Mechatronic system with shunted piezoelectric damper modelled with structural damping

Paper presents analysis of an one-dimension flexural vibrating mechatronic system. The considered system is a cantilever beam with a piezoelectric transducer bonded to the beam's surface. An external electric circuit is adjoined to the transducer's clamps in order to damp vibrations. System was analyzed on the basis of an approximate Galerkin method. Verification and assumptions of the approximate method were described in the previous papers where analysis of the mechatronic system with piezoelectric shunt damper was presented. Structural damping of all system's components was being taken into consideration. Rheological properties were introduced using Kelvin-Voigt model of materials. Influences of component's structural damping coefficients values on the system's dynamic flexibility were defined. Obtained results were presented on 3D graphs as dynamic flexibility dependence on the structural damping coefficient and frequency of an external force that was applied to the system. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Calculation of Flexibility of Vibrating Beam as the Subsystem of Mechatronic System by Means the Exact and Approximate Methods

The main aim of this paper is to investigate the transients of characteristics of vibrating beams obtained by the exact and approximate methods and to answer to the question – if the method can be used to nominate the characteristics of mechatronic systems. The approach was to nominate the relevance or irrelevance between the characteristics obtained by considered methods – especially concerning the relevance of the natural frequencies-poles of characteristics of mechanical part of mechatronic system. The main subject of the research is the continuous vibrating beam. Findings of this approach is fact, that approximate solutions fulfill all conditions for vibrating beams and some conditions only, particularly for vibrating beams as the subsystems of mechatronic systems. Practical implications of this paper is the main point is the analysis and the examination of flexibly vibrating discrete-continuous mechatronic systems which characteristics can be nominated with approximate methods only. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Interpolation of Vector – Valued Banach Lattices and Calderón – Lozanovskii Construction

We establish the connection between the variants of Schechter's complex interpolation methods, Peetre – Gustavsson's interpolation methods, and the Calderón – Lozanovskii construction on vector – valued Banach lattices. As applications, we show that the uniform convexity and the UMD property are stable by interpolation.     

Algorithm of Exact Methods Obtaining of the Solution and Dynamical Flexibilities of Subsystem of the Mechatronic system

In this paper the application of analysis of transverse vibrating subsystem of mechatronic systems by means of the exact were the main purposes of work to solve the task of assignment of frequency-modal analysis and characteristics of mechatronic system. At first the problem of analysis in the form of the one differential equation of motion of mechanical subsystem or of the set of state equations of considered mechatronic model of object has been formulated and solved. Classic method to solve this problem have been used. The considered transverse vibrating mechanical subsystems of mechatronic system are a continuous beams with constant cross-section, with free ends and/or clamped on one end. A ring transducer, which is the integral part of mechatronic system, extorted by harmonic force or voltage excitation, is assumed to be perfectly bonded to the beam surface. Parameters of the transducer have important influence on values of natural frequencies and on form of characteristics of considered mechatronic system. The poles of dynamical characteristic calculated by mathematical exact method and the Galerkin's method have approximately different or the same values; it is depended on the combination of boundary conditions of elementary beam. The results of the calculations were not only presented in mathematical form but also as a transients of examined dynamical characteristic which are function of frequency of assumed excitation. Practical implications of this work is to present the introduction to synthesis of considered class of mechanical and/or mechatronic beam-systems with a constant changeable cross-section. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The exact and approximate method in mechanical system's analysis

The main aim of this work is to present results of the mechanical system's analysis based on the exact and approximate Galerkin's methods. The considered system is the flexural vibrating one-dimension bending beam. The exact and approximate method were used to assign the dynamic flexibility of the considered system and results of this work were juxtaposed to verify the approximate method's accuracy. The correction coefficients were introduced into the approximate method to unify results of both methods. The aim of this work was to check accuracy of the approximate method and to verify if this method may be used to mechatronic system's analysis, where it is impossible to use the exact method. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermomagnetic convection induced by a time-modulated driving force in magnetic fluids

It is well-known that the flow properties of magnetic fluids – so called ferrofluids – can be modified by applying an external magnetic field. Under certain conditions, the magnetic force induced by this external field causes a convective flow. What has yet to be investigated is what happens when this driving force is modulated in time. For this purpose, a horizontal ferrofluid layer has been exposed to an intermittent magnetic field, which causes a time-modulated force. This force depends on the strength of the external magnetic field and the fluid temperature, and therefore the flow phenomenon generated is called thermomagnetic convection. In addition, if the fluid layer is heated from below, the classical thermal convection contributes to the flow system. In our studies, both effects – thermomagnetic and thermal – contribute together to the convection. The experimental results presented here confirm previous theoretical investigations about the influence of the frequency of the driving force on the strength of the convective flow, which reach minimum values at certain frequencies. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Frequency characteristics of flexibly vibration discrete-continuous mechatronic system

The purpose of this paper is formulating of problem of flexibly vibrating mechatronic system. The main approach of the subject was to formulate the problem in the form of set of differential equation of motion and state equation of considered mechatronic model of object. The considered flexibly vibrating mechanical system is a continuous beam, clamped at one of its end. Integral part of mechatronic system is a transducer, extorted by harmonic voltage. In the paper the linear mechanical subsystem and linear electric subsystem of mechatronic system has been considered. The methods of analysis and obtained results can be base on design and investigation for this type of mechatronic systems. The mechatronic system formed from mechanical and electric subsystems with electromechanical bondage has been considered. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

DNS of laminar separation nubble flows with free-stream fluctuations

A series of Direct Numerical Simulations (DNS) of Laminar Separation Bubble (LSB) flow in the presence of external disturbances has been performed. In all simulations, the primary mechanism for the transition to turbulence was found to be a two-dimensional Kelvin-Helmholtz (KH) instability of the separated shear layer that was triggered by the external fluctuation(s). The KH instability caused the shear layer to roll up. Inside the rolled up shear layer, entrained disturbances triggered elliptic instabilities which led to a rapid transition to fully three-dimensional (3D) turbulence. In the simulations with inflow oscillations the streamwise variation of the location of transition was found to decrease with the amplitude of the inflow oscillation. In the simulations with free-stream turbulence the size of the separation bubble – measured by the shape factor – was found to drastically decrease with increasing free-stream turbulence level. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mechatronic Subsystem Studied of Approximate Method Modeled by Hypergraph

The transverse vibrating mechatronic subsystem is considered. Integral parts of this system are: a continuous beam with known boundary conditions and a transducer, extorted by harmonic voltage excitation, to be perfectly bonded to the beam surface. Findings this article are dynamical characteristics of the discussed mechatronic and mechanical system to model them by hypergraphs. Research limitation is that the linear mechanical subsystem and linear electric subsystem of mechatronic system has been considered, however for this kind of systems the approach is sufficient. Practical implications of this researches was that global approach is presented, that means in the domain of frequency spectrum analysis. The methods of analysis and obtained results can be base of design and investigation for this type of mechatronic systems. Originality of this paper is that the mechatronic system created from mechanical and electric subsystems with electromechanical bondage has been considered. This approach is different from those considered so far because is it relies on application approximate methods of analysis of mechatronic subsystem and modeling the one by hypergraph [1-7]. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of parametric modulation on the onset of thermomagnetic convection

Magnetic fluids – so called ferrofluids – are suspensions of nano-scaled particles in an appropriate carrier liquid. The flow properties of these fluids can be influenced by applying an external magnetic field. It is possible to introduce a magnetic force in a horizontal ferrofluid layer which is able to drive a convective flow. The magnetic force arises in the presence of an external magnetic field if a temperature gradient exists in the fluid gap. The behaviour of the onset of convection depends on the strength of the external magnetic field and on the temperature gradient. In this paper the onset of convection under the influence of time-modulated magnetic field has been investigated. The experimental results presented here show a shift in the onset of convection depending on the frequency of the external magnetic field. This behaviour confirms in principle the theoretical predictions which are also presented here. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A mathematical model of oxidation of Co in a thin layer of a Pd zeolite catalyst

We construct and study a distributed mathematical model of oxidation ofCO in a planar layer of aPd zeolite catalyst. The model is a system of ordinary differential equations describing a chain of locally connected chemical oscillators. Each oscillator is an oscillatory process of the reaction occurring in the corresponding layer of zeolite. The peculiarity of this chain system is that the connection between the oscillators is parametric, since it is implemented through diffusion ofCO in the gaseous phase. We find conditions for existence and uniqueness of various types of oscillations in the system, including synchronous, quasi-periodic, and chaotic. We construct the phase diagram on the plane of two external parameters and give a bifurcation analysis, studying the scenario of transition to chaos. Two tables, 12 figures. Bibliography: 15 titles. Translated fromProblemy Matematicheskoi Fiziki, 1998, pp. 113–132.     

Integrated circuit generating 3- and 5-scroll attractors

This paper introduces the experimental realization of the first integrated circuit of a multi-scroll continuous chaotic oscillator showing 3- and 5-scroll attractors. It is based on a variant of the Chua’s system. The most relevant issue is the implementation of a saw-tooth-like nonlinear function, which is designed by using floating gate MOS (FGMOS) transistors. Therefore, the realization of a voltage-to-current nonlinear cell by a piecewise-linear approach allows us to have only two external control inputs instead of numerous external voltage references, as usually done in current circuit realizations. Experimental results of the proposed integrated multi-scroll oscillator along with its corner analysis are provided.     

Quadratic optimal synchronization of uncertain chaotic systems

This paper investigates the quadratic optimal synchronization of uncertain chaotic systems with parameter mismatch, parametric perturbations and external disturbances on both master and slave systems. A robust control scheme based on Lyapunov stability theory and quadratic optimal control approach is derived to realize chaotic synchronization. The sufficient criterion for stability condition is formulated in a linear matrix inequality (LMI) form. The effect of uncertain parameters and external disturbance is suppressed to an H_∞ norm constraint. An adaptive algorithm is proposed to adjust the uncertain bound in the robust controller avoiding the chattering phenomena. The simulation results for synchronization of the Chua’s circuit system and the Lorenz system demonstrate the effectiveness of the proposed scheme.     

Mechatronic Design of the 2 DOF PRRRP Parallel Robot

Mechatronics consists in integration of three fields in engineering: mechanics, electronics and information technology. The paradigm of mechatronics is the integration concept, being the first step in the design of complex mechatronic systems. The need for an integrated approach to the design of complex engineering system involving electronic engineering, mechanical engineering and computing has led to the growth of the concept of mechatronics. The paper presents details regarding the integration process for the kinematic axis in mechatronic. The example of the positioning system based on dc motor and screw–nut transmission is analysed. This actuator is further used for driving a 2 DOF PRRRP parallel robot. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Note on models

The first part of this note deals with the importance of the polytechnical tradition for mathematical models.¹ In the second part I discuss the question of the “semantic shift” in the mathematical usage of the word “model” (M. Epple),² that means, the passage from concrete material objects to models in the modern sense of the word – abstract entities satisfying a certain system of axioms. My aim is to provide some new information on the theme and to open a new and in my opinion essential aspect – the polytechnical tradition – to look at it. The two parts are only in a loose connection.     

Some two-echelon style-goods inventory models with asymmetric market information

A “two-echelon” newsboy problem considers the interactive decisions between the “manufacturer” and the “retailer” – now recognized as two separate entities. Earlier papers on this problem assumed that the two parties share the same market information. We extend this problem by studying the situation in which the retailer has better market information than the manufacturer. Presented are several decision models that should be useful for guiding a manufacturer's decisions. Moreover, solutions to these models lead to various unexpected and interesting conclusions. For example, we found that improved retailer's market-knowledge always benefits the manufacturer and the system, though not necessarily the retailer himself. In contrast, improved manufacturer's knowledge benefits only the manufacturer himself at the expense of the retailer and of the system.     

Nonstandard singular perturbation systems and higher index differential-algebraic systems

In order to obtain trajectory approximation results for a given singular perturbation system (SPS), two systems are derived from it: the slow and the fast one. Tikhonov's theorem gives sufficient conditions on them to ensure a good approximation for a standard SPS, i.e., its corresponding slow system is a differential-algebraic system (DAS) of index 1. In this paper it is shown that a nonstandard SPS with the parameter set to zero can be seen as a DAS of higher index. This connection allows us to obtain a Tikhonov's theorem when this DAS is of index 2.     

Two-dimensional Green's function of orthotropic three-phase material under a normal line force with application in the design of composite

Green's function of orthotropic three-phase material is an important and basic problem in the study of mechanics of materials. It is also the foundation of further theoretical researches and engineering applications. Most of adhesive structures in engineering can be well simulated by the mechanical model of orthotropic three-phase material, such as composite laminate, integrated circuit (IC) packaging, micro-electro-mechanical systems (MEMS) and biomedical materials, etc. In order to understand the mechanical properties of the adhesive structure, a two-dimensional Green's function of orthotropic three-phase material loaded with a normal line force is presented. Based on the Green's function proposed in this paper, the stress field of adhesive structure under arbitrary normal loadings can be obtained with superposition method. Besides, this Green's function is convenient to be used in further studies, because it is expressed explicitly in form of elementary functions. Numerical examples are proposed to study the mechanical properties of the adhesive structure in five difference aspects: (1) the distribution rule of stress fields of the adhesive structure; (2) the influence from fiber orientation of composite to the stress fields of the adhesive structure; (3) the influence from elastic modulus of adhesive layer to the stress transfer of the adhesive structure; (4) the influence from the thickness of adhesive layer to the stress transfer of the adhesive structure; (5) the reasonability of spring interface model.     

On quasi-static models hidden in Maxwell's equations

In this paper we introduce the electromagnetic quasi-static models in a simple but meaningful way, relying on the dimensional analysis of Maxwell's equations. This analysis puts in evidence the three characteristic times of an electromagnetic phenomenon. It allows to define the range of validity of well-known models, such as the eddy-current (MQS) or the electroquasistatic (EQS) ones, and thus their pertinence to describe a given phenomenon. The role of the so-called “small parameters” of a model is explained in detail for two classical examples, namely a capacitor and a solenoid. We show how the MQS and EQS models result from having replaced fields by their first order truncations of Taylor expansions with respect to these small parameters. We finally investigate the connection between quasi-static models and circuit theory, clarifying the role of the fields with respect to classical circuit elements, and provide an example of application to study the electromagnetic fields in a simple case.     

Hopf bifurcation and the centers on center manifold for a class of three-dimensional Circuit system

In this paper, Hopf bifurcation and center problem for a generic three-dimensional Chua's circuit system are studied. Applying the formal series method of computing singular point quantities to investigate the two cases of the generic circuit system, we find necessary conditions for the existence of centers on a local center manifold for the systems, then Darboux method is applied to show the sufficiency. Further, we determine the maximum number of limit cycles that can bifurcate from the corresponding equilibrium via Hopf bifurcation.