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Eigenfrequency shift mechanism due to variation in the cross sectional area of a conduit
Journal of Hydraulic Research/De Recherches Hydrauliques, 2017 Eigenfrequency (i.e. natural resonant frequency) shift due to variation in the cross sectional area of a conduit is observed in different applications such as vocal tracts, musical instruments and water supply systems.
Moez Louati, Mohamed S Ghidaoui
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Zero Eigenfrequencies in the Vibrating Polygon
Journal of Sound and Vibration, 1994Abstract It is pointed out that the number of zero eigenfrequencies previously predicted by group theoretical techniques for the in-plane modes of a vibrating regular polygon, consisting of identical particles at the vertices connected along the sides by identical springs, seems excessive. The apparent excess is due to unstable modes. Similar systems
Perrin, R., Swallowe, G. M.
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Annals of Physics, 1972
Abstract This paper is concerned with the oscillations which appear in the smoothed density of eigenvalues when the smoothing width is relatively small. The existence of these oscillations is demonstrated by evaluating exactly the smoothed eigenvalue density for simple shapes of the volume—flat parallelepiped, sphere.
Balian, R., Bloch, C.
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Abstract This paper is concerned with the oscillations which appear in the smoothed density of eigenvalues when the smoothing width is relatively small. The existence of these oscillations is demonstrated by evaluating exactly the smoothed eigenvalue density for simple shapes of the volume—flat parallelepiped, sphere.
Balian, R., Bloch, C.
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Electromagnetic Eigenfrequencies in a Spheroidal Cavity
Journal of Electromagnetic Waves and Applications, 1997Summary: The electromagnetic eigenfrequencies \(f_{nsm}\) in a perfectly conducting spheroidal cavity are determined analytically, by a shape perturbation method. The analytical determination is possible in the case of small values of the quantity \(v= 1- a^2/b^2\), \((|v|\ll 1)\), where \(2a\) and \(2b\) are the lengths of the rotation axis and the ...
Kokkorakis, G. C., Roumeliotis, J. A.
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Conformal cloaks at eigenfrequencies
Journal of Physics D: Applied Physics, 2013(Chen et al 2011 Phys. Rev. A 83 055801) show that conformal cloak can not only work in geometrical optics limit but also in wave optics, if the working frequency is at the eigenfrequencies of the refractive index profile applied in the lower Riemann sheet (the profile is a special one that pushes light rays to propagate in close orbits). In this paper,
Hui Li, Yadong Xu, Huanyang Chen
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2018
In Sect. 3.3, the DE for eigenfrequencies is derived and discussed in relation to simply supported BC. Now including rotational end springs to get further BC, the analytical solutions complicate and generalized basic Berry functions with an added tilde notation must be introduced.
Wiggers, Sine Leergaard, Pedersen, Pauli
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In Sect. 3.3, the DE for eigenfrequencies is derived and discussed in relation to simply supported BC. Now including rotational end springs to get further BC, the analytical solutions complicate and generalized basic Berry functions with an added tilde notation must be introduced.
Wiggers, Sine Leergaard, Pedersen, Pauli
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On Eigenfrequencies of an Anisotropic Sphere
Journal of Applied Mechanics, 2000This note presents exact frequency equations of two independent classes of vibrations of a spherically isotropic solid sphere with fixed boundary conditions. Numerical calculations are performed and comparison between two different materials is made. Some useful observations are obtained. [S0021-8936(00)00102-1]
W. Q. Chen, +3 more
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EIGENFREQUENCIES OF NONUNIFORM BEAMS
AIAA Journal, 1963Summary Most of the approximate methods (Rayleigh-Ritz, iteration, etc.) for computing eigenfrequencies of structures yield upper bounds. Lower bounds are usually less easy to estimate and often present larger discrepancies from the exact values. There are cases, however, where methods of mass and/or flexibility decomposition, applicable to composite ...
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Reality of the eigenfrequencies of periodic elastic composites
Physical Review B, 1995We analyze the properties of the eigenvalue problem for acoustic waves propagating in a three-dimensional periodic, elastic composite. Although the acoustic eigenvalue problem is not Hermitian, we prove that the eigenfrequencies are real for an arbitrary crystal structure and arbitrary filling fraction of the binary composite.
, Hernández-Cocoletzi +2 more
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The Location of Eigenfrequencies of Electrical Networks
Journal of the Society for Industrial and Applied Mathematics, 19640. Introduction. Let us begin with some definitions and notation. Let 9 be an oriented graph with r branches and s nodes which fulfills the conditions: 1. 9 contains neither a branch beginning and ending in the same node ior an isolated node; 2. 9 contains at least one loop.
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