scholarly journals Analysis of Two Colliding Thin Spherical Shells

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Shock Waves ◽  
Wave Theory ◽  
Contact Theory ◽  
Hertz Contact ◽  
Wave Fronts ◽  
Spherical Shells ◽  
Elastic Shells ◽  
Hertz Contact Theory ◽  
The Moment ◽  
Contact Domain

In the present paper, the collision of two elastic spherical shells is investigated using the wave theory of impact. The model developed here suggests that after the moment of impact quasi-longitudinal and quasi-transverse shock waves are generated, which then propagate along the spherical shells. The solution behind the wave fronts is constructed with the help of the theory of discontinuities. Since the local bearing of the materials of the colliding elastic shells is taken into account, then the solution in the contact domain is found via the Hertz contact theory.

Fractional Derivative Viscoelastic Model for the Analysis of Two Colliding Spherical Shells

2012 ◽  
Author(s):  
Yury A. Rossikhin ◽  
Marina V. Shitikova
Keyword(s):  
Fractional Derivative ◽  
Equations Of Motion ◽  
Viscoelastic Model ◽  
Wave Fronts ◽  
Spherical Shells ◽  
Reflected Waves ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
The Moment ◽  
Contact Domain

The collision of two isotropic spherical shells is investigated for the case when the viscoelastic features of the shells represent themselves only in the place of contact and are governed by the standard linear solid model with fractional derivatives. Thus, the problem concerns the shock interaction of two shells, wherein the generalized fractional-derivative standard linear law instead of the Hertz contact law is employed as a low of interaction. The pans of the shells beyond the contact domain are assumed to be elastic, and their behavior is described by the equations of motion which take rotary inertia and shear deformations into account. The model developed here suggests that after the moment of impact quasi-longitudinal and quasi-transverse shock waves are generated, which then propagate along the spherical shells. Due to the short duration of contact interaction, the reflected waves are not taken into account. The solution behind the wave fronts is constructed with the help of the theory of discontinuities. To determine the desired values behind the wave fronts, one-term ray expansions are used, as well as the equations of motion of the contact domains for the both spherical shells.

scholarly journals Investigation on indentation rolling resistance of belt conveyor based on Hertz contact theory compared with one-dimensional Winkler foundation

2018 ◽  
Vol 10 (7) ◽  
pp. 168781401878393 ◽  
Author(s):  
Lu Yan
Keyword(s):  
Rolling Resistance ◽  
Contact Theory ◽  
Theoretical Formula ◽  
Winkler Foundation ◽  
Hertz Contact ◽  
Belt Conveyor ◽  
One Dimensional ◽  
Hertz Contact Theory ◽  
Viscoelastic Theory ◽  
Indentation Rolling Resistance

Based on Hertz contact theory and one-dimensional Winkler foundation combination with viscoelastic theory, the author derived theoretical formulas of indentation rolling resistance, respectively. Using the laboratorial apparatus of indentation rolling resistance, the author mainly concentrates on the error analysis about two kinds of theoretical formula which bear on indentation rolling resistance compared with experimental result. The reason why author employs Hertz contact theory to discuss indentation rolling resistance is that indentation rolling resistance is a sort of contact resistance. As a result, Hertz contact theory is generally applicable to study it. On the other hand, because conveyor belt has viscoelastic property, it is appropriate to use viscoelastic theory by the aid of three-parameter Maxwell viscoelastic model combination with one-dimensional Winkler foundation. Ultimately, this article infers that theoretical formula based on the Hertz contact is brief and clear compared with one-dimensional Winkler foundation in principle. However, it is noticeable that when the belt is at high speed, the reliability of formula based on Hertz theory has decreased obviously. This conclusion can give a beneficial reference for the energy saving of belt conveyor.

scholarly journals Compliant contact force models in multibody dynamics: Evolution of the Hertz contact theory

2012 ◽  
Vol 53 ◽  
pp. 99-121 ◽  
Author(s):  
Margarida Machado ◽  
Pedro Moreira ◽  
Paulo Flores ◽  
Hamid M. Lankarani
Keyword(s):  
Multibody Dynamics ◽  
Contact Force ◽  
Contact Theory ◽  
Hertz Contact ◽  
Hertz Contact Theory

Analysis of the Gearing Theoretic between Plastic Helical Gear and Steel Worm

2010 ◽  
Vol 34-35 ◽  
pp. 232-237
Author(s):  
Yi Shu Hao ◽  
Bin Nan Yue ◽  
Xin Xing Zhu
Keyword(s):  
Deformation Process ◽  
Helical Gear ◽  
Tooth Profile ◽  
Contact Theory ◽  
Hertz Contact ◽  
Stress Strain ◽  
Hertz Contact Theory ◽  
Potential Contact ◽  
The Law ◽  
Strain Status

The gearing transmission equation was deduced by the principle of the engagement characteristics between plastic helical gear and steel worm. This paper makes an analysis on the law which is the deformation process of tooth profile and potential contact in different kinds of load by means of Hertz contact theory. The paper also uses MSC.Nastran to simulate the stress-strain status, the deformation process and arrives at the law of gearing changing, which was verified the correctness of the analysis above.

Contact Model of Double Circular Arc Gear Based on Fractal Theory

2010 ◽  
Vol 43 ◽  
pp. 414-419
Author(s):  
Kang Huang ◽  
Song Bo Han ◽  
Rong De Yang ◽  
Shun Xu
Keyword(s):  
Fractal Theory ◽  
Strength Calculation ◽  
Contact Model ◽  
Contact Theory ◽  
Contact Strength ◽  
Hertz Contact ◽  
Circular Arc ◽  
Hertz Contact Theory

Aiming at the problem that it is difficult to solve contact strength calculation of double circular arc gear with the method of traditional the Hertz contact theory and FEM, methods of fractal theory had been used to establish the contact model of double arc gear based on fractal theory, and an example of calculation was given away. This article results that it is feasible to calculate contact strength with fractal theory in the driving of concave convex meshing gear and this contact model of double circular arc gear based on fractal theory would provide a new way of the research of contact strength calculation of double circular arc gear.

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