On one-dimensional vibrating systems

1963 ◽  
Vol 276 (1366) ◽  
pp. 418-435 ◽  
Keyword(s):  
Exact Expression ◽  
Frequency Equation ◽  
Alternative Formulation ◽  
Vibration Band ◽  
One Dimensional ◽  
Power Series Expansions ◽  
Wave Region ◽  
Band Spectra ◽  
The Masses ◽  
Vibrating Systems

An exact expression is derived for the frequency equation of a linear vibrating system with arbitrary masses. By considering the particular case in which all the masses are equal but for a few isolated exceptions, the properties of isotopic mass defects in a homogeneous one-dimensional chain are simply deduced. A stochastic model in which the masses follow a given probability distribution is then discussed, and following a method introduced by Weiss & Maradudin (1958) expansions for the spectrum are obtained in terms of moments about the mean mass. Hence power series expansions are derived for the long-wave region of the spectrum, and these are extended to models in which short-range order is present. An alternative formulation offers reasonable hope of calculating spectra over the whole frequency range. Finally, a number of general properties of vibration band spectra in one dimension are obtained.

The Analysis and Synthesis of Vibrating Systems

1954 ◽  
Vol 58 (526) ◽  
pp. 703-719 ◽  
Author(s):  
R. E. D. Bishop
Keyword(s):  
Composite System ◽  
Frequency Equation ◽  
Computational Effort ◽  
Analytical Treatment ◽  
Principal Mode ◽  
Oscillatory Systems ◽  
Composite Systems ◽  
Analysis And Synthesis ◽  
Simple Systems ◽  
Vibrating Systems

SummaryComplicated oscillatory systems may be broken down into component “ sub-systems ” for the purpose of vibration analysis. These will generally submit more readily to analytical treatment. After an introduction to the concept of receptance, the principles underlying this form of analysis are reviewed.The dynamical properties of simple systems (in the form of their receptances) may be tabulated. By this means the properties of a complicated system may be found by first analysing it into convenient sub-systems and then extracting the properties of the latter from a suitable table. A catalogue of this sort is given for the particular case of conservative torsional systems with finite freedom.The properties of the composite system which may be readily found in this way are (i) its receptances and (ii) its frequency equation. Tables are given of expressions for these in terms of the receptances of the component sub-systems. All of the tables may easily be extended. The tabulated receptances may also be used for determining relative displacements during free vibration in any principal mode.A method of presenting information on the vibration characteristics of machinery, which is effectively due to Carter, is illustrated by means of an example. More general adoption by manufacturers of this method (which requires no more computational effort than must normally be made) would lead to enormous savings of labour in calculating natural frequencies of composite systems.

On approach to determine the internal potential and gravitational energy of ellipsoid

2021 ◽  
Vol 8 (3) ◽  
pp. 359-367
Author(s):  
М. M. Fys ◽  
◽  
А. M. Brydun ◽  
М. I. Yurkiv ◽  
◽  
...  
Keyword(s):  
Distribution Function ◽  
Mass Distribution ◽  
Special Form ◽  
Iterative Process ◽  
Three Dimensional ◽  
Gravitational Energy ◽  
One Dimensional ◽  
Piecewise Continuous ◽  
The Masses ◽  
Internal Potential

Formulas are derived for the calculation of the potential of bodies, which surface is a sphere or an ellipsoid, and the distribution function has a special form: a piecewise continuous one-dimensional function and a three-dimensional mass distribution. For each of these cases, formulas to calculate both external and internal potentials are derived. With their help, further the expressions are given for calculation of the potential (gravitational) energy of the masses of such bodies and their corresponding distributions. For spherical bodies, the exact and approximate relations for determining the energy are provided, which makes it possible to compare the iterative process and the possibility of its application to an ellipsoid. The described technique has been tested by a specific numerical example.

scholarly journals HST-FGS Astrometry of the Low Mass Binary L722-22

1999 ◽  
Vol 172 ◽  
pp. 405-407
Author(s):  
L.G. Taff ◽  
John L. Hershey
Keyword(s):  
Main Sequence ◽  
Hubble Space Telescope ◽  
Brown Dwarf ◽  
One Dimensional ◽  
Photographic Images ◽  
System A ◽  
Data Points ◽  
Low Mass ◽  
The Masses ◽  
M Dwarf

The M dwarf L722-22 (= LHS 1047) was discovered to be a binary system by Ianna 20 years ago. The analysis of the ground- based data indicated a mass 0.06M⊙ for the secondary. This is below the nominal stellar mass limit of 0.08M⊙. The importance of potential “brown-dwarf” candidates, and the fact that the masses of both components place them near the end of the main sequence, made this system a prime object for further, intensive, study.This close (separation 0."3), faint (V = 11.m5, 14.m4) binary was near the limit for ground-based work. The residuals of an individual night’s photographic data were typically at the 50% level. Also, the photographic images are completely blended. The few one-dimensional speckle data points yielded a merged, asymmetric image profile. Finally, this system is too faint for HIPPARCOS. Our proposal for Hubble Space Telescope Fine Guidance Sensor (FGS) observing was approved in 1992.

Intervalley kinetic energy terms in the effective mass equation: a one-dimensional analytical study

1989 ◽  
Vol 67 (9) ◽  
pp. 896-903 ◽  
Author(s):  
Lorenzo Resca
Keyword(s):  
Kinetic Energy ◽  
Effective Mass ◽  
Analytical Study ◽  
Three Dimensional ◽  
Real Space ◽  
The Other ◽  
Alternative Formulation ◽  
One Dimensional ◽  
Symmetry Properties ◽  
Band Case

We show that a one-dimensional analytical study allows us to test and clarify the derivation, assumptions, and symmetry properties of the intervalley effective mass equation (IVEME). In particular, we show that the IVEME is consistent with a two-band case, and is in fact exact for a model that satisfies exactly all its assumptions. On the other hand, an alternative formulation in k-space that includes intervalley kinetic energy terms is consistent with a one-band case, provided that intra-valley kinetic energy terms are also calculated consistent with one band. We also show that the standard symmetry assumptions for both real space and k-space formulations are not actually exact, but are consistent with a "total symmetric" projection, or with taking spherical averages in a three-dimensional case.

ESR Measurements on One-Dimensional Quantum Ferrimagnets A3Cu3(PO4)4 with A=Sr and Ca in Submillimeter-Wave Region

2006 ◽  
Vol 75 (9) ◽  
pp. 094718 ◽  
Author(s):  
Shojiro Kimura ◽  
Hirofumi Ishikawa ◽  
Yuji Inagaki ◽  
Makoto Yoshida ◽  
Susumu Okubo ◽  
...  
Keyword(s):  
Submillimeter Wave ◽  
One Dimensional ◽  
Wave Region

scholarly journals Masses of asteroids and total mass of the main asteroid belt

2015 ◽  
Vol 10 (S318) ◽  
pp. 212-217
Author(s):  
E. V. Pitjeva ◽  
N. P. Pitjev
Keyword(s):  
Total Mass ◽  
Radar Data ◽  
Asteroid Belt ◽  
Two Dimensional ◽  
Binary Asteroids ◽  
One Dimensional ◽  
Main Asteroid Belt ◽  
The Individual ◽  
The Masses ◽  
Academy Of Sciences

AbstractAn estimation of the mass of the main asteroid belt was made on the basis of the new version of EPM2014 ephemerides of the Institute of Applied Astronomy of Russian Academy of Sciences using about 800000 positional observations of planets and spacecraft. We obtained the individual estimations of masses of large asteroids from radar data, as well as estimates of the masses of asteroids by using known diameters and estimated average densities for the three taxonomic types (C, S, M), and used the known mass values of binary asteroids and asteroids to which spacecraft approached. A two-dimensional homogeneous annulus with dimensions corresponding observed width of the main asteroid belt (2.06 au and 3.27 au) was used instead of a previous massive one-dimensional ring for modeling total perturbations from small asteroids. The obtained value of the total mass of the main asteroid belt is (12.25 ± 0.19)10−10M⊙.

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