Structural-Acoustic Vibration Problems in the Presence of Strong Coupling

Free vibrations of fluid–solid structures are governed by unsymmetric eigenvalue problems. A common approach which works fine for weakly coupled systems is to project the problem to a space spanned by modes of the uncoupled system. For strongly coupled systems, however, the approximation properties are not satisfactory. This paper reports on a framework for taking advantage of the structure of the unsymmetric eigenvalue problem allowing for a variational characterization of its eigenvalues and structure preserving iterative projection methods. We further cover an adjusted automated multilevel substructuring (AMLS) method for huge fluid–solid structures. The reliability and efficiency of the method are demonstrated by the free vibrations of a structure completely filled with water.

Download Full-text

Free Vibrations of Fluid–Solid Structures With Strong Coupling

ASME 2010 Pressure Vessels and Piping Conference: Volume 4 ◽

10.1115/pvp2010-25207 ◽

2010 ◽

Cited By ~ 1

Author(s):

Heinrich Voss ◽

Markus Stammberger

Keyword(s):

Eigenvalue Problems ◽

Projection Methods ◽

Free Vibrations ◽

Coupled Systems ◽

Approximation Properties ◽

Strongly Coupled ◽

Weakly Coupled ◽

Weakly Coupled Systems ◽

Multi Level

Free vibrations of fluid-solid structures are governed by unsymmetric eigenvalue problems. A common approach which works fine for weakly coupled systems is to project the problem to a space spanned by modes of the uncoupled system. For strongly coupled systems however the approximation properties are not satisfactory. This paper reports on a framework for taking advantage of the structure of the unsymmetric eigenvalue problem allowing for a variational characterization of its eigenvalues, and structure preserving iterative projection methods. We further cover an adjusted automated multi-level sub-structuring method for huge fluid-solid structures.

Download Full-text

Article

Canadian Journal of Chemistry ◽

10.1139/v99-157 ◽

1999 ◽

Vol 77 (11) ◽

pp. 1810-1812 ◽

Cited By ~ 7

Author(s):

Alex D Bain

Keyword(s):

Spin System ◽

Coupled System ◽

Coupled Systems ◽

Physical Reason ◽

Strongly Coupled ◽

System Combination ◽

First Order ◽

Weakly Coupled ◽

Quantum Transitions ◽

Weakly Coupled Systems

Strongly coupled spin systems provide many curious and interesting effects in NMR spectra, one of which is the presence of unexpected (from a first-order viewpoint) lines. A physical reason is given for the presence of these combination lines. The X part of the spectrum of an ABX spin system is analysed as an example. For an ABX system, it is well known that the AB nuclei give a spectrum consisting of two AB-type spectra, corresponding to the two orientations of the X nucleus. It can also be shown that the X part of the spectrum corresponds to the X nucleus undergoing a transition in the presence of an AB-like spin system. For weakly coupled systems, the four observed lines correspond to the four different orientations of the A and B nuclei. For a strongly coupled system, two additional lines may appear, the combination lines. The resulting six lines correspond to the four spin orientations, plus the two zero-quantum transitions. It is shown that these six lines are such that there is no net excitation of the AB-like spin system associated with the X transitions. There is no AB coherence created directly by a pulse applied to X. AB coherence is created as the system evolves, and this is responsible for many of the curious effects. This is shown to be true for all spin sub-systems, which are weakly coupled to a strongly coupled sub-system.Key words: NMR, strong coupling, second-order spectra, ABX spin system, combination lines, spectral analysis.

Download Full-text

Cosmological expansion and local systems: exact solutions

Canadian Journal of Physics ◽

10.1139/p07-129 ◽

2008 ◽

Vol 86 (4) ◽

pp. 663-667

Author(s):

V Faraoni

Keyword(s):

Exact Solutions ◽

Coupled Systems ◽

De Sitter ◽

Strongly Coupled ◽

New Exact Solutions ◽

Cosmological Expansion ◽

Weakly Coupled ◽

Weakly Coupled Systems ◽

Sitter Background ◽

04.20 Jb

We study the competition between cosmological expansion and local attraction for relativistic objects embedded in a generic Friedmann universe. The recently discovered “all or nothing” behaviour (i.e., weakly coupled systems are comoving while strongly coupled ones do not expand at all) is found to be limited to the de Sitter background. New exact solutions are presented describing black holes co-moving with a surrounding universe.PACS Nos.: 98.80.–k,04.20.Jb, 04.20.–q

Download Full-text

Cycle characterization of the Aubry set for weakly coupled Hamilton–Jacobi systems

Communications in Contemporary Mathematics ◽

10.1142/s021919971750095x ◽

2018 ◽

Vol 20 (06) ◽

pp. 1750095

Author(s):

H. Ibrahim ◽

A. Siconolfi ◽

S. Zabad

Keyword(s):

Lagrangian Approach ◽

Coupled Systems ◽

Scalar Case ◽

Cycle Condition ◽

Weakly Coupled ◽

Weakly Coupled Systems ◽

Aubry Set ◽

Jacobi Equations

We study a class of weakly coupled systems of Hamilton–Jacobi equations using the random frame introduced in [H. Mitake, A. Siconolfi, H. V. Tran and N. Yamada, A Lagrangian approach to weakly coupled Hamilton–Jacobi systems, SIAM J. Math. Anal. 48(2) (2016) 821–846; doi: https://doi.org/10.1137/15M1010841 ]. We provide a cycle condition characterizing the points of Aubry set. This generalizes a property already known in the scalar case.

Download Full-text