Flexural rigidity of layers and its manifestation in the vibrational characteristics of strongly anisotropic layered crystals. Characteristic frequencies and stability conditions in quasi-two-dimensional systems

2009 ◽  
Vol 35 (2) ◽  
pp. 158-165 ◽  
Author(s):  
E. S. Syrkin ◽  
S. B. Feodos’ev ◽  
K. V. Kravchenko ◽  
A. V. Eremenko ◽  
B. Ya. Kantor ◽  
...  
Keyword(s):  
Flexural Rigidity ◽  
Stability Conditions ◽  
Two Dimensional ◽  
Characteristic Frequencies ◽  
Vibrational Characteristics ◽  
Layered Crystals

Chaos in the Rulkov Neuron Model Based on Marotto’s Theorem

2021 ◽  
Vol 31 (15) ◽  
Author(s):  
Penghe Ge ◽  
Hongjun Cao
Keyword(s):  
Neuron Model ◽  
Initial Conditions ◽  
Stability Conditions ◽  
Two Dimensional ◽  
Bifurcation Diagrams ◽  
Fast Subsystem ◽  
One Dimensional ◽  
Sensitive Dependence ◽  
The Stability ◽  
Slow Subsystem

The existence of chaos in the Rulkov neuron model is proved based on Marotto’s theorem. Firstly, the stability conditions of the model are briefly renewed through analyzing the eigenvalues of the model, which are very important preconditions for the existence of a snap-back repeller. Secondly, the Rulkov neuron model is decomposed to a one-dimensional fast subsystem and a one-dimensional slow subsystem by the fast–slow dynamics technique, in which the fast subsystem has sensitive dependence on the initial conditions and its snap-back repeller and chaos can be verified by numerical methods, such as waveforms, Lyapunov exponents, and bifurcation diagrams. Thirdly, for the two-dimensional Rulkov neuron model, it is proved that there exists a snap-back repeller under two iterations by illustrating the existence of an intersection of three surfaces, which pave a new way to identify the existence of a snap-back repeller.

scholarly journals Magnetic two‐dimensional layered crystals meet with ferromagnetic semiconductors

InfoMat ◽  
2020 ◽  
Vol 2 (4) ◽  
pp. 639-655 ◽  
Author(s):  
Yilv Guo ◽  
Bing Wang ◽  
Xiwen Zhang ◽  
Shijun Yuan ◽  
Liang Ma ◽  
...  
Keyword(s):  
Ferromagnetic Semiconductors ◽  
Two Dimensional ◽  
Layered Crystals

STABILITY OF NUMERICAL DISCRETIZATIONS IN MODELLING VIBRATIONAL CHARACTERISTICS OF PIEZOELECTRIC CYLINDRICAL SHELLS

2002 ◽  
Vol 02 (02) ◽  
pp. 241-264
Author(s):  
R. V. N. MELNIK ◽  
K. N. MELNIK
Keyword(s):  
Conventional Treatment ◽  
Numerical Approximation ◽  
Piezoelectric Materials ◽  
Analytical Techniques ◽  
Stability Conditions ◽  
Cylindrical Shape ◽  
Vibrational Characteristics ◽  
Electromechanical Energy ◽  
The Stability ◽  
Piezoelectric Structures

Many problems in applications of piezoelectric materials are essentially time-dependent, and a conventional treatment of such problems with analytical or semi-analytical techniques based on the analysis of harmonic oscillations become inadequate in those cases where a complete dynamic picture of electromechanical energy transfer is required. For such situations we have developed an efficient explicit numerical methodology allowing us to compute dynamic electromechanical characteristics of piezoelectric structures and devices under various loading conditions. In this paper we demonstrate that the stability conditions for our numerical approximation can be obtained from a discrete conservation law, and can be cast in a form similar to that of the classical CFL condition. However, in our case the velocities of wave propagations, participating in the formulation of the stability conditions, are clearly dependent on the pattern of electromectromechanical coupling. Our discussion in this paper, including computational examples, is centred around finite piezoelectric shells of cylindrical shape.

Effect of size polydispersity on the structural and vibrational characteristics of two-dimensional granular assemblies

2014 ◽  
Vol 23 (7) ◽  
pp. 076301 ◽  
Author(s):  
Guo-Hua Zhang ◽  
Qi-Cheng Sun ◽  
Zhi-Ping Shi ◽  
Xu Feng ◽  
Qiang Gu ◽  
...  
Keyword(s):  
Two Dimensional ◽  
Granular Assemblies ◽  
Vibrational Characteristics

A Method for Generating Desired Contact Pressure Distributions in Experimental Interfacial Studies

1985 ◽  
Vol 107 (3) ◽  
pp. 241-246 ◽  
Author(s):  
M. H. Attia ◽  
L. Kops
Keyword(s):  
Rigid Body ◽  
Contact Pressure ◽  
Flexural Rigidity ◽  
Thermal Contact ◽  
Contact Length ◽  
Wear Testing ◽  
Elastic Response ◽  
Rigid Base ◽  
Two Dimensional ◽  
Pressure Distributions

Computer simulation of the thermal deformation behavior of machine tools requires a priori knowledge of the correlation between the contact pressure distribution and the thermal contact resistance distribution along the structural joint. To establish this correlation experimentally, a method for generating different distributions of contact pressure has been devised in the present work. The method provides also a basic tool toward the satisfaction of the requirements of simulative wear testing. In this paper, the effect of the relative flexural rigidity of two solids in contact on the shape of the distribution of contact pressure is presented as a means for generating desired contact pressure distributions. The theoretical background of the concept is discussed considering two limiting cases: a rigid body on an elastic semi-infinite mass, and an elastic layer on a rigid base. Through a photoelastic analysis, the geometric parameters of contacting bodies, which allow us to generate the desired distributions, have been defined. The results of the analysis were verified by a two-dimensional, plane-stress finite element model. The results indicated that a finite plate, whose dimensions are not less than threefold the contact length can simulate a two-dimensional rigid base or a semi-infinite elastic mass. A change in the height-to-contact length ratio of the contacting beam from 0.5 to 2.5, causes a significant change in its elastic response from a flexural to a rigid body.

scholarly journals TWO-DIMENSIONAL REGULAR AGGREGATES OF LAYERED CRYSTALS

1970 ◽  
Vol 6 (3) ◽  
pp. 172-185 ◽  
Author(s):  
Shigeho SUENO ◽  
Hiroshi TAKEDA ◽  
Ryoichi SADANAGA
Keyword(s):  
Two Dimensional ◽  
Layered Crystals

Tapered Beams

1942 ◽  
Vol 46 (381) ◽  
pp. 227-236
Author(s):  
E. H. Atkin
Keyword(s):  
Flexural Rigidity ◽  
Constant Thickness ◽  
Stress System ◽  
Two Dimensional ◽  
Aircraft Engineering

In a previous paper (Aircraft Engineering, November and December, 1938) the writer gave an account of proposed methods of calculating the stresses in tapered girders of a special type. The beam was assumed to have a web of constant thickness which could be dealt with as a two-dimensional stress system, while the booms were assumed to be concentrated lines of material having no flexural rigidity.It was this latter assumption which appeared to represent one of the main limitations of the theory, so an attempt has been made to remove this limitation; a solution has been found, for the case of tapering booms at any rate, which puts the theory at least on the same level of rigour as the well known theory for parallel beams.

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