Symmetrical enchondromatosis is associated with duplication of 12p11.23 to 12p11.22 including PTHLH
Symmetrical enchondromatosis is associated with duplication of 12p11.23 to 12p11.22 including PTHLH
The characteristic frequencies ? of the vibrations of an elastic solid subject to boundary conditions of either zero displacement or zero traction are given by the Rayleigh quotient expressed in terms of the corresponding exact eigenfunctions. In problems that can be analytically expanded in a small parameter ?, it is shown that when an approximate eigenfunction is known with an error O(?N), the Rayleigh quotient gives the frequency with an error O(?2N), a gain of N orders. This result generalizes a well-known theorem for N=1. A non-trivial example is presented for N=4, whereby knowledge of the 3rd-order eigenfunction (error being 4th order) gives the eigenvalue with an error that is 8th order; the 6th-order term thus determined provides an unambiguous derivation of the shear coefficient in Timoshenko beam theory.
3124-3128
Collinson, M.
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Leonard, S.J.
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Charlton, J.
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Crolla, J.A.
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Silve, C.
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Hall, C.M.
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Oglivie, C.
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James, M.A.
14f3f356-3fba-4871-afe9-de5d5d0665cf
Smithson, S.F.
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December 2010
Collinson, M.
3941a8b6-83e6-4350-a8ef-a3331ec5ba44
Leonard, S.J.
6e30413c-2a7f-4d48-b372-88b25f112773
Charlton, J.
0177b4df-4db7-4de8-b4bd-143b8e3ba169
Crolla, J.A.
c5f23751-8de9-4a55-9cc5-ca2fb635769c
Silve, C.
565c604d-709b-4e16-92b4-3b529b53f00d
Hall, C.M.
8b7e030b-6e6f-47b0-aa07-c163864fd689
Oglivie, C.
70b90bf6-94ee-4e58-a030-99b575586757
James, M.A.
14f3f356-3fba-4871-afe9-de5d5d0665cf
Smithson, S.F.
3a4cd2f8-ce0e-4083-aa35-43215fc1877c
Collinson, M., Leonard, S.J., Charlton, J., Crolla, J.A., Silve, C., Hall, C.M., Oglivie, C., James, M.A. and Smithson, S.F.
(2010)
Symmetrical enchondromatosis is associated with duplication of 12p11.23 to 12p11.22 including PTHLH.
American Journal of Medical Genetics part A, 152A (12), .
(doi:10.1002/ajmg.a.33567).
(PMID:21082660)
Abstract
The characteristic frequencies ? of the vibrations of an elastic solid subject to boundary conditions of either zero displacement or zero traction are given by the Rayleigh quotient expressed in terms of the corresponding exact eigenfunctions. In problems that can be analytically expanded in a small parameter ?, it is shown that when an approximate eigenfunction is known with an error O(?N), the Rayleigh quotient gives the frequency with an error O(?2N), a gain of N orders. This result generalizes a well-known theorem for N=1. A non-trivial example is presented for N=4, whereby knowledge of the 3rd-order eigenfunction (error being 4th order) gives the eigenvalue with an error that is 8th order; the 6th-order term thus determined provides an unambiguous derivation of the shear coefficient in Timoshenko beam theory.
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Published date: December 2010
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Local EPrints ID: 169281
URI: http://eprints.soton.ac.uk/id/eprint/169281
ISSN: 1552-4825
PURE UUID: 5d104431-7958-4e48-b5ef-1b3d82304dc6
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Date deposited: 13 Dec 2010 14:14
Last modified: 14 Mar 2024 02:20
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Author:
M. Collinson
Author:
S.J. Leonard
Author:
J. Charlton
Author:
J.A. Crolla
Author:
C. Silve
Author:
C.M. Hall
Author:
C. Oglivie
Author:
M.A. James
Author:
S.F. Smithson
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