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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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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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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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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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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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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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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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Magnetic field and rotational eigenfrequencies
Physics of the Earth and Planetary Interiors, 1999Abstract The theory of the rotation of the fluid core is modified in order to take into account the magnetic field within the core. Because of the conductivity of the lower mantle, there is a frictional magnetic torque which appears at the core–mantle boundary (CMB); the magnitude of this torque depends on the conductivity profile within the mantle ...
Marianne Greff-Lefftz, Hilaire Legros
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Eigenfrequencies of tuning-forks
Computer Methods in Applied Mechanics and Engineering, 1972Abstract The problem to find the natural frequencies and the appropriate modes of vibration of tuning-forks of quite general geometry is investigated. The tuning-fork is first discretized, and then the method of transfer matrices is applied. Numerical results are presented for three test examples to illustrate the accuracy of the method.
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Approximate Evaluation of Eigenfrequencies
2013Approximate evaluation of rotors flexural eigenfrequencies is investigated in Chap. 1. However, the formulation is similar for torsional vibrations of shafts or even vibrations of elastic systems in general. The Dunkerley's rule for the determination of lowest eigenfrequency of a lumped-mass, multi-degree-of-freedom elastic shaft is applied along with ...
Andrew D. Dimarogonas +2 more
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