scholarly journals Hysteresis Modelling of Mechanical Systems at Nonstationary Vibrations

2018 ◽  
Vol 2018 ◽  
pp. 1-15
Author(s):  
A. N. Danilin ◽  
A. D. Shalashilin

This paper considers and reviews a number of known phenomenological models, used to describe hysteretic effects of various natures. Such models consider hysteresis system as a “black box” with experimentally known input and output, related via formal mathematical dependence to parameters obtained from the best fit to experimental data. In particular, we focus on the broadly used Bouc-Wen and similar phenomenological models. The current paper shows the conditions which the Bouc-Wen model must meet. An alternative mathematical model is suggested where the force and kinematic parameters are related by a first-order differential equation. In contrast to the Bouc-Wen model, the right hand side is a polynomial with two variables representing hysteresis trajectories in the process diagram. This approach ensures correct asymptotic approximation of the solution to the enclosing hysteresis cycle curves. The coefficients in the right side are also determined experimentally from the hysteresis cycle data during stable oscillations. The proposed approach allows us to describe hysteretic trajectory with an arbitrary starting point within the enclosed cycle using only one differential equation. The model is applied to the description of forced vibrations of a low-frequency pendulum damper.

1988 ◽  
Vol 03 (04) ◽  
pp. 953-1021 ◽  
Author(s):  
RICCARDO D’AURIA ◽  
PIETRO FRÉ ◽  
MARIO RACITI ◽  
FRANCO RIVA

Using a theorem by Bonora-Pasti and Tonin on the existence of a solution for D=10N=1 Bianchi identities in the presence of a Lorentz Chern Simons term, we find an explicit parametrization of the superspace curvatures. Our solution depends only on one free parameter which can be reabsorbed in a field redefinition of the dilaton and of the gravitello. We emphasize that the essential point which enables us to obtain a closed form for the curvature parametrizations and hence for the supersymmetry transformation rules is the use of first order formalism. The spin connection is known once the torsion is known. This latter, rather than being identified with Hµνρ as it is usually done in the literature, is related to it by a differential equation which reduces to the algebraic relation Hµνρ = - 3Tµνρ e4/3σ only at γ1=0 (γ1 being proportional to κ/g2). The solution of the Bianchi identities exhibited in this paper corresponds to a D=10 anomaly free supergravity (AFS). This theory is unique in first order formalism but corresponds to various theories in second order formalism. Indeed the torsion equation is a differential equation which, in order to be solved must be supplemented with boundary conditions. One wonders whether supplemented with a judicious choice of boundary conditions for the torsion equation, AFS yields all the interaction terms found in the effective theory of the heterotic string (ETHS). In this respect two remarks are in order. Firstly it appears that solving the torsion equation iteratively with Tµνρ = -1/3Hµνρ e-4/3σ as starting point all the terms of ETHS except those with a ζ(3) coefficient show up. (Whether the coefficient agree is still to be checked.) Secondly, as shown in this paper the rheonomic solution of the super Poincaré Bianchi identities is unique. Hence additional interaction terms can be added to the Lagrangian only by modifying the rheonomic parametrization of the [Formula: see text]-curvature. The only assumption made in our paper is that [Formula: see text] has at most ψ∧ψ∧V components (sector (1,2)). Correspondingly the only room left for a modification of the present theory is the addition of a (0, 3) part in the rheonomic parametrization of [Formula: see text]. When this work was already finished a conjecture was published by Lechner Pasti and Tonin that such a generalization of AFS might exist and be responsible for the ζ(3) missing term. Indeed if we were able to solve the [Formula: see text]-Bianchi with this new (0, 3)-part then the torsion equation would be modified via new terms which, in second order formalism, lead to additional gravitational interactions. The equation of motion of Anomaly Free Supergravity can be worked out from the Bianchi identities: we indicate through which steps. The corresponding Lagrangian could be constructed with the standard procedures of the rheonomy approach. In this paper we limit ourselves to the bosonic sector of such a Lagrangian and we show that it can indeed be constructed in such a way as to produce the relation between Hµνρ and Tµνρ as a variational equation.


2020 ◽  
Vol 69 (1) ◽  
pp. 7-11
Author(s):  
A.K. Abirov ◽  
◽  
N.K. Shazhdekeeva ◽  
T.N. Akhmurzina ◽  
◽  
...  

The article considers the problem of solving an inhomogeneous first-order differential equation with a variable with a constant coefficient in a hypercomplex system. The structure of the solution in different cases of the right-hand side of the differential equation is determined. The structure of solving the equation in the case of the appearance of zero divisors is shown. It turns out that when the component of a hypercomplex function is a polynomial of an independent variable, the differential equation turns into an inhomogeneous system of real variables from n equations and its solution is determined by certain methods of the theory of differential equations. Thus, obtaining analytically homogeneous solutions of inhomogeneous differential equations in a hypercomplex system leads to an increase in the efficiency of modeling processes in various fields of science and technology.


Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1937
Author(s):  
Yakun Wang ◽  
Fanwei Meng

In this paper, we focus on the second-order neutral differential equations with deviating arguments which are under the canonical condition. New oscillation criteria are established, which are based on a first-order delay differential equation and generalized Riccati transformations. The idea of symmetry is a useful tool, not only guiding us in the right way to study this function but also simplifies our proof. Our results are generalizations of some previous results and we provide an example to illustrate the main results.


1992 ◽  
Vol 114 (1) ◽  
pp. 8-16 ◽  
Author(s):  
H. L. Chang ◽  
Y. C. Tsai

A general mathematical model for describing the geometries and geometric properties of conjugate tooth profiles is presented. Three kinematic parameters and a first order differential equation are introduced to characterize this model. The condition for determining the cusp of tooth profiles is also presented. Using this model, two types of tooth fillets with their minimum radii of curvatures generated by the rack cutter and pinion cutter are described. The peculiar application of this model is that the investigated tooth profiles can be parameterized by specifying one of the three kinematic parameters as a parametric function. It is believed that the parameterization may provide a logical method for gear design.


Author(s):  
L.I. Rubina ◽  
O.N. Ul'yanov

An algorithm is proposed for obtaining solutions of partial differential equations with right-hand side defined on the grid $\{ x_{1}^{\mu}, x_{2}^{\mu}, \ldots, x_{n}^{\mu}\},\ (\mu=1,2,\ldots,N)\colon f_{\mu}=f(x_{1}^{\mu}, x_{2}^{\mu}, \ldots, x_{n}^{\mu}).$ Here $n$ is the number of independent variables in the original partial differential equation, $N$ is the number of rows in the grid for the right-hand side, $f=f( x_{1}, x_{2}, \ldots, x_{n})$ is the right-hand of the original equation. The algorithm implements a reduction of the original equation to a system of ordinary differential equations (ODE system) with initial conditions at each grid point and includes the following sequence of actions. We seek a solution to the original equation, depending on one independent variable. The original equation is associated with a certain system of relations containing arbitrary functions and including the partial differential equation of the first order. For an equation of the first order, an extended system of equations of characteristics is written. Adding to it the remaining relations containing arbitrary functions, and demanding that these relations be the first integrals of the extended system of equations of characteristics, we arrive at the desired ODE system, completing the reduction. The proposed algorithm allows at each grid point to find a solution of the original partial differential equation that satisfies the given initial and boundary conditions. The algorithm is used to obtain solutions of the Poisson equation and the equation of unsteady axisymmetric filtering at the points of the grid on which the right-hand sides of the corresponding equations are given.


1970 ◽  
Vol 13 (1) ◽  
pp. 37-40
Author(s):  
Gary Thompson ◽  
Marie Denman

Bone-conduction tests were administered to subjects who feigned a hearing loss in the right ear. The tests were conducted under two conditions: With and without occlusion of the non-test ear. It was anticipated that the occlusion effect, a well-known audiological principle, would operate to draw low frequency bone-conducted signals to the occluded side in a predictable manner. Results supported this expectation and are discussed in terms of their clinical implications.


2020 ◽  
Author(s):  
Anat Feldman ◽  
Michael Shmueli ◽  
Dror Dotan ◽  
Joseph Tzelgov ◽  
Andrea Berger

In recent years, there has been growing interest in the development of mental number line (MNL) representation examined using a number-to-position task. In the present study, we investigated the development of number representation on a 0-10 number line using a computerized version of the number-to-position task on a touchscreen, with restricted response time; 181 children from first through sixth grade were tested. We found that the pattern of estimated number position on the physical number line was best fit by the sigmoidal curve function–which was characterized by underestimation of small numbers and overestimation of large numbers–and that the breakpoint changed with age. Moreover, we found that significant developmental leaps in MNL representation occurred between the first and second grades and again between the second and third grades, which was reflected in the establishment of the right endpoint and the number 5 as anchor points, yielding a more accurate placement of other numbers along the number line.


2019 ◽  
Author(s):  
Valentina Escotet Espinoza

UNSTRUCTURED Over half of Americans report looking up health-related questions on the internet, including questions regarding their own ailments. The internet, in its vastness of information, provides a platform for patients to understand how to seek help and understand their condition. In most cases, this search for knowledge serves as a starting point to gather evidence that leads to a doctor’s appointment. However, in some cases, the person looking for information ends up tangled in an information web that perpetuates anxiety and further searches, without leading to a doctor’s appointment. The Internet can provide helpful and useful information; however, it can also be a tool for self-misdiagnosis. Said person craves the instant gratification the Internet provides when ‘googling’ – something one does not receive when having to wait for a doctor’s appointment or test results. Nevertheless, the Internet gives that instant response we demand in those moments of desperation. Cyberchondria, a term that has entered the medical lexicon in the 21st century after the advent of the internet, refers to the unfounded escalation of people’s concerns about their symptomatology based on search results and literature online. ‘Cyberchondriacs’ experience mistrust of medical experts, compulsion, reassurance seeking, and excessiveness. Their excessive online research about health can also be associated with unnecessary medical expenses, which primarily arise from anxiety, increased psychological distress, and worry. This vicious cycle of searching information and trying to explain current ailments derives into a quest for associating symptoms to diseases and further experiencing the other symptoms of said disease. This psychiatric disorder, known as somatization, was first introduced to the DSM-III in the 1980s. Somatization is a psycho-biological disorder where physical symptoms occur without any palpable organic cause. It is a disorder that has been renamed, discounted, and misdiagnosed from the beginning of the DSMs. Somatization triggers span many mental, emotional, and cultural aspects of human life. Our environment and social experiences can lay the blueprint for disorders to develop over time; an idea that is widely accepted for underlying psychiatric disorders such as depression and anxiety. The research is going in the right direction by exploring brain regions but needs to be expanded on from a sociocultural perspective. In this work, we explore the relationship between somatization disorder and the condition known as cyberchondria. First, we provide a background on each of the disorders, including their history and psychological perspective. Second, we proceed to explain the relationship between the two disorders, followed by a discussion on how this relationship has been studied in the scientific literature. Thirdly, we explain the problem that the relationship between these two disorders creates in society. Lastly, we propose a set of intervention aids and helpful resource prototypes that aim at resolving the problem. The proposed solutions ranged from a site-specific clinic teaching about cyberchondria to a digital design-coded chrome extension available to the public.


2020 ◽  
Vol 11 ◽  
Author(s):  
Elena Laura Georgescu Margarint ◽  
Ioana Antoaneta Georgescu ◽  
Carmen Denise Mihaela Zahiu ◽  
Stefan-Alexandru Tirlea ◽  
Alexandru Rǎzvan Şteopoaie ◽  
...  

The execution of voluntary muscular activity is controlled by the primary motor cortex, together with the cerebellum and basal ganglia. The synchronization of neural activity in the intracortical network is crucial for the regulation of movements. In certain motor diseases, such as dystonia, this synchrony can be altered in any node of the cerebello-cortical network. Questions remain about how the cerebellum influences the motor cortex and interhemispheric communication. This research aims to study the interhemispheric cortical communication between the motor cortices during dystonia, a neurological movement syndrome consisting of sustained or repetitive involuntary muscle contractions. We pharmacologically induced lateralized dystonia to adult male albino mice by administering low doses of kainic acid on the left cerebellar hemisphere. Using electrocorticography and electromyography, we investigated the power spectral densities, cortico-muscular, and interhemispheric coherence between the right and left motor cortices, before and during dystonia, for five consecutive days. Mice displayed lateralized abnormal motor signs, a reduced general locomotor activity, and a high score of dystonia. The results showed a progressive interhemispheric coherence decrease in low-frequency bands (delta, theta, beta) during the first 3 days. The cortico-muscular coherence of the affected side had a significant increase in gamma bands on days 3 and 4. In conclusion, lateralized cerebellar dysfunction during dystonia was associated with a loss of connectivity in the motor cortices, suggesting a possible cortical compensation to the initial disturbances induced by cerebellar left hemisphere kainate activation by blocking the propagation of abnormal oscillations to the healthy hemisphere. However, the cerebellum is part of several overly complex circuits, therefore other mechanisms can still be involved in this phenomenon.


Sign in / Sign up

Export Citation Format

Share Document