Bridging scales: An attempt to incorporate cellular responses within a three-dimensional FEM model of active muscle contraction

A mathematical model of the cellular responses of skeletal muscles has been integrated within a three-dimensional biomechanical Finite Element (FEM) model. The FEM model is based on a tri-cubic Hermite Finite Element discretisation of the governing equations of finite elasticity theory and a transversely isotropic constitutive law. To incorporate the cellular information, homogenised values of key physiological parameters, e.g. the pre- and post-power stroke concentration of crossbridge attachments, are computed at the Gauss points of the FEMintegration scheme. These values are then used to modify the stress tensor in such a way that it resembles the contractile response. The advantages of such an improved three-dimensional FEM model are far reaching. These models can be used, for example, to investigate and study local muscle contraction, muscle recruitment patterns, force generation, or fatigue response of skeletal muscles. As an illustrative example, one twitch of the tibialis anterior, in which 25% of the muscle fibres are excited by a nerve stimulus, is simulated. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Exact boundary controllability of vibrating non-classical Euler–Bernoulli micro-scale beams

This study investigates the exact controllability problem for a vibrating non-classical Euler–Bernoulli micro-beam whose governing partial differential equation (PDE) of motion is derived based on the non-classical continuum mechanics. In this paper, it is proved that via boundary controls, it is possible to obtain exact controllability which consists of driving the vibrating system to rest in finite time. This control objective is achieved based on the PDE model of the system which causes that spillover instabilities do not occur.     

Modifications of hypergraphs of subsystems of mechatronic system as an effect of their analysis by means of different methods

Purpose of this paper is creating of the hypergraphs of the beam concerning of two methods of analysis of vibrating beam by the exact and approximate methods. This approach make possible to nominate the relevance or irrelevance between the characteristics obtained by considered methods – especially concerning the relevance of the natural frequencies-poles of beams characteristics. The main subject of the research is the continuous free-sliding (F-S) beam as a subsystems of vibrating beam-system. Findings this approach is a fact, that approximate solutions fulfill all conditions for vibrating beams and can be introduction to synthesis of these systems modeled by hypergraphs. Research limitation is that linear continuous transverse vibrating (F-S) beam is considered. Practical implications of this study is the main point is the introduction to synthesis of transverse vibrating continuous beam-systems. Originality of this approach considers the application Galerkin's method which concerns the analysis of beams and modeling them of transformed hypergraphs. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

我国军事人才能力素质测评方法研究

围绕我国各类军事人才能力素质的测评,以某部为实证对象,按照总政治部有关人才考评的文件精神和未来信息化战争对人才的要求,构建了军队人才测评指标体系和测评方法,并对当前军队人才培养的主要途径进行了比较分析,研究结果表明,通过构建科学的测评指标体系和测评方法,能够对部队各种人才的能力素质进行科学、定量的评估,为选好用好人才提供科学依据;研究结果也表明,当前军队自行培养人才和委托地方科研院所培养人才的方式各有优劣,需要进行资源、信息等各方面的融合互补,     

An inverse eigenvalue method for frequency isolation in spring–mass systems

The action of external vibrating forces on mechanical structures can cause severe damages when resonance occurs. The removal of natural frequencies of the structure from resonance bands is therefore of great importance. This problem is called frequency isolation problem and is the subject of this paper. A new inverse eigenvalue method is proposed and applied to spring–mass systems, which have generated much interest in the literature as prototypes of vibrating structures. The novelty of the method lies in using the zeros of the frequency response function at the last mass as control variables in an optimization problem to minimize the impact of redesign. Numerically accurate algorithms for computing the sensitivity with respect to the control variables are presented, which form the basis of an efficient multidimensional search strategy to solve the frequency isolation problem. Copyright © 2001 by John Wiley & Sons, Ltd.     

Solution of Inverse Task of Mechatronic Systems by Means the Classical and Unclassical Methods of Modelling and Analysis

In this paper the modelling by means of the different category graphs and analysis of vibrating subsystem of mechatronic systems by means of the exact and approximate methods have been presented. That approach was to nominate the relevance or irrelevance between the characteristics obtained by means of the exact method (only for the mechanical subsystem) and the approximate method. Such formulation concerns mostly the relevance of the natural frequencies-poles of the characteristics both mechanical subsystems and mechatronic systems. Approximate solutions requiring all the conditions for vibrating mechanical and/or mechatronic systems have been finding and it may be introduction to synthesis of these systems, modeled by different category graphs. Research limitation is following, that torsional vibrating continuous mechanical subsystem and mechatronic systems are linear type. Presentation the introduction to synthesis of considered class of mechatronic bar-systems with a constant changeable cross-section is practical implications of this work. Originality of such formulation is focused on the use of the different category graphs for modelling and synthesising by different methods represented by graphs of vibrating bars to the synthesis of considered discrete-continuous mechatronic systems. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On boundary controllability of one-dimensional vibrating systems

In this paper boundary controllability of one-dimensional vibrating system such as the vibrating string or the vibrating beam is studied. In particular we are concerned with the question whether it is possible to transfer a given initial state of vibration into rest within a given time such that the system stays in rest when the control is turned off. This problem is rephrased as a typical trigonometric moment problem which is solved within the framework of an abstract moment problem in a Hilbert space. The results of null-controllability which are obtained are substantially based on classical results of Ingham and Redheffer concerning trigonometric inequalities and incompleteness of certain sequences of trigonometric functions, respectively. The representation of the general statements follows closely the lines of a paper of Russell. Besides a special case is treated where explicit representations of boundary controls can be given that transfer the system to a permanent rest position. This special case includes amplitude boundary control of the vibrating string and the freely supported beam.     

Tabu search with strategic oscillation for the maximally diverse grouping problem

We propose new heuristic procedures for the maximally diverse grouping problem (MDGP). This NP-hard problem consists of forming maximally diverse groups—of equal or different size—from a given set of elements. The most general formulation, which we address, allows for the size of each group to fall within specified limits. The MDGP has applications in academics, such as creating diverse teams of students, or in training settings where it may be desired to create groups that are as diverse as possible. Search mechanisms, based on the tabu search methodology, are developed for the MDGP, including a strategic oscillation that enables search paths to cross a feasibility boundary. We evaluate construction and improvement mechanisms to configure a solution procedure that is then compared to state-of-the-art solvers for the MDGP. Extensive computational experiments with medium and large instances show the advantages of a solution method that includes strategic oscillation.     

Symmetry and bifurcation in vestibular system

The vestibular system in almost all vertebrates, humans included, controls balance by employing a set of six semicircular canals, three in each inner ear, to detect angular accelerations of the head. Signals from the canals are transmitted to neck motoneurons and activate eight corresponding muscle groups. These signals may be either excitatory or inhibitory, depending on the direction of acceleration. McCollum and Boyle have observed that in the cat the network of neurons concerned possesses octahedral symmetry, a structure deduced from the known innervation patterns (connections) from canals to muscles. We re-derive the octahedral symmetry from mathematical features of the probable network architecture, and model the movement of the head in response to the activation patterns of the muscles concerned. We assume that connections among neck muscles can be modeled by a ‘coupled cell network’, a system of coupled ODEs whose variables correspond to the eight muscles, and that network also has octahedral symmetry. The network and its symmetries imply that these ODEs must be equivariant under a suitable action of the octahedral group. Using results of Ashwin and Podvigina, we show that with the appropriate group actions, there are six possible spatiotemporal patterns of time-periodic states that can arise by Hopf bifurcation from an equilibrium corresponding to natural head motions. (© 2008 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)     

Modelling and Flatness‐Based Control of a Carriage Actuated by Pneumatic Muscles

Pneumatic muscles are innovative tension actuators consisting of textile‐fibre reinforced vulcanised rubber tubing and connection flanges at both ends. They offer several advantages as compared to pneumatic cylinders: significantly less weight, no moving parts within the muscle, and higher maximum force. The main drawback is given by their non‐linear characteristics demanding for sophisticated non‐linear feedback control schemes. This contribution presents a non‐linear control concept for a carriage driven by two pneumatic muscles in parallel connection. First, the modelling of the muscle driven carriage is described in detail. For the resulting non‐linear model the differential flatness property is proven and utilised for a decoupled position and pressure trajectory control. Experimental results from an implementation of this flatness‐based control scheme at a test rig demonstrate the high tracking performance and point out the potential of this new actuator. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A unified approach via convexity for optimal energy decay rates of finite and infinite dimensional vibrating damped systems with applications to semi-discretized vibrating damped systems

The Liapunov method is celebrated for its strength to establish strong decay of solutions of damped equations. Extensions to infinite dimensional settings have been studied by several authors (see e.g. Haraux, 1991 [11], and Komornik and Zuazua, 1990 [17] and references therein). Results on optimal energy decay rates under general conditions of the feedback is far from being complete. The purpose of this paper is to show that general dissipative vibrating systems have structural properties due to dissipation. We present a general approach based on convexity arguments to establish sharp optimal or quasi-optimal upper energy decay rates for these systems, and on comparison principles based on the dissipation property, and interpolation inequalities (in the infinite dimensional case) for lower bounds of the energy. We stress the fact that this method works for finite as well as infinite dimensional vibrating systems and as well as for applications to semi-discretized nonlinear damped vibrating PDE's. A part of this approach has been introduced in Alabau-Boussouira (2004, 2005) [1] and [2]. In the present paper, we identify a new, simple and explicit criteria to select a class of nonlinear feedbacks, for which we prove a simplified explicit energy decay formula comparatively to the more general but also more complex formula we give in Alabau-Boussouira (2004, 2005) [1] and [2]. Moreover, we prove optimality of the decay rates for this class, in the finite dimensional case. This class includes a wide range of feedbacks, ranging from very weak nonlinear dissipation (exponentially decaying in a neighborhood of zero), to polynomial, or polynomial-logarithmic decaying feedbacks at the origin. In the infinite dimensional case, we establish a comparison principle on the energy of sufficiently smooth solutions through the dissipation relation. This principle relies on suitable interpolation inequalities. It allows us to give lower bounds for the energy of smooth initial data for the one-dimensional wave equation with a distributed polynomial damping, which improves Haraux (1995) [12] lower estimate of the energy for this case. We also establish lower bounds in the multi-dimensional case for sufficiently smooth solutions when such solutions exist. We further mention applications of these various results to several classes of PDE's, namely: the locally and boundary damped multi-dimensional wave equation, the locally damped plate equation and the globally damped coupled Timoshenko beams system but it applies to several other examples. Furthermore, we show that these optimal energy decay results apply to finite dimensional systems obtained from spatial discretization of infinite dimensional damped systems. We illustrate these results on the one-dimensional locally damped wave and plate equations discretized by finite differences and give the optimal energy decay rates for these two examples. These optimal rates are not uniform with respect to the discretization parameter. We also discuss and explain why optimality results have to be stated differently for feedbacks close to linear behavior at the origin.     

Brief note: viscoelastic modelling of cantilever vibration absorbers

Internal damping is considered in a cantilever beam supported on a single degree-of-freedom vibrating system. The internal damping mechanism is modelled by a Voigt viscoelastic coefficient in the stress-strain law. The governing equations reduce to a partial differential equation with time-dependent boundary conditions. The solution yields expressions for the amplitude ratio in terms of the tuning and frequency ratios, as well as the viscoelastic damping coefficient. These results are simulated numerically on the computer to obtain three different plots of the frequency response. The first plot has parametric values of the number of cantilevers. In the second plot, three parametric values of the internal damping coefficient are portrayed; the third plot shows the frequency response with various values of the natural frequency of the main system. These results show advantages in using cantilever beams with internal damping as dynamic vibration absorbers.     

Quasi-dynamical systems and the stabilization of elastic vibrations with controls whose range is restricted to a finite number of values

This paper concerns the stabilization of a certain class of control problems, which require the controls to have only a finite number of values. The problem is approached by quasi-dynamical system theory. A stabilization strategy is given for the vibrating beam cantilevered at one end and with the control force restricted to have a finite number of values.     

基于小波分形理论的股价指数信息量测度研究

本把小波分析和分形理论引入到股价指数时间序列的分析中，给出了股价指数波动复杂性的信息量测度方法——信息熵和分形维方法。通过对上证综指和深证成指1994年1月3日至2002年3月4日期间的数据进行的实证分析显示，两种方法均能刻画股价指数波动的复杂程度，这对初步了解我国股市场的波动规律有一定的实际意义。     

Absence of Critical Mass Densities for a Vibrating Membrane

We study the dependence of the eigenvalues of a N-dimensional vibrating membrane upon variation of the mass density. We prove that the elementary symmetric functions of the eigenvalues depend real-analytically on the mass density and that such functions have no critical points with constant mass constraint. In particular, the elementary symmetric functions of the eigenvalues, hence all simple eigenvalues, have no local maxima or minima on the set of those mass densities with a prescribed total mass.     

A Modal Analysis of Resonance during the Whole-Body Vibration

The mechanism of resonance of a damping system of multi‐degrees of freedom such as the human body and the dependence of resonance on system parameters, particularly on the damping level, are studied in terms of detailed mathematical solutions of both the whole‐body vibrations and the eigen modes for a simple model. It is revealed that resonance would only occur near the eigen frequencies of neutral modes for which the complex eigen frequencies of the corresponding damping modes for the given damping level of the system have not moved far from the starting point (damping‐free case) along the corresponding tracks in the plane of complex eigen frequency yet. The major resonance would occur near the eigen frequency of the neutral mode where the modulus of the characteristic function of the system has the strongest, i.e., the deepest and sharpest, local minimum. For the present model, this neutral mode is the lowest neutral mode. It is found that the resonance and eigen frequencies increase with the stiffness of muscles and decrease with the body mass, with the portion of wobbling mass in the upper body, and with the portion of upper body mass in the whole body. Both the modal analysis and the analysis of the whole‐body vibration show that the phase differences among different parts of the system are still small at the unique or the lowest resonance frequency and increase dramatically only when the frequency of the vibrating source goes beyond the resonance frequency. Thus, some effects of body vibrations, e.g., internal loads, may reach their maximum not at the resonance frequency, but at a frequency somewhat higher than the resonance frequency. This may account for the fact that the frequency ranges for abdominal pain and for lumbosacral pain caused by body vibrations are not exactly the same as the frequency range for major body resonance but shifted to somewhat higher frequency ranges. It is therefore suggested that the frequency used for strength training in terms of vibrating devices should be above 20 Hz in order to avoid not only the major resonance but also the maximal internal loads.     

Hereditary effects of exponentially damped oscillators with past histories

This paper presents hereditary effects of exponentially damped oscillators with past histories. Unlike the classical viscously damped oscillators, the nonviscously damped ones involve damping forces which depend on time-histories of vibrating motions via convolution integrals. As a result, equations of motion of such systems are a set of coupled second-order Volterra integro-differential equations. In this work, initial value problems for the integro-differential equations are revisited. The initial conditions should contain time-histories of vibrating motions. Then, initialization response of exponentially damped oscillators is obtained. It is used to characterize the hereditary effects on the dynamic response. At last, stability of initialization response is proved from the theoretical viewpoint and verified by numerical simulations. This reveals that the hereditary effects gradually recede with increasing of time.     

A Case Study in the Use of Computer-Based Training in Statistical Process Control

This article describes a pilot case study in the use of computer-based training (C.B.T.) in statistical process control (S.P.C.) for suppliers of parts and small components to a major manufacturer of automotive components. It is argued that C.B.T. has particular advantages over other forms of training, particularly where statistical concepts are involved.     

An evaluation of technical efficiency and managerial correlates of solid waste management by Welsh SMEs using parametric and non-parametric techniques

Strong economic growth and environmental regulation stimulus make Welsh small and medium enterprises' (SMEs) sustainability performance merit investigation in the context of European Union (EU) sustainability initiatives. This is due in part to strong economic growth and the stimulus provided by environmental regulation. We use stochastic frontier analysis, a parametric econometric technique to generate estimates of the technical efficiency of solid waste management by 299 Welsh SMEs in 2003. We demonstrate that the ranking and efficiency scores of the Welsh SMEs studied correlate significantly with non-parametric data envelopment analysis efficiency measures and are related to the use of environmental auditing practices and the use of local business support groups, but not to monitoring of waste expenditures and publication of environmental policies.