Generic frequency equation for one-dimensional waveguides with incipient cracks based on the phase closure principle

2021 ◽  
pp. 116675
Author(s):  
Hyun Woo Park ◽  
Jin Ho Hwang

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.


1953 ◽  
Vol 20 (2) ◽  
pp. 173-177
Author(s):  
James L. Lubkin ◽  
Yudell L. Luke

Abstract The natural frequencies of a slender, homogeneous, fixed-free rod of variable section are studied in a one-dimensional theory. The rod is uniform at the fixed end for a certain distance L1, and then tapers for a distance L2 so that the cross-sectional area varies linearly. The frequency equation is derived and its first five zeros are tabulated for several ratios of L1 to L2, and various tapers. The first few terms of asymptotic expansions for the roots of the frequency equation are presented and discussed.


1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.


Author(s):  
Teruo Someya ◽  
Jinzo Kobayashi

Recent progress in the electron-mirror microscopy (EMM), e.g., an improvement of its resolving power together with an increase of the magnification makes it useful for investigating the ferroelectric domain physics. English has recently observed the domain texture in the surface layer of BaTiO3. The present authors ) have developed a theory by which one can evaluate small one-dimensional electric fields and/or topographic step heights in the crystal surfaces from their EMM pictures. This theory was applied to a quantitative study of the surface pattern of BaTiO3).


Author(s):  
Peter Sterling

The synaptic connections in cat retina that link photoreceptors to ganglion cells have been analyzed quantitatively. Our approach has been to prepare serial, ultrathin sections and photograph en montage at low magnification (˜2000X) in the electron microscope. Six series, 100-300 sections long, have been prepared over the last decade. They derive from different cats but always from the same region of retina, about one degree from the center of the visual axis. The material has been analyzed by reconstructing adjacent neurons in each array and then identifying systematically the synaptic connections between arrays. Most reconstructions were done manually by tracing the outlines of processes in successive sections onto acetate sheets aligned on a cartoonist's jig. The tracings were then digitized, stacked by computer, and printed with the hidden lines removed. The results have provided rather than the usual one-dimensional account of pathways, a three-dimensional account of circuits. From this has emerged insight into the functional architecture.


Author(s):  
A.Q. He ◽  
G.W. Qiao ◽  
J. Zhu ◽  
H.Q. Ye

Since the first discovery of high Tc Bi-Sr-Ca-Cu-O superconductor by Maeda et al, many EM works have been done on it. The results show that the superconducting phases have a type of ordered layer structures similar to that in Y-Ba-Cu-O system formulated in Bi2Sr2Can−1CunO2n+4 (n=1,2,3) (simply called 22(n-1) phase) with lattice constants of a=0.358, b=0.382nm but the length of c being different according to the different value of n in the formulate. Unlike the twin structure observed in the Y-Ba-Cu-O system, there is an incommensurate modulated structure in the superconducting phases of Bi system superconductors. Modulated wavelengths of both 1.3 and 2.7 nm have been observed in the 2212 phase. This communication mainly presents the intergrowth of these two kinds of one-dimensional modulated structures in 2212 phase.


Author(s):  
J. Fink

Conducting polymers comprises a new class of materials achieving electrical conductivities which rival those of the best metals. The parent compounds (conjugated polymers) are quasi-one-dimensional semiconductors. These polymers can be doped by electron acceptors or electron donors. The prototype of these materials is polyacetylene (PA). There are various other conjugated polymers such as polyparaphenylene, polyphenylenevinylene, polypoyrrole or polythiophene. The doped systems, i.e. the conducting polymers, have intersting potential technological applications such as replacement of conventional metals in electronic shielding and antistatic equipment, rechargable batteries, and flexible light emitting diodes.Although these systems have been investigated almost 20 years, the electronic structure of the doped metallic systems is not clear and even the reason for the gap in undoped semiconducting systems is under discussion.


Author(s):  
Edson de Faria ◽  
Welington de Melo
Keyword(s):  

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