The Constant Stress Hanging String with Bottom Load — An Exact Solution

2021 ◽  
pp. 2171005
Author(s):  
C. Y. Wang
Keyword(s):  
Exact Solution ◽  
Numerical Solution ◽  
Unique Solution ◽  
Characteristic Equation ◽  
Maximum Stress ◽  
Cross Sectional Area ◽  
Vibration Frequencies ◽  
Sectional Area ◽  
Cross Sectional ◽  
Two Parameters

The unique solution for the fully stressed hanging string with a bottom load is found. For a given length of string, the problem depends on two parameters, representing the ratio of string density to maximum stress, and the ratio of bottom mass to maximum stress. The cross-sectional area of the string decays exponentially downward. Vibration frequencies are found from the exact characteristic equation. Results from analytic perturbation formulas compare well with those of numerical solution.

The Influence of Specimen Attachment and Dimension on Microtensile Strength

2004 ◽  
Vol 83 (5) ◽  
pp. 420-424 ◽  
Author(s):  
A.A. El Zohairy ◽  
A.J. de Gee ◽  
N. de Jager ◽  
L.J. van Ruijven ◽  
A.J. Feilzer
Keyword(s):  
Finite Element Analysis ◽  
Maximum Stress ◽  
Cross Sectional Area ◽  
Testing Device ◽  
Sectional Area ◽  
Microtensile Bond Strength ◽  
Element Analysis ◽  
Cross Sectional ◽  
Surface Flaws ◽  
Stress Patterns

The higher microtensile bond strength values found for specimens with a smaller cross-sectional area are often explained by the lower occurrence of internal defects and surface flaws. We hypothesized that this aberrant behavior is mainly caused by the lateral way of attachment of the specimens to the testing device, which makes the strength dependent on the thickness. This study showed that composite bars of 1×1×10, 1×2×10, and 1×3×10mm attached at their 1-mm-wide side (situation A) fractured at loads of the same magnitude, as a result of which the microtensile strength (μTS), calculated as F/A (force at fracture/cross-sectional area), significantly increased for specimens with decreasing thickness. Attachment at the 1-, 2-, or 3-mm-wide side (situation B) resulted in equal μTS values (P > 0.05). Finite element analysis showed different stress patterns for situation A, but comparable patterns for situation B. Both situations showed the same maximum stress at fracture.

scholarly journals influence of the palate shape on articulatory token-to-token variability

2005 ◽  
Vol 42 ◽  
pp. 43-67
Author(s):  
Jana Brunner ◽  
Susanne Fuchs ◽  
Pascal Perrier
Keyword(s):  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Acoustic Variability ◽  
The Cross ◽  
Two Parameters ◽  
Acoustic Output ◽  
The Relationship ◽  
Modelling Study ◽  
Motor Constraints

Articulatory token-to-token variability not only depends on linguistic aspects like the phoneme inventory of a given language but also on speaker specific morphological and motor constraints. As has been noted previously (Perkell (1997), Mooshammer et al. (2004)), speakers with coronally high "domeshaped" palates exhibit more articulatory variability than speakers with coronally low "flat" palates. One explanation for that is based on perception oriented control by the speaker. The influence of articulatory variation on the cross sectional area and consequently on the acoustics should be greater for flat palates than for domeshaped ones. This should force speakers with flat palates to place their tongue very precisely whereas speakers with domeshaped palates might tolerate a greater variability. A second explanation could be a greater amount of lateral linguo-palatal contact for flat palates holding the tongue in position. In this study both hypotheses were tested. In order to investigate the influence of the palate shape on the variability of the acoustic output a modelling study was carried out. Parallely, an EPG experiment was conducted in order to investigate the relationship between palate shape, articulatory variability and linguo-palatal contact. Results from the modelling study suggest that the acoustic variability resulting from a certain amount of articulatory variability is higher for flat palates than for domeshaped ones. Results from the EPG experiment with 20 speakers show that (1.) speakers with a flat palate exhibit a very low articulatory variability whereas speakers with a domeshaped palate vary, (2.) there is less articulatory variability if there is lots of linguo-palatal contact and (3.) there is no relationship between the amount of lateral linguo-palatal contact and palate shape. The results suggest that there is a relationship between token-to-token variability and palate shape, however, it is not that the two parameters correlate, but that speakers with a flat palate always have a low variability because of constraints of the variability range of the acoustic output whereas speakers with a domeshaped palate may choose the degree of variability. Since linguo-palatal contact and variability correlate it is assumed that linguo-palatal contact is a means for reducing the articulatory variability.  

scholarly journals Application of the vibration method for damage identification of a beam with a variable cross-sectional area

2018 ◽  
Vol 157 ◽  
pp. 08012
Author(s):  
Izabela Zamorska ◽  
Dawid Cekus ◽  
Mateusz Miara
Keyword(s):  
Function Method ◽  
Damage Identification ◽  
Cross Sectional Area ◽  
Variable Cross ◽  
Vibration Frequencies ◽  
Sectional Area ◽  
Cross Sectional ◽  
Vibration Method ◽  
The Subject ◽  
Non Destructive

The subject of the paper is an application of the non-destructive vibration method for identifying the location of two cracks occurring in a beam. The vibration method is based on knowledge of a certain number of vibration frequencies of an undamaged element and the knowledge of the same number of vibration frequencies of an element with a defect. The analyzed beam, with a variable cross-sectional area, has been described according to the Bernoulli-Euler theory. To determine the values of free vibration frequencies the analytical solution, with the help of the Green’s function method, has been used.

Pelvic Canal Narrowing Caused by Triple Pelvic Osteotomy in the Dog

1994 ◽  
Vol 07 (03) ◽  
pp. 110-113 ◽  
Author(s):  
D. L. Holmberg ◽  
M. B. Hurtig ◽  
H. R. Sukhiani
Keyword(s):  
Postoperative Complications ◽  
Pelvic Osteotomy ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Canal Width ◽  
Operative Complications ◽  
Post Operative Complications

SummaryDuring a triple pelvic osteotomy, rotation of the free acetabular segment causes the pubic remnant on the acetabulum to rotate into the pelvic canal. The resulting narrowing may cause complications by impingement on the organs within the pelvic canal. Triple pelvic osteotomies were performed on ten cadaver pelves with pubic remnants equal to 0, 25, and 50% of the hemi-pubic length and angles of acetabular rotation of 20, 30, and 40 degrees. All combinations of pubic remnant lengths and angles of acetabular rotation caused a significant reduction in pelvic canal-width and cross-sectional area, when compared to the inact pelvis. Zero, 25, and 50% pubic remnants result in 15, 35, and 50% reductions in pelvic canal width respectively. Overrotation of the acetabulum should be avoided and the pubic remnant on the acetabular segment should be minimized to reduce postoperative complications due to pelvic canal narrowing.When performing triple pelvic osteotomies, the length of the pubic remnant on the acetabular segment and the angle of acetabular rotation both significantly narrow the pelvic canal. To reduce post-operative complications, due to narrowing of the pelvic canal, overrotation of the acetabulum should be avoided and the length of the pubic remnant should be minimized.

DETERMINATION OF THE FUNCTION OF THE ROD’S CROSS-SECTIONAL AREA USING VIBRATION EIGENFREQUENCIES

2020 ◽  
Vol 0 (4) ◽  
pp. 19-24
Author(s):  
I.M. UTYASHEV ◽  
◽  
A.A. AITBAEVA ◽  
A.A. YULMUKHAMETOV ◽  
◽  
...  
Keyword(s):  
Cross Sectional Area ◽  
Variable Cross ◽  
Sectional Area ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Method Error ◽  
Various Boundary Conditions ◽  
Elastic Fixation ◽  
Crosssectional Area

The paper presents solutions to the direct and inverse problems on longitudinal vibrations of a rod with a variable cross-sectional area. The law of variation of the cross-sectional area is modeled as an exponential function of a polynomial of degree n . The method for reconstructing this function is based on representing the fundamental system of solutions of the direct problem in the form of a Maclaurin series in the variables x and λ. Examples of solutions for various section functions and various boundary conditions are given. It is shown that to recover n unknown coefficients of a polynomial, n eigenvalues are required, and the solution is dual. An unambiguous solution was obtained only for the case of elastic fixation at one of the rod’s ends. The numerical estimation of the method error was made using input data noise. It is shown that the error in finding the variable crosssectional area is less than 1% with the error in the eigenvalues of longitudinal vibrations not exceeding 0.0001.

Changes in the parameters of nasal breathing and parameters of the upper respiratory tract during orthognathic operations in patients with II and III skeletal class of jaw anomalies

2020 ◽  
pp. 22-27
Author(s):  
S.Sh. Gammadaeva ◽  
M.I. Misirkhanova ◽  
A.Yu. Drobyshev
Keyword(s):  
Respiratory Tract ◽  
Nasal Cavity ◽  
Nasal Septum ◽  
Cross Sectional Area ◽  
Upper Respiratory Tract ◽  
Sectional Area ◽  
Nasal Breathing ◽  
Cross Sectional ◽  
Skeletal Class ◽  
Upper Respiratory

The study analyzed the functional parameters of nasal breathing, linear parameters of the nasal aperture, nasal cavity and nasopharynx, volumetric parameters of the upper airways in patients with II and III skeletal class of jaw anomalies before and after orthognathic surgery. The respiratory function of the nose was assessed using a rhinomanometric complex. According to rhinoresistometry data, nasal resistance and hydraulic diameter were assessed. According to the data of acoustic rhinometry, the minimum cross-sectional area along the internal valve, the minimum cross-sectional area on the head of the inferior turbinate and nasal septum and related parameters were estimated. According to the CBCT data, the state of the nasal septum, the inferior turbinates, the nasal aperture, the state of the nasal cavity, and the linear values of the upper respiratory tract (nasopharynx) were analyzed. The patients were divided into 4 groups according to the classification of the patency of the nasal passages by

Unequal Probability Scheme for Fruit Count in a Guava Tree

2016 ◽  
Vol 3 (4) ◽  
Author(s):  
R. C. BHARATI
Keyword(s):  
Cross Sectional Area ◽  
Equal Probability ◽  
Sampling Scheme ◽  
Research Station ◽  
Sectional Area ◽  
Cross Sectional ◽  
Unequal Probability ◽  
Selection Probabilities ◽  
Horticultural Research ◽  
Number Of Branches

Data on fruit count corresponding to primary, secondary and tertiary branches of a randomly selected guava CV. Allahabad Safeda were recorded from the guava orchard of Horticultural Research Station, Birauli. The proposed sampling scheme in which the selection probabilities are based on length of braches between two forking points was compared with equal probability(PE), probability proportional to the number of branches(PPN), probability proportional to the cross sectional area (PPA) and probability proportional to volume (PPV) method of sampling and found to be more efficient.

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