The breaking crack build-up in perforated planes by uniform ring switching

1996 ◽  
Vol 79 (1) ◽  
pp. R17-R21 ◽  
Author(s):  
V. M. Mirsalimov ◽  
E. A. Allahyarov
Keyword(s):  
Uniform Ring

scholarly journals MATHEMATICAL MODELLING OF VIBRATIONS OF NON-UNIFORM RING-SHAPED ULTRASONIC WAVEGUIDES

2021 ◽  
Vol 3 (56) ◽  
pp. 90-96
Author(s):  
Dmitry A. STEPANENKO ◽  
◽  
Ksenija A. BUNCHUK ◽  
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Central Line ◽  
Balance Method ◽  
Vibration Modes ◽  
Constant Sign ◽  
Algebraic Equations ◽  
Bending Vibrations ◽  
Singular Matrices ◽  
Uniform Ring

The article describes technique for modelling of ultrasonic vibrations amplifiers, which are implemented in the form of non-uniform ring-shaped waveguides, based on application of harmonic balance method. Bending vibrations of the waveguide are described by means of non-uniform integral and differential equations equivalent to Euler–Bernoulli equations in order to simplify calculation of amplitude-frequency characteristics of vibrations, particularly, to exclude the need of working with singular matrices. Using harmonic balance method, equations of vibrations are reduced to overdetermined non-uniform linear system of algebraic equations, which least-squares solution is determined by means of pseudo-inverse matrix. On the basis of analysis of numerical example possibility of existence of variable-sign and constant-sign vibration modes of the waveguide is shown and it is determined that for realization of amplifying function it is necessary to use waveguide at constant-sign vibration mode. The constant-sign vibration modes are combinations of bending defor-mation and extensional deformation of central line of the waveguide and they are detected due to accounting extensibility of the central line in equations of vibrations. Validity of the obtained results is confirmed by comparing them to the results of modelling by means of finite element method.

On the radial structure of planetary rings

1984 ◽  
Vol 75 ◽  
pp. 431-437 ◽  
Author(s):  
A.W. Harris ◽  
W.R. Ward
Keyword(s):  
Shear Stress ◽  
Optical Depth ◽  
Orbital Velocity ◽  
Planetary Rings ◽  
Radial Gradient ◽  
Viscous Shear Stress ◽  
Viscous Shear ◽  
Radial Structure ◽  
Uniform Ring ◽  
Increasing Function

ABSTRACTA ring of particles in orbit about a planet experiences a viscous shear stress due to the radial gradient of orbital velocity. This stress tends to spread the ring with time. At low optical depth (τ ≲ 0.5), and again at high optical depth (τ ≳ 2), the shear stress is an increasing function of optical depth. In the intermediate range (0.5 ≲ x ≲ 2), stress may decrease with increasing τ, leading to a diffusive instability which will tend to break an Initially uniform ring into ringlets of high and low optical depths.

A note on free flexural vibrations of a non-uniform ring with fixed supports

1989 ◽  
Vol 129 (1) ◽  
pp. 45-49
Author(s):  
M.B. Rosales ◽  
C.P. Filipich ◽  
P.A.A. Laura
Keyword(s):  
Flexural Vibrations ◽  
Uniform Ring

scholarly journals Asymmetric circular graph with Hosoya index and negative continued fractions

2021 ◽  
Vol 13 (3) ◽  
pp. 608-618
Author(s):  
T. Komatsu
Keyword(s):  
Continued Fractions ◽  
Continued Fraction ◽  
Bond Graph ◽  
Ring Structure ◽  
Hosoya Index ◽  
General Graph ◽  
Multidimensional Continued Fractions ◽  
Radial Graphs ◽  
Uniform Ring ◽  
Circular Graph

It has been known that the Hosoya index of caterpillar graph can be calculated as the numerator of the simple continued fraction. Recently in [MATCH Commun. Math. Comput. Chem. 2020, 84 (2), 399-428], the author introduces a more general graph called caterpillar-bond graph and shows that its Hosoya index can be calculated as the numerator of the general continued fraction. In this paper, we show how the Hosoya index of the graph with non-uniform ring structure can be calculated from the negative continued fraction. We also give the relation between some radial graphs and multidimensional continued fractions in the sense of the Hosoya index.

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