Mode localization up to high frequencies in coupled one-dimensional subsystems

1995 ◽  
Vol 185 (1) ◽  
pp. 79-91 ◽  
Author(s):  
R.S. Langley
Keyword(s):  
Mode Localization ◽  
High Frequencies ◽  
One Dimensional

Mode Localization and Delocalization in Constrained Strings and Beams

1997 ◽  
Author(s):  
Chris H. Riedel ◽  
Chin An Tan
Keyword(s):  
Bernoulli Beam ◽  
Constrained System ◽  
Reflection And Transmission ◽  
Mode Localization ◽  
High Frequencies ◽  
Transmission Coefficients ◽  
Curve Veering ◽  
Elastic Constraints ◽  
Euler Bernoulli Beam ◽  
Free Vibration Response

Abstract The free vibration response of a string and a Euler-Bernoulli beam supported by intermediate elastic constraints is studied and analyzed by the transfer function method. The constrained system consists of three subsystems coupled by constraints imposed at the subsystem interfaces. For both the string and beam systems, curve veering and mode localization are observed in the lower modes when the distance between the elastic constraints is varied. As the mode number increases, the modes of the system become extended indicating that the coupling springs have little effect on the system at higher modes. A wave analysis is employed to further investigate the behavior of the systems at high frequencies. Reflection and transmission coefficients are formulated to show the effects of the constraints on the coupling of the subsystems. The weakly bi-coupled beam produces an interesting phenomena where a particular mode experiences no localization while neighboring modes are localized. The frequency at which this occurs is termed the delocalization frequency. Only one delocalization frequency exists and it occurs where the reflection coefficient of the propagating wave becomes zero.

scholarly journals Skin effect in rectangular conductors at high frequencies

1929 ◽  
Vol 122 (790) ◽  
pp. 533-542 ◽  
Keyword(s):  
High Frequency ◽  
Skin Effect ◽  
General Nature ◽  
Rectangular Section ◽  
Electrical Force ◽  
High Frequencies ◽  
One Dimensional ◽  
Finite Breadth ◽  
Parallel Strips ◽  
Cylindrical Conductors

There is at present little exact information either theoretical or experimental on the high frequency resistance of cylindrical conductors of rectangular section, although the general nature of the phenomenon is quite well known and has been exhaustively treated in the case of circular conductors by Kelvin, Heaviside, Russell and others. The first method of attack on the problem of the rectangular conductor is to treat it as a strip of infinite breadth when the problem becomes one dimensional and requires simply a solution of ∂ 2 E/∂ x 2 = 4πμ/ρ ∂E/∂ t E being the electrical force and μ and ρ the permeability and resistivity respectively. The solution of the problem for two parallel strips was first given by Rayleigh and it was shown that for high frequencies the current decreases exponentially toward the centre of the conductor, being confined effectively to a surface layer so that the resistance of the conductor was the same as if composed of surface strips of thickness (2πμω/ρ) -½ , ω to being the periodicity. This approximation, however, gives much too low values for the high frequency resistance of a conductor of finite breadth.

WIDEBAND UHF LOADS BASED ON STEPPED-HETEROGENEOUS LINES WITH LOSSES

2018 ◽  
pp. 68-72
Author(s):  
G. G. Savenkov ◽  
V. P. Razinkin ◽  
V. A. Khrustalev
Keyword(s):  
Transmission Lines ◽  
High Power ◽  
Basic Structure ◽  
High Frequencies ◽  
Line Segments ◽  
One Dimensional ◽  
Modelling Method ◽  
Large Length ◽  
One Step ◽  
Frequency Properties

The relevance of wideband load devices application in the modern UHF equipment is described in this paper. The basic structure and principle of operation of microstrip load are described. Design methods of high power wideband UHF loads in a series connection of line segments with increasing value of dissipative losses are considered in this paper. The stepped-heterogeneous loads frequency properties analysis based on one-dimensional transmission lines theory and numeric electrodynamic modelling is carried out. It was shown, that considered loads based on large length transmit lines with dissipative losses have good matching quality on high frequencies, which worsen with frequency reduction. Frequency characteristics, calculated via numeric electrodynamic modelling method of one-step and two-step centimeter wavelength microstrip loads are represented. A convergence of modelling and theoretic characteristics is shown.

Vibration Mode Localization in One-Dimensional Systems

AIAA Journal ◽  
10.2514/2.4 ◽  
1997 ◽  
Vol 35 (10) ◽  
pp. 1645-1652 ◽  
Author(s):  
Wei-Chau Xie ◽  
Xing Wang
Keyword(s):  
Vibration Mode ◽  
Mode Localization ◽  
One Dimensional

scholarly journals Inverses of Matérn Covariances on Grids

Biometrika ◽  
2021 ◽  
Author(s):  
Joseph Guinness
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Covariance Function ◽  
Grid Spacing ◽  
Regular Grid ◽  
High Frequencies ◽  
One Dimensional ◽  
Covariance Functions ◽  
The One

Abstract We conduct a study of the aliased spectral densities of Matérn covariance functions on a regular grid of points, providing clarity on the properties of a popular approximation based on stochastic partial differential equations. While others have shown that it can approximate the covariance function well, we find that it assigns too much power at high frequencies and does not provide increasingly accurate approximations to the inverse as the grid spacing goes to zero, except in the one-dimensional exponential covariance case.

scholarly journals ALGORITHM FOR VERTICAL DIFFUSION

1976 ◽  
Vol 1 (15) ◽  
pp. 190
Author(s):  
Soren Peter Kjeldsen
Keyword(s):  
Diffusion Coefficients ◽  
Vertical Mixing ◽  
Computing Methods ◽  
Vertical Diffusion ◽  
Governing Parameter ◽  
High Frequencies ◽  
One Dimensional ◽  
Two Fluids ◽  
Cyclic Frequency ◽  
Constant Coefficients

A mathematical method and a computer algorithm is developed for the case of one-dimensional vertical mixing for an estuary with rather small advection. In the case under consideration varies the diffusion coefficients both with time and depth, and the case is therefore closer to actual estuaries than earlier computing methods that applies constant coefficients. Model experiments with a small grid oscilliating with high frequencies in two fluids with different densities were performed to test the algorithm. Reynolds number for turbulence was near 1.6-101'. The results showed that the ratio between the stabilizing Brunt-Vaisala frequency and the agitating cyclic frequency was a governing parameter for the system, and dimensionless. diffusion coefficients could be expressed as a function of this parameter.

Vibration mode localization in one-dimensional systems

AIAA Journal ◽  
1997 ◽  
Vol 35 ◽  
pp. 1645-1652
Author(s):  
Wei-Chau Xie ◽  
Xing Wang
Keyword(s):  
Vibration Mode ◽  
Mode Localization ◽  
One Dimensional
Sign in / Sign up

Export Citation Format

Share Document