Stiffness of Annular Bonded Rubber Flanged Bushes

2006 ◽  
Vol 79 (2) ◽  
pp. 233-248 ◽  
Author(s):  
J. M. Horton ◽  
G. E. Tupholme
Keyword(s):  
Closed Form ◽  
Finite Length ◽  
Classical Theory ◽  
Theory Of Elasticity ◽  
Numerical Results ◽  
Torsional Stiffness ◽  
Radial Stiffness ◽  
Physical Data

Abstract Closed-form expressions are derived for the torsional stiffness, radial stiffness and tilting stiffness of annular rubber flanged bushes of finite length in three principal modes of deformation, based upon the classical theory of elasticity. Illustrative numerical results are deduced with realistic physical data of typical flanged bushes.

Stiffness of Rubber Bush Mountings Subjected to Radial Loading

2000 ◽  
Vol 73 (2) ◽  
pp. 253-264 ◽  
Author(s):  
J. M. Horton ◽  
M. J. C. Gover ◽  
G. E. Tupholme
Keyword(s):  
Experimental Data ◽  
Finite Length ◽  
Classical Theory ◽  
Bessel Functions ◽  
Exact Expression ◽  
Theory Of Elasticity ◽  
Modified Bessel Functions ◽  
Approximate Representation ◽  
Radial Stiffness ◽  
Radial Loading

Abstract Based on the classical theory of elasticity, an exact expression is derived for the radial stiffness of a cylindrical rubber bush mounting of finite length, in terms of modified Bessel functions. From this a convenient approximate representation is deduced. Some exact and approximate numerical results are compared with the experimental data which are available.

The Elastic Plane With a Circular Insert, Loaded by a Tangentially Directed Force

1962 ◽  
Vol 29 (2) ◽  
pp. 362-368 ◽  
Author(s):  
M. Hete´nyi ◽  
J. Dundurs
Keyword(s):  
Closed Form ◽  
Elastic Properties ◽  
Classical Theory ◽  
Theory Of Elasticity ◽  
Elastic Plane ◽  
Elementary Functions ◽  
Explicit Formulas ◽  
Concentrated Force

The problem treated is that of a plate of unlimited extent containing a circular insert and subjected to a concentrated force in the plane of the plate and in a direction tangential to the circle. The elastic properties of the insert are different from those of the plate, and a perfect bond is assumed between the two materials. The solution is exact within the classical theory of elasticity, and is in a closed form in terms of elementary functions. Explicit formulas are given for the components of stress in Cartesian co-ordinates, and also in polar co-ordinates at the circumference of the insert.

Axial Loading of Annular Bonded Rubber Blocks

2003 ◽  
Vol 76 (5) ◽  
pp. 1194-1211 ◽  
Author(s):  
J. M. Horton ◽  
G. E. Tupholme ◽  
M. J. C. Gover
Keyword(s):  
Experimental Data ◽  
Stress Distribution ◽  
Closed Form ◽  
Cross Section ◽  
Classical Theory ◽  
Cross Sections ◽  
Axial Loading ◽  
Theory Of Elasticity ◽  
Governing Equations ◽  
Annular Cross Section

Abstract Closed-form expressions are derived using a superposition approach for the axial deflection and stress distribution of axially loaded rubber blocks of annular cross-section, whose ends are bonded to rigid plates. These satisfy exactly the governing equations and conditions based upon the classical theory of elasticity. Readily calculable relationships are derived for the corresponding apparent Young's modulus, Ea, and the modified modulus, Ea′, and their numerical values are compared with the available experimental data. Elementary expressions for evaluating Ea and Ea′ approximately are deduced from these, in forms which are closely analogous to those given previously for blocks of circular and long, thin rectangular cross-sections. The profiles of the deformed lateral surfaces of the block are discussed and it is confirmed that the assumption of parabolic lateral profiles is not valid generally.

The Elastic Plane With a Circular Insert, Loaded by a Radial Force

1961 ◽  
Vol 28 (1) ◽  
pp. 103-111 ◽  
Author(s):  
J. Dundurs ◽  
M. Hete´nyi
Keyword(s):  
Closed Form ◽  
Elastic Properties ◽  
Classical Theory ◽  
Radial Force ◽  
Theory Of Elasticity ◽  
Elastic Plane ◽  
Elementary Functions ◽  
Explicit Formulas

The problem treated is that of a plate of unlimited extent containing a circular insert and subjected to a concentrated radial force in the plane of the plate. The elastic properties of the insert are different from those of the plate, and a perfect bond is assumed between the two materials. The solution is exact within the classical theory of elasticity, and is in a closed form in terms of elementary functions. Explicit formulas are given for the components of stress in Cartesian co-ordinates, and also in polar co-ordinates at the circumference of the insert.

Analytical Solutions of Stresses in Functionally Graded Circular Hollow Cylinder with Finite Length

2004 ◽  
Vol 261-263 ◽  
pp. 651-656 ◽  
Author(s):  
Z.S. Shao ◽  
L.F. Fan ◽  
Tie Jun Wang
Keyword(s):  
Young’S Modulus ◽  
Hollow Cylinder ◽  
Finite Length ◽  
Analytical Solutions ◽  
Radial Direction ◽  
Young's Modulus ◽  
Functionally Graded ◽  
Numerical Results ◽  
Stress Fields ◽  
Simply Supported

Analytical solutions of stress fields in functionally graded circular hollow cylinder with finite length subjected to axisymmetric pressure loadings on inner and outer surfaces are presented in this paper. The cylinder is simply supported at its two ends. Young's modulus of the material is assumed to vary continuously in radial direction of the cylinder. Moreover, numerical results of stresses in functionally graded circular hollow cylinder are appeared.

Study of internal stresses in rock massif within the framework of elastic layered block models with inclusions of the hierarchical structure of the L-rank.

2021 ◽  
Author(s):  
Olga Hachay ◽  
Andrey Khachay
Keyword(s):  
Hierarchical Structure ◽  
Classical Theory ◽  
Acoustic Waves ◽  
Degrees Of Freedom ◽  
Heterogeneous Media ◽  
Theory Of Elasticity ◽  
Rock Massif ◽  
Local Theory ◽  
Internal Stresses ◽  
Non Local

<p>In recent years, new models of continuum mechanics, generalizing the classical theory of elasticity, have been intensively developed. These models are used to describe composite and statistically heterogeneous media, new structural materials, as well as in complex massifs in mine conditions. The paper presents an algorithm for the propagation of longitudinal acoustic waves in the framework of active well monitoring of elastic layered block media with inclusions of hierarchical type of L-th rank. Relations for internal stresses and strains for each hierarchical rank are obtained, which constitute the non local theory of elasticity. The essential differences between the non local theory of elasticity and the classical one and the connection between them are investigated. A characteristic feature of the theory of media with a hierarchical structure is the presence of scale parameters in explicit or implicit form. This work focuses on the study of the effects of non locality and internal degrees of freedom, reflected in internal stresses, which are not described by the classical theory of elasticity and which can be potential precursors of the development of a catastrophic process in a rock massif. Thanks to the use of a model of a layered block medium with hierarchical inclusions, it is possible, using borehole acoustic monitoring, to determine the position of the highest values ​​of internal stresses and, with less effort, to implement the method of unloading the rock massif. If it is necessary to conduct short-term predictive monitoring of geodynamic regions and determine a more accurate position of the source of a dynamic phenomenon using borehole active acoustic observations, it is necessary to use the values ​​of the tensor of internal hierarchical stresses as a monitored parameter.</p>

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