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.

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.

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.

Asymptotic expansions and converging factors V. Lommel, Struve, modified Struve, Anger and Weber functions, and integrals of ordinary and modified Bessel functions

1959 ◽  
Vol 249 (1257) ◽  
pp. 284-292 ◽  
Keyword(s):  
Asymptotic Expansions ◽  
Bessel Functions ◽  
Modified Bessel Functions ◽  
Lommel Functions ◽  
Special Cases

A theory of Lommel functions is developed, based upon the methods described in the first four papers (I to IV) of this series for replacing the divergent parts of asymptotic expansions by easily calculable series involving one or other of the four ‘basic converging factors’ which were investigated and tabulated in I. This theory is then illustrated by application to the special cases of Struve, modified Struve, Anger and Weber functions, and integrals of ordinary and modified Bessel functions.

(p, q)-Extended Bessel and Modified Bessel Functions of the First Kind

2017 ◽  
Vol 72 (1-2) ◽  
pp. 617-632 ◽  
Author(s):  
Dragana Jankov Maširević ◽  
Rakesh K. Parmar ◽  
Tibor K. Pogány
Keyword(s):  
Bessel Functions ◽  
Modified Bessel Functions

Approximated Fundamental Frequency for Thin Circular Plates Clamped or Pinned at the Edge

2007 ◽  
Author(s):  
George Weiss
Keyword(s):  
Circular Plate ◽  
Fundamental Frequency ◽  
Bessel Functions ◽  
Unit Area ◽  
Continuous System ◽  
Modified Bessel Functions ◽  
Circular Plates ◽  
Numerical Parameter ◽  
Elliptical Plate ◽  
Distributed Load

Calculating the exact solution to the differential equations that describe the motion of a circular plate clamped or pinned at the edge, is laborious. The calculations include the Bessel functions and modified Bessel functions. In this paper, we present a brief method for calculating with approximation, the fundamental frequency of a circular plate clamped or pinned at the edge. We’ll use the Dunkerley’s estimate to determine the fundamental frequency of the plates. A plate is a continuous system and will assume it is loaded with a uniform distributed load, including the weight of the plate itself. Considering the mass per unit area of the plate, and substituting it in Dunkerley’s equation rearranged, we obtain a numerical parameter K02, related to the fundamental frequency of the plate, which has to be evaluated for each particular case. In this paper, have been evaluated the values of K02 for thin circular plates clamped or pinned at edge. An elliptical plate clamped at edge is also presented for several ratios of the semi–axes, one of which is identical with a circular plate.

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