On wave propagation in repetitive structures: two forms of transfer matrix
On wave propagation in repetitive structures: two forms of transfer matrix
Two forms of dynamic transfer matrix are derived for a one-dimensional (beam-like) repetitive pin-jointed structure with point masses located at nodal cross-sections, the displacement-force transfer matrix G, and the displacement-displacement transfer matrix, H. Similarity matrices are introduced to relate G and H, together with their respective metrics. Symplectic orthogonality relationships for the eigenvectors of both G and H are derived, together with relationships between their respective sets of eigenvectors. New expressions for the group velocity are derived. For repetitive structures of finite length, natural frequency equations are derived employing both G and H, including phase-closure and the direct application of boundary (end) conditions. Besides an exposition of the theory, some familiar but much new, the focus of the present paper is on the relationships between the two forms of transfer matrix, including their respective (dis)advantages. Numerical results, together with further theory necessary for interpretation, are presented in companion papers.
wave propagation; repetitive structures; transfer matrices; symplectic orthogonality; group velocity
99-112
Stephen, N.G.
af39d0e9-b190-421d-86fe-28b793d5bca3
Ashari, A.K.
9f3df59f-2d1d-4b19-bd2c-bf3005eabd96
20 January 2019
Stephen, N.G.
af39d0e9-b190-421d-86fe-28b793d5bca3
Ashari, A.K.
9f3df59f-2d1d-4b19-bd2c-bf3005eabd96
Stephen, N.G. and Ashari, A.K.
(2019)
On wave propagation in repetitive structures: two forms of transfer matrix.
Journal of Sound and Vibration, 439, .
(doi:10.1016/j.jsv.2018.09.036).
Abstract
Two forms of dynamic transfer matrix are derived for a one-dimensional (beam-like) repetitive pin-jointed structure with point masses located at nodal cross-sections, the displacement-force transfer matrix G, and the displacement-displacement transfer matrix, H. Similarity matrices are introduced to relate G and H, together with their respective metrics. Symplectic orthogonality relationships for the eigenvectors of both G and H are derived, together with relationships between their respective sets of eigenvectors. New expressions for the group velocity are derived. For repetitive structures of finite length, natural frequency equations are derived employing both G and H, including phase-closure and the direct application of boundary (end) conditions. Besides an exposition of the theory, some familiar but much new, the focus of the present paper is on the relationships between the two forms of transfer matrix, including their respective (dis)advantages. Numerical results, together with further theory necessary for interpretation, are presented in companion papers.
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Paper1_NGS_Final
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Accepted/In Press date: 16 September 2018
e-pub ahead of print date: 24 September 2018
Published date: 20 January 2019
Keywords:
wave propagation; repetitive structures; transfer matrices; symplectic orthogonality; group velocity
Identifiers
Local EPrints ID: 423134
URI: http://eprints.soton.ac.uk/id/eprint/423134
ISSN: 0022-460X
PURE UUID: 6bbe773e-9737-4cea-aec9-272520e80ffa
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Date deposited: 19 Sep 2018 11:04
Last modified: 16 Mar 2024 07:05
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Author:
A.K. Ashari
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