Differential equations of three-dimensional vibrations for one-dimensional mechanical systems with variable parameters

This paper studies a class of partial differential equations of second order , with arbitrary functions and , with the help of the group classification. The main Lie algebra of infinitely infinitesimal symmetries is three-dimensional. We use the method of preliminary group classification for obtaining the classifications of these equations for a one-dimensional extension of the main Lie algebra.

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Differential equations of motion of mechanical systems with variable parameters

Soviet Applied Mechanics ◽

10.1007/bf00882968 ◽

1974 ◽

Vol 10 (6) ◽

pp. 671-674

Author(s):

V. A. Lazaryan ◽

L. A. Manashkin ◽

A. V. Yurchenko

Keyword(s):

Differential Equations ◽

Equations Of Motion ◽

Mechanical Systems ◽

Variable Parameters

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Dynamic Analysis of 3D Roll Forming Equipment in Mechanical System

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.740.323 ◽

2013 ◽

Vol 740 ◽

pp. 323-331 ◽

Cited By ~ 1

Author(s):

Zhen Feng Yang ◽

Qiang Li ◽

Yan Zhi Guan

Keyword(s):

Differential Equations ◽

High Strength Steel ◽

Dynamic Balance ◽

Three Dimensional ◽

Mechanical Systems ◽

High Strength ◽

Roll Forming ◽

System Response ◽

Forming Process ◽

Element Simulation

In this paper, the high-strength steel three-dimensional roll forming production line prototype is studied. The dynamic differential equations of 3D roll forming machine mechanical systems are established by the principle of dynamic balance. The dynamic differential equations are solved out by using MATLAB with the engineering example finite element simulation data. The dynamic characteristics of the forming process of 1.5mm TRIP590 high-strength steel sheet are obtained by the System response. The results can help to improve the performance of the prototype mechanical systems.

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Characteristic Forms of Differential Equations for Wave Propagation in Nonlinear Media

Journal of Applied Mechanics ◽

10.1115/1.3157726 ◽

1981 ◽

Vol 48 (4) ◽

pp. 743-748 ◽

Cited By ~ 9

Author(s):

T. C. T. Ting

Keyword(s):

Wave Propagation ◽

Differential Equations ◽

Constitutive Equations ◽

Equations Of Motion ◽

Three Dimensional ◽

Compressible Fluids ◽

Elastic Solids ◽

Nonlinear Media ◽

Nonlinear Materials ◽

One Dimensional

Characteristic forms of differential equations for wave propagation in nonlinear media are derived directly from equations of motion and equations which combine the constitutive equations and the equations of continuity. Both Lagrangian coordinates and Eulerian coordinates are considered. The constitutive equations considered here apply to a large class of nonlinear materials. The characteristic forms derived here clearly show which components of the stress and velocity are involved in the differentiation along the bicharacteristics. Moreover, the reduction to one-dimensional cases from three-dimensional problems is obvious for the characteristic forms obtained here. Examples are given and compared with the known solution in the literature for wave propagation in linear isotropic elastic solids and isentropic compressible fluids.

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TRAVELLING WAVES IN A CIRCULAR ARRAY OF CHUA’S CIRCUITS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127496000199 ◽

1996 ◽

Vol 06 (03) ◽

pp. 473-484 ◽

Cited By ~ 9

Author(s):

VLADIMIR I. NEKORKIN ◽

VICTOR B. KAZANTSEV ◽

MANUEL G. VELARDE

Keyword(s):

Differential Equations ◽

Periodic Orbits ◽

Travelling Waves ◽

Three Dimensional ◽

Dimensional System ◽

Circular Array ◽

One Dimensional ◽

Numerical Studies ◽

The Individual ◽

Three Dimensional System

The possibility of travelling waves in a one-dimensional circular array of Chua's circuits is investigated. It is shown that the problem can be reduced to the analysis of the periodic orbits of a three-dimensional system of ordinary differential equations (ODEs) describing the individual dynamics of Chua's circuit. The results of analytical and numerical studies of the bifurcation associated with the appearance of the periodic orbits are presented. A criterion for stability of the travelling waves is also provided.

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Structure and function of neural networks in the retina

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100102213 ◽

1988 ◽

Vol 46 ◽

pp. 26-27

Author(s):

Peter Sterling

Keyword(s):

Ganglion Cells ◽

Three Dimensional ◽

Structure And Function ◽

Synaptic Connections ◽

Visual Axis ◽

One Dimensional ◽

Cat Retina ◽

Ultrathin Sections ◽

And Function ◽

Insight Into

The synaptic connections in cat retina that link photoreceptors to ganglion cells have been analyzed quantitatively. Our approach has been to prepare serial, ultrathin sections and photograph en montage at low magnification (˜2000X) in the electron microscope. Six series, 100-300 sections long, have been prepared over the last decade. They derive from different cats but always from the same region of retina, about one degree from the center of the visual axis. The material has been analyzed by reconstructing adjacent neurons in each array and then identifying systematically the synaptic connections between arrays. Most reconstructions were done manually by tracing the outlines of processes in successive sections onto acetate sheets aligned on a cartoonist's jig. The tracings were then digitized, stacked by computer, and printed with the hidden lines removed. The results have provided rather than the usual one-dimensional account of pathways, a three-dimensional account of circuits. From this has emerged insight into the functional architecture.

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Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

Swiss Journal of Psychology ◽

10.1024/1421-0185.67.1.51 ◽

2008 ◽

Vol 67 (1) ◽

pp. 51-60 ◽

Cited By ~ 26

Author(s):

Stefano Passini

Keyword(s):

Social Dominance ◽

Factor Model ◽

Three Dimensional ◽

Social Dominance Orientation ◽

Model Fit ◽

Regression Analyses ◽

One Dimensional ◽

Confirmatory Factor ◽

The One ◽

Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

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