Effects of Flexibility and Damping on Momentum Transfer During Locking of Two Moving Links, Part II: Analytical Approach

1998 ◽  
Vol 65 (2) ◽  
pp. 485-488
Author(s):  
W. Szyszkowski ◽  
K. Fielden
Keyword(s):  
Numerical Analysis ◽  
Momentum Transfer ◽  
Analytical Approach ◽  
Governing Equations ◽  
Physical Understanding ◽  
Damping Effects ◽  
Characteristic Features

The numerical analysis presented in Part I of this paper revealed that small and seemingly negligible flexibility and damping effects influence significantly the post-locking motion of the assembly consisting of two joint-connected links. Here we concentrate on a more physical understanding and explanation of the phenomenon observed. It is shown that the main characteristic features of the post-locking motion can be recovered by decomposing it into the “fast” and “slow” modes. The governing equations of these two modes of motion are derived and discussed in detail.

scholarly journals A New Analytical Approach for Nonlinear Global Buckling of Spiral Corrugated FG-CNTRC Cylindrical Shells Subjected to Radial Loads

2020 ◽  
Vol 10 (7) ◽  
pp. 2600
Author(s):  
Tho Hung Vu ◽  
Hoai Nam Vu ◽  
Thuy Dong Dang ◽  
Ngoc Ly Le ◽  
Thi Thanh Xuan Nguyen ◽  
...  
Keyword(s):  
Analytical Approach ◽  
Cylindrical Shells ◽  
Equation System ◽  
Functionally Graded ◽  
Governing Equations ◽  
Reinforced Composite ◽  
Global Buckling ◽  
Homogenization Model ◽  
Corrugated Structure ◽  
The Galerkin Method

The present paper deals with a new analytical approach of nonlinear global buckling of spiral corrugated functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical shells subjected to radial loads. The equilibrium equation system is formulated by using the Donnell shell theory with the von Karman’s nonlinearity and an improved homogenization model for spiral corrugated structure. The obtained governing equations can be used to research the nonlinear postbuckling of mentioned above structures. By using the Galerkin method and a three term solution of deflection, an approximated analytical solution for the nonlinear stability problem of cylindrical shells is performed. The linear critical buckling loads and postbuckling strength of shells under radial loads are numerically investigated. Effectiveness of spiral corrugation in enhancing the global stability of spiral corrugated FG-CNTRC cylindrical shells is investigated.

ON THE STRUCTURE OF π AND K MESONS

1987 ◽  
Vol 02 (06) ◽  
pp. 1829-1838 ◽  
Author(s):  
S.N. BANERJEE ◽  
R.K. DAS ◽  
A.K. SARKER
Keyword(s):  
Differential Cross Section ◽  
Statistical Model ◽  
Momentum Transfer ◽  
Cross Section ◽  
Differential Cross ◽  
Form Factors ◽  
Scattering Data ◽  
Elastic Differential Cross Section ◽  
K Mesons ◽  
Characteristic Features

We have investigated the form factors of the π and K mesons within the framework of the statistical model. Our results reveal several well-spaced minima and maxima for different values of Q2, the square of the momentum transfer. The characteristic features of the elastic differential cross section, dσ/dt, for π±P and K±P scattering data are well reproduced, as a consequence.

Effects of Flexibility and Damping on Momentum Transfer During Locking of Two Moving Links, Part I: Numerical Simulation

1998 ◽  
Vol 65 (2) ◽  
pp. 479-484 ◽  
Author(s):  
W. Szyszkowski ◽  
K. Fielden
Keyword(s):  
Numerical Simulation ◽  
Momentum Transfer ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Slow Motion ◽  
Critical Values ◽  
Governing Equations ◽  
Two Degrees Of Freedom

The system consisting of two links and two joints is examined. The joints are idealy frictionless when unlocked. Due to flexibility of the links, the locking generates some damped vibrations. It is demonstrated that the presence of these vibrations, even of very small and seemingly neglegible amplitudes, have dramatic effects on the after-locking motion of the links. Depending on the level of flexibility and damping involved, the locking triggers a large-scale “slow” motion that may have either oscillatory or circular (clockwise or counterclockwise) characters. The links will stop at some resting configuration only at certain “critical” values of damping. The set of “critical dampings” seems to be infinite, though only two degrees-of-freedom are used to model the system. Governing equations for these phenomena are derived and discussed in Part II of this paper.

Properties of X-ray resonant scattering in the Bragg case revealed on the Riemann surface

2016 ◽  
Vol 72 (4) ◽  
pp. 472-479 ◽  
Author(s):  
Takashi Saka
Keyword(s):  
Riemann Surface ◽  
Numerical Analysis ◽  
Strength Characteristic ◽  
Resonant Scattering ◽  
Dynamical Theory ◽  
Acta Cryst ◽  
Rocking Curve ◽  
X Ray ◽  
Dispersion Surface ◽  
Characteristic Features

Continuing the work described in the previous paper [Saka (2016).Acta Cryst.A72, 338–348], the dynamical theory for perfect crystals in the Bragg case is reformulated using the Riemann surface. In particular, diffraction under resonant scattering conditions is investigated. The characteristic features of the dispersion surface and the rocking curve are analytically revealed using four parameters, which are the real and imaginary parts of two quantities specifying the degree of departure from the exact Bragg conditions and the reflection strength. Characteristic properties that have been deduced through numerical analysis are derived analytically using these four parameters. Visualization of the geometric relationships between the four parameters on the Riemann surface is useful for understanding many properties such as symmetry and sharpness of the rocking curve under special conditions. Therefore, employing the Riemann surface is instructive for numerical analysis and useful for understanding dynamical diffraction in the Bragg case.

scholarly journals Spherical-multipole analysis of an arbitrarily directed complex-source beam diffracted by an acoustically soft or hard circular cone

2015 ◽  
Vol 13 ◽  
pp. 57-61 ◽  
Author(s):  
A. Reinhardt ◽  
H. Bruens ◽  
L. Klinkenbusch ◽  
M. Katsav ◽  
E. Heyman
Keyword(s):  
Numerical Analysis ◽  
Boundary Value Problem ◽  
Analytical Approach ◽  
Circular Cone ◽  
Legendre Functions ◽  
Soft Or ◽  
Associated Legendre Functions ◽  
Multipole Analysis ◽  
Complex Source ◽  
Complex Valued

Abstract. An analytical approach to analyze the diffraction of an arbitrarily directed complex-source beam (CSB) by an acoustically soft or hard semi-infinite circular cone is presented. The beam is generated by assigning a complex-valued location to a point source; its waist and direction are defined by the real and imaginary parts of the source coordinate, respectively. The corresponding scalar boundary-value problem is solved by a spherical-multipole analysis. The solution requires the calculation of associated Legendre functions of the first kind for complex-valued arguments which turns out to be a non-trivial task. Beside a numerical analysis of the corresponding algorithms we present numerical results for the total near- and scattered far-fields.

On the Collapse of Offshore Pipelines under External Pressure and Axial Force

2013 ◽  
Vol 419 ◽  
pp. 134-139
Author(s):  
Neng Gan ◽  
Jiang Hong Xue
Keyword(s):  
Hydrostatic Pressure ◽  
Axial Force ◽  
Analytical Approach ◽  
Shell Theory ◽  
Ritz Method ◽  
Morphological Characteristics ◽  
External Pressure ◽  
Governing Equations ◽  
Offshore Pipelines ◽  
Axial Tension

The elastic collapse of long cylinders under combined external pressure and axial force was investigated using analytical approach. Long cylindrical pipelines laid on the seabed are subjected to external pressure, initial defect will cause the local collapse of the pipelines. Due to the change of subsea environments and construction conditions, circular pipelines are subjected not only to the hydrostatic pressure, but also to forces of other forms, such as axial tension or compression, so on and so forth. This paper studies the local collapse and the morphological characteristics of a circular pipelines subjected to hydrostatic pressure and axial force. Governing equations based on Karman-Donnell`s shell theory are derived and are solved using Ritz method.

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