Hand Vibrations of the Human Operator in the Working Space

The paper contains the identification and the taking into account the vibrations produced by the machines, the lathe with different number of rotation, and them action over the human bodies inside the working space. For the identification of vibrations is applied a new method, the Moiré projection method, that did not used until this moment regarding the vibrations action over the human body. Our research was to apply the Moiré projection method to the human hand. They were compared with the measured vibrations using a classic vibrometer with three-axial accelerometer. The results in the booth situation were in the same order of the unit scale, and the optical method named Moiré projection method can be considered a valid method for the human vibrations measurements without touch of the surface. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Vibration by shocks of the human bodies in the working spaces

The paper contains the transmitted vibrations produce by shocks to the human bodies into the working space.There are the methods for measuring the vibration experiments transmitted through the shock of the human body by the foundation of forging hammer. There are the results given by the different sorts of accelerations into to special conditions of work in the working space. They are of the vibrometer adding the three directions accelerometer. In this way can be analyze taking into account the vibrations action over the human bodies under the action of the equipment in the working space produced by shocks. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Study of human body stability under the vertical vibration action into an autovehicle using Laplace transforms

The paper presents a study for imagining of generalized mechanical model for the human body/seat assembly. The model will be used for the dynamics analyze of the human body constituent parts, under the vertical vibrations influence, transmitted by the vehicle seat during its displacement. Measures of the dynamic responses of the body are represented by the transfer functions. The human body stability is given by the found poles. The human body motion laws with four independent coordinates have been as graphical representations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Vibrating Portable Machine-Tools Acting on Human Operator

This paper will be a short presentation of the specialized literature and international standards about the importance of vibration action of portable machine tools on human body and particularly on the hand-arm system. Exposure to harmful vibrations can lead to health problems and disorders, especially in the upper joints and dorsal region of the human body. A detailed understanding of the undesirable effects of vibration on the human body is essential to achieve administrative and technical prevention. In modern times, vibration studies become more frequent, decisive for the many machines, vehicles and construction. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Characterization of subdual latticial cones in Hilbert spaces by the isotonicity of the metric projection

The subdual latticial cones in Hilbert spaces are characterized by the isotonicity of a generalization of the positive part mapping which can be expressed in terms of the metric projection only. Although Németh characterized the positive cone of Hilbert lattices with the metric projection and ordering only [A.B. Németh, Characterization of a Hilbert vector lattice by the metric projection onto its positive cone, J. Approx. Theory 123 (2) (2003), pp. 295–299.], this has been done for the first time for subdual latticial cones in this article. We also note that the normal generating pointed closed convex cones for which the projection onto the cone is isotone are subdual latticial cones, but there are subdual latticial cones for which the metric projection onto the cone is not isotone [G. Isac, A.B. Németh, Monotonicity of metric projections onto positive cones of ordered Euclidean spaces, Arch. Math. 46 (6) (1986), pp. 568–576; G. Isac, A.B. Néemeth, Every generating isotone projection cone is latticial and correct, J. Math. Anal. Appl. 147 (1) (1990), pp. 53–62; G. Isac, A.B. Németh, Isotone projection cones in Hilbert spaces and the complementarity problem, Boll. Un. Mat. Ital. B 7 (4) (1990), pp. 773–802; G. Isac, A.B. Németh, Projection methods, isotone projection cones, and the complementarity problem, J. Math. Anal. Appl. 153 (1) (1990), pp. 258–275; G. Isac, A.B. Németh, Isotone projection cones in Eucliden spaces, Ann. Sci. Math Québec 16 (1) (1992), pp. 35–52].     

Error analysis of a fully discrete projection method for magnetohydrodynamic system

In this paper, we develop and analyze a finite element projection method for magnetohydrodynamics equations in Lipschitz domain. A fully discrete scheme based on Euler semi-implicit method is proposed, in which continuous elements are used to approximate the Navier–Stokes equations and H ( curl ) conforming Nédélec edge elements are used to approximate the magnetic equation. One key point of the projection method is to be compatible with two different spaces for calculating velocity, which leads one to obtain the pressure by solving a Poisson equation. The results show that the proposed projection scheme meets a discrete energy stability. In addition, with the help of a proper regularity hypothesis for the exact solution, this paper provides a rigorous optimal error analysis of velocity, pressure and magnetic induction. Finally, several numerical examples are performed to demonstrate both accuracy and efficiency of our proposed scheme.     

Unfolding the torus: Oscillator geometry from time delays

Summary We present a simple method of plotting the trajectories of systems of weakly coupled oscillators. Our algorithm uses the time delays between the “firings” of the oscillators. For any system ofn weakly coupled oscillators there is an attracting invariantn-dimensional torus, and the attractor is a subset of this invariant torus. The invariant torus intersects a suitable codimension-1 surface of section at an (n−1)-dimensional torus. The dynamics ofn coupled oscillators can thus be reduced,in principle, to the study of Poincaré maps of the (n−1)-dimensional torus. This paper gives apractical algorithm for measuring then−1 angles on the torus. Since visualization of 3 (or higher) dimensional data is difficult we concentrate onn=3 oscillators. For three oscillators, a standard projection of the Poincaré map onto the plane yields a projection of the 2-torus which is 4-to-1 over most of the torus, making it difficult to observe the structure of the attractor. Our algorithm allows a direct measurement of the 2 angles on the torus, so we can plot a 1-to-1 map from the invariant torus to the “unfolded torus” where opposite edges of a square are identified. In the cases where the attractor is a torus knot, the knot type of the attractor is obvious in our projection.     

Dynamic proper colorings of a graph

We solve an axisymmetric problem of the interaction of harmonic waves with a thin elastic circular inclusion located in an elastic isotropic body (matrix). On both sides of the inclusion, between it and the body (matrix), conditions of smooth contact are realized. The method of solution is based on the representation of displacements in the matrix in terms of discontinuous solutions of Lamé equations for harmonic vibrations. This enables us to reduce the problem to Fredholm integral equations of the second kind for functions related to jumps of normal stress and radial displacement on the inclusion.     

On the O(1/t) convergence rate of the projection and contraction methods for variational inequalities with Lipschitz continuous monotone operators

Nemirovski’s analysis (SIAM J. Optim. 15:229–251, 2005) indicates that the extragradient method has the O(1/t) convergence rate for variational inequalities with Lipschitz continuous monotone operators. For the same problems, in the last decades, a class of Fejér monotone projection and contraction methods is developed. Until now, only convergence results are available to these projection and contraction methods, though the numerical experiments indicate that they always outperform the extragradient method. The reason is that the former benefits from the ‘optimal’ step size in the contraction sense. In this paper, we prove the convergence rate under a unified conceptual framework, which includes the projection and contraction methods as special cases and thus perfects the theory of the existing projection and contraction methods. Preliminary numerical results demonstrate that the projection and contraction methods converge twice faster than the extragradient method.     

Research about moving restrictions of cervical spine under the action of mechanical vibrations

The cervical spine is very important human body part, because it sustains the head and it has a higher mobility than the other parts of human spine. The vibration could influence the work performance but also could have a negative influence on human body health. There are many elements, which could be damaged: eyes, ears, brain, mandible, neck's muscle, C1 to C7 vertebras. When the operator is exposed to vibrations for a long time, he can fill a strong pain at the neck. Injuries to the cervical spine are common at the level of the second cervical vertebrae, but neurological injury is uncommon. If it does occur, however, it may cause death or profound disability, including paralysis of the arms or legs. We purpose in this study to develop a biomechanical model for the cervical vertebras and identify the influence of mechanical vibrations on human cervical spine and human head. For this study is necessary to compute the entire moving system of the neck-head. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Development of a biomechanical model to study the horizontal vibration transmitted from shoulder to head

On daily activity a human operator is exposed to vibration in working environment. So, the human body will react in different way. The problem is how much from the initial signal will be sent to the other parts of the body and how much that motion will be damped along the studied parts. The vibrations in horizontal plane are some unexpected, so the human operator will not take any position to prevent them. In this condition the horizontal vibrations will have the higher effect possible. In this paper, the shoulder, neck and the head are modeled together like a mechanical system with four degree of freedom. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Responses Study of the Seated Human Body Exposed to Vertical Vibration in Various Automotive Postures

In a seated posture into an autovehicle, humans are most sensitive to whole-body vibrations under low-frequency excitation. This research is focused only on the effect of the backrest angle on the biodynamic response functions. In this paper there are present the results of investigations for 10 participants, whose mean body mass was 61.4 kg. For the biodynamic responses of a seated human body subjected to vertical vibrations, three automotive postures was study: without backrest support, with backrest inclined 7° and respectively 15°, by measurement of transmitted vibration in two different situations: with belt and respectively without this. Knowledge of human responses to vibration provides information about the position of backrest support to mitigate vibration transmitted through the body ensuring the health, comfort and performance. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the investigation of free vibrations of nonthin cylindrical shells of variable thickness by the spline-collocation method

For determining the dynamic characteristics of free vibrations of circular unclosed cylindrical shells of variable thickness in two coordinate directions, we have used the spline-collocation method together with the method of discrete orthogonalization. The problem has been solved within the framework of the refined Timoshenko–Mindlin theory. We have also investigated the influence of different laws of change in the shell thickness on the character of its natural vibrations. Our calculations have been carried out for different geometrical and elastic parameters of the shell under study and different boundary conditions.     

Lattice geometry and pythagorean triangles

By drawing a Pythagorean triangle in a quadratic lattice and attaching a congruent lattice at the hypotenuse there will occur a Moiré effect with a new quadratic lattice of enlarged scale in the superposition. This new lattice is related to the parameterization of the Pythagorean triangle. A similar effect occurs with triangles with integer side lengths and an angle of 120° in a regular triangular lattice. We work with dot lattices on transparencies to visualize the optical effects.     

A new method of measuring the viscoelastic properties of polymer systems in fluid and highly elastic states using forced vibrations in the ultralow-frequency region

A method is considered for measuring the dynamic mechanical characteristics of polyer systems using forced vibrations in the ultralow-frequency region down to 10^–6 Hz. The essence of this method lies in the fact that during the measurement process the motion of the polymer sample is controlled with a set amplitude and frequency, and the dynamic characteristics of the polymer are determined from the controlling mechanical stress. The method is illustrated using the results of measurements of the components of the complex modulus for polybutadiene over a wide range of temperatures and frequencies without making use of superimposition.The Central Constructional Bureau for Prototype Instrument Construction, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 344–347, March–April, 1976.     

Identification of Finite-Motion Parameters of Serial Chains via Measurement of 6 × 6 Stiffness Matrices

This paper describes a procedure for identifying geometric and stiffness parameters of a mechanical serial chain of know structure by measuring spatial 6×6 stiffness matrices at different positions. The method uses standard optimization routines to determine model parameters such that the model stiffness matrix features in the Frobenius norm the closest distance possible to the measured matrix. From this local identification, a rough model of parameters of finite-motion is created, from which new measuring positions are guessed. By applying this step repeatedly, a model for finite-displacement parameters can be obtained by a sequence of small force-displacement tests. The method is tested with a dummy device consisting of a revolute joint connecting two rigid links dressed with soft material to mimic for example muscle masses of a surrogate mechanism for the elbow joint of a human arm. Two robots grasping the upper and lower arm generate the motion while the force measurement is carried out by a six-axis force sensor. This makes the method potentially suitable for detecting anatomical parameters by in-vivo measurements. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical modeling of the active damping of forced thermomechanical resonance vibrations of viscoelastic shells of revolution with the help of piezoelectric inclusions

We consider the problem of active damping of forced resonance vibrations of viscoelastic shells of revolution with the help of piezoelectric sensors and actuators. Here, the interaction of electromechanical and thermal fields is taken into account. For modeling of vibrations, we use the Kirchhoff–Love hypotheses as well as hypotheses adequate to them and describing the distribution of temperature and electric field quantities. The shell temperature increases as a result of dissipative heating. For the active damping of vibrations, piezoelectric sensors and actuators are used. It is supposed that the electromechanical characteristics of materials depend on the temperature. The solution of this complex nonlinear problem has been obtained by the iterative method and finite element method. We have investigated the influence of temperature of dissipative heating on the efficiency of active damping of vibrations of a viscoelastic cylindrical panel with rigid restraint of its edges.     

Generalized intersection and projection bodies

Generalized intersection and projection bodies are defined and constructed for a spatial convex polytope P. The generalized intersection body extends the definition of the classical Petty body, while the generalized projection body can be considered a dual formulation of the base construction. The method of construction is outlined and an example is used to illustrate the induced structures.     

Construction of fundamental solutions of two-dimensional problems of the nonstationary theory of elasticity

We propose a method of constructing the images of the fundamental solutions in the space of the Laplace transform with respect to time, leading to simple formulas. The method is illustrated using three dynamical problems: planar deformation for an anisotropic body; flexural vibrations of an anisotropic plate; and vibrations of a shallow isotropic shell of arbitrary Gaussian curvature. Quadrature formulas are given for computing the values of the fundamental solutions. We give a new interpretation and a new method of computing the values of the special functions used in the construction of singular solutions in problems of the static theory of shells. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 86–92.