landing and buffering. In particular, to analyze the buffering process conveniently, an equivalent vibration dynamic model of the bionic locust mechanism is proposed. Given the support forces of the ground to the leg links, which can be obtained from the dynamic model, the spring forces of the legs and the impact resistance of each leg are the important parameters affecting buffering performance, and evaluation principles for buffering performance are proposed according to the aforementioned parameters. Based on the dynamic model and these evaluation principles, the buffer-ing performances are analyzed and compared in different modes of landing and buffering on a horizontal plane and an inclined plane. The results show that the mechanism with the ends of the legs sliding can obtain a better dynamic per-formance. This study offers primary theories for buffering dynamics and an evaluation of landing buffer performance, and it establishes a theoretical basis for studies and engineer-ing applications.     

The Space of Inextensional Displacements for a Partially Clamped Linearly Elastic Shell with an Elliptic Middle Surface

We consider a linearly elastic shell with an “elliptic” middle surface, clamped along a portion of its lateral face and subjected to body forces. Under weak regularity assumptions on the middle surface, we prove that the space of linearized inextensional displacements is reduced to zero, by using unique continuation results. Consequently, when the thickness of the shell goes to zero, the limit of the average with respect to the thickness of the three-dimensional displacement vector solves the “generalized membrane” shell model, according to the terminology introduced by P.G. Ciarlet and the first author. This revised version was published online in August 2006 with corrections to the Cover Date.     

Elastic field of a composite cylinder with a spatially varying dynamic eigenstrain

The analytical solutions of displacements and stresses for an eigenstrain problem in a composite bi-layered coaxial cylinder are presented in this article. The inner cylinder is assumed to undergo a dynamic, spatially varying eigenstrain. The spatial distribution of the eigenstrian is taken to be a quadratic polynomial with arbitrary coefficients along the radial direction. Furthermore, the eigenstrain is assumed to be harmonically time-dependent. Elasticity equations are constructed to directly solve the problem. The effect of spatial distribution, as well as the angular frequency of the eigenstrain on the elastic response of the composite cylinder has been illustrated graphically.     

内模控制及其在机构振动主动控制中的应用

振动主动控制通常采用最优控制,文中根据柔性机构的特点,采用内模控制策略。内模控制主要适合于具有周期性扰动信号的调节问题和具有周期性参考信号的跟踪问题,它的优点是对控对象参数具有鲁棒性,克服了最优控制需要精确掌握被控对象参数的缺点,文中首先介绍了内模控制的基本原理,然后给出了数值仿真结果,最后将算法应用柔性四连杆机构振动主动控制试验中,试验结果证明了方案的可行性。     

Vibration reduction of floating elastic plates in surface waves

Based on dynamical theories of water waves and dynamics of Mindlin thick plates,the investigation of the wave-induced responses and the vibration reduction of an elastic floating plate are presented using the Wiener-Hopf technique.Without regard to the case of elastic connector,the calculated results obtained by the present method are in good agreement with those from the literature and the experiment.It can be shown that the present method is valid.Relations between the spring stiffness to be used to connect the sea bottom and the floating plate and the parameters of wave-induced responses of floating plates are investigated using the present method.Therefore, these results can be used as theoretical bases for the design stage of super floating platform systems.     

Design and experimental validation of piecewise-linear state observers for flexible link mechanisms

The design of an observer estimating the state variables of a plant is an essential step towards the synthesis of high-performance model-based control schemes. In this paper, the problem of designing accurate state observers for flexible link mechanisms is tackled. The complexity of such a problem is considerable due to the nonlinear characteristics of flexible link mechanism dynamic models. Since nonlinear state observers have limited practical utility, in this work an investigation is made on the possibility of employing the Kalman filter theory together with suitable piecewise-linear truncated dynamic models. A general approach is developed and experimental results are given for the case of a four bar linkage with flexible links. Not only do these results confirm the theoretical and numerical results, but they also prove the practical effectiveness and efficiency of the proposed approach.     

Synchronization motions of a two-link mechanism with an improved OPCL method

An improved OPCL method is developed and applied to both small swing and giant rotation synchronization of a two-link mechanism. Transition processes of the two kinds of synchronization are discussed. Comparisons of different motion characteristics of the two-link synchronization and the effects of different control parameters on synchronous processes are investigated with numerical simulations.     

On displacements and stresses in a semi-infinite laminated layer: comparative results

This paper deals with some comparison results for displacements and stresses in a periodically stratified elastic semi-infinite layer determined within the framework of two approaches: (1) based on the homogenized model with microlocal parameters [Woźniak (1987) Int J Eng Sci 25: 483–499; Woźniak (1987) Bull Ac Pol Tech Sci 35: 143–151]; (2) obtained directly from the theory of elasticity. A body is assumed to be composed of n elastic two-component periodically repeated laminae. The perfect mechanical bonding between the layers is assumed. The normal displacements and zero shear stresses on the boundary being a cross-section of the composite component are taken into account. The lateral boundary surfaces are assumed to be rigid fixed. The obtained results from the two approaches are compared and presented in the form of figures.     

Electroelastic Analysis of an Internal Interface Crack in a Half-Plane Consisting of Two Bonded Dissimilar Piezoelectric Quarter-Planes

The problem of an interface crack in a half-plane consisting of two bonded dissimilar piezoelectric quarters is considered under antiplane shear and inplane electric loading. The problem is solved under the electrically permeable assumption for a crack. The integral transform technique is employed to reduce the problem to triple integral equations, which is further converted to a hypersingular integral equation for the crack sliding displacement. By solving the resulting equation analytically, the electroelastic field along the interface and the energy release rate are obtained in explicit form, respectively. Several examples are given to illustrate the influence of the material properties and the crack position on the energy release rate.     

Vibration band gap analysis of a new periodic beam model using GDQR method

In this study, a new periodic beam model is introduced. This beam consists of the concentrated rigid masses and tapered beam elements with linearly variable width. The theoretical equations are derived by employing the Euler-Bernoulli beam and the Bloch–Floquet theorem and then solved using the generalized differential quadrature rule method to calculate the first two band gaps. The effects of the mass, mass moment of inertia and taper ratio on the widths and central frequencies of the first two band gaps are investigated. Results show that the wide band gaps at low frequency ranges can be obtained by changing the geometrical parameters. This is of interest for different applications of the band gap phenomenon such as broadband piezoelectric energy harvesting. Finally, the finite element simulation (ANSYS software) is used to validate the analytical method and good agreement is found.     

Vibration reduction evaluation of a linear system with a nonlinear energy sink under a harmonic and random excitation

The nonlinear behaviors and vibration reduction of a linear system with a nonlinear energy sink(NES) are investigated. The linear system is excited by a harmonic and random base excitation, consisting of a mass block, a linear spring, and a linear viscous damper. The NES is composed of a mass block, a linear viscous damper, and a spring with ideal cubic nonlinear stiffness. Based on the generalized harmonic function method,the steady-state Fokker-Planck-Kolmogorov equation is presented to reveal...