Mathematical expressions for reliability, availability, maintainability and maintenance support terms

2016 ◽  
Keyword(s):  
Mathematical Expressions

scholarly journals Interdependence of friction, wear, and noise: A review

Friction ◽  
2021 ◽  
Author(s):  
Kevin Lontin ◽  
Muhammad Khan
Keyword(s):  
Mathematical Models ◽  
Friction And Wear ◽  
Review Paper ◽  
Acoustic Noise ◽  
Friction Noise ◽  
Mathematical Expressions ◽  
Mechanical Contacts ◽  
Exact Relationship ◽  
Modelling Approach ◽  
Frictional Noise

AbstractPhenomena of friction, wear, and noise in mechanical contacts are particularly important in the field of tribomechanics but equally complex if one wants to represent their exact relationship with mathematical models. Efforts have been made to describe these phenomena with different approaches in past. These efforts have been compiled in different reviews but most of them treated friction, wear mechanics, and acoustic noise separately. However, an in-depth review that provides a critical analysis on their interdependencies is still missing. In this review paper, the interdependencies of friction, wear, and noise are analysed in the mechanical contacts at asperitical level. The origin of frictional noise, its dependencies on contact’s mechanical properties, and its performance under different wear conditions are critically reviewed. A discussion on the existing mathematical models of friction and wear is also provided in the last section that leads to uncover the gap in the existing literature. This review concludes that still a comprehensive analytical modelling approach is required to relate the interdependencies of friction, noise, and wear with mathematical expressions.

On the Maximum Value of the Maximum Degree of Kinematic Chains

1987 ◽  
Vol 109 (4) ◽  
pp. 487-490 ◽  
Author(s):  
Hong-Sen Yan ◽  
Frank Harary
Keyword(s):  
Graph Theory ◽  
Maximum Degree ◽  
Design Methodology ◽  
Creative Design ◽  
Systematic Design ◽  
Kinematic Chains ◽  
Maximum Value ◽  
Mathematical Expressions

One of the major steps in the development of a systematic design methodology for the creative design of vehicle mechanisms is to obtain all possible link assortments, and then to generate the catalogs of kinematic chains. If the generalized mathematical expressions for the maximum value M of the maximum number of joints incident to a link of kinematic chains with N links and J joints can be derived, the process of solving link assortments can be more systematic. Using elementary concepts of graph theory, we derived explicit relationships for M for two regions of the J-N plane.

Vibration-Based Crack Detection in L-Frames

2014 ◽  
Vol 658 ◽  
pp. 261-268
Author(s):  
Jean Louis Ntakpe ◽  
Gilbert Rainer Gillich ◽  
Florian Muntean ◽  
Zeno Iosif Praisach ◽  
Peter Lorenz
Keyword(s):  
Strain Energy ◽  
Crack Detection ◽  
Natural Frequencies ◽  
Vibration Modes ◽  
Structural Elements ◽  
Element Analysis ◽  
Accurate Localization ◽  
Mathematical Expressions ◽  
Measurement Results ◽  
Non Destructive

This paper presents a novel non-destructive method to locate and size damages in frame structures, performed by examining and interpreting changes in measured vibration response. The method bases on a relation, prior contrived by the authors, between the strain energy distribution in the structure for the transversal vibration modes and the modal changes (in terms of natural frequencies) due to damage. Using this relation a damage location indicator DLI was derived, which permits to locate cracks in spatial structures. In this paper an L-frame is considered for proving the applicability of this method. First the mathematical expressions for the modes shapes and their derivatives were determined and simulation result compared with that obtained by finite element analysis. Afterwards patterns characterizing damage locations were derived and compared with measurement results on the real structure; the DLI permitted accurate localization of any crack placed in the two structural elements.

Rise times of attenuated seismic pulses detected in both empty and fluid‐filled cylindrical boreholes

Geophysics ◽  
1984 ◽  
Vol 49 (4) ◽  
pp. 398-410 ◽  
Author(s):  
D. P. Blair
Keyword(s):  
Stress Wave ◽  
Particle Motion ◽  
P Wave ◽  
Wave Incident ◽  
Stress Wave Propagation ◽  
Linear Phase ◽  
Phase Filter ◽  
Mathematical Expressions ◽  
Plane P Wave ◽  
Theory And Experiment

Fourier‐Bessel theory is used to derive filters representing the influence of both empty and fluid‐filled cylindrical boreholes on particle motion induced in rock by a plane P-wave incident perpendicular to the borehole axis. For wavelengths greater than 10 times the borehole circumference, the effect of the borehole on particle motions is shown to be negligible; thus the results have little relevance for the long wavelengths commonly encountered in earthquake seismology. The results are, however, relevant to the study of stress wave propagation at ultrasonic frequencies in rock masses. For small wavelengths (αa > 3.0) the filter representing particle motion on the wave incident site of an empty borehole reduces to a linear phase filter which increases all amplitudes by a factor of 2 while the filter representing fluid stress at the center of a fluid‐filled borehole may be reduced to simple mathematical expressions. Experimental results were obtained for the interaction of a stress wave with either accelerometers mounted in an empty borehole or a hydrophone located centrally in a fluid‐filled borehole. Both theory and experiment show a similar distortion in the rise time of the pulse traveling past the borehole.

Dynamic responses of clearance-type non-linear systems subjected to base harmonic excitation and their experimental verification

2021 ◽  
pp. 107754632110128
Author(s):  
K Renji
Keyword(s):  
Linear Systems ◽  
Experimental Verification ◽  
Harmonic Excitation ◽  
Dynamic Responses ◽  
Maximum Response ◽  
Base Excitation ◽  
Mathematical Expressions ◽  
Non Linear Systems ◽  
Propellant Tank ◽  
Different Levels

Realistic joints in a spacecraft structure have clearances at the interfacing parts. Many such systems can be considered to be having bilinear stiffness. A typical example is the propellant tank assembled with the structure of a spacecraft. However, it is seen that the responses of such systems subjected to base excitation are rarely reported. In this work, mathematical expressions for theoretically estimating the amplitude of its response, the frequency at which the response is the maximum and the maximum response when it is subjected to base sine excitation are derived. Several experiments are conducted on a typical such system subjecting it to different levels of base sine excitation. The frequency at which the response is the maximum reduces with the magnitude of excitation. The expressions derived in this work can be used in estimating the amplitudes of responses and their characteristics reasonably well.

Types and uses of mathematical expressions

2021 ◽  
Vol 11 (3) ◽  
pp. 746-749
Author(s):  
Gulomova Muxabbat Maxmudovna ◽  
Tufliyev Egamberdi Olimovich ◽  
Bozarov Dilmurod Uralovich
Keyword(s):  
Mathematical Expressions
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