The Static Profile for a Floating Particle

A study is made of the linear theory of free vibrations of membranes in which, owing to the self-weight of the membrane, some sag is present in the static profile. The theory applies only to those membranes with relatively shallow profiles. However, because a major application of the theory relates to the use of certain types of cable networks to support the roofs of buildings of large span, and because such networks must be relatively flat if structural efficiency is to be achieved, the theory is of some practical importance. A detailed examination is made of the circular membrane and the rectangular membrane. It is found that the symmetric modes of vibration are heavily dependent on the value of a characteristic geometric and elastic parameter - a parameter which can vary by several orders of magnitude in the suspended membranes typical of those under consideration. In particular, when the parameter is very large the membrane may be considered inextensible. In a practical sense, this corresponds to a membrane of shallow, although appreciable, curvature. For certain intermediate values of the parameter, situations arise in which the natural frequency of a symmetric mode is identical to that of an antisymmetric mode. And when it is very small, the symmetric modes of the classical circular and rectangular membranes are recovered, although, in the case of the classical square membrane, the theory points to conclusions which could not have been drawn from classical membrane theory alone.

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Static profile and dynamic behavior of COBOL programs

ACM SIGPLAN Notices ◽

10.1145/953411.953414 ◽

1978 ◽

Vol 13 (4) ◽

pp. 44-57 ◽

Cited By ~ 13

Author(s):

R. J. Chevance ◽

T. Heidet

Keyword(s):

Dynamic Behavior ◽

Static Profile

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Static profile of COBOL programs

ACM SIGPLAN Notices ◽

10.1145/956028.956031 ◽

1975 ◽

Vol 10 (8) ◽

pp. 20-33 ◽

Cited By ~ 11

Author(s):

A Salvadori ◽

J. Gordon ◽

C. Capstick

Keyword(s):

Static Profile

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Surface Profile Measurement During Turning Using Fringe-Field Capacitive Profilometry

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2896520 ◽

1992 ◽

Vol 114 (2) ◽

pp. 234-243 ◽

Cited By ~ 9

Author(s):

J. L. Garbini ◽

Sih-Ping Koh ◽

Jens E. Jorgensen ◽

Mamidala Ramulu

Keyword(s):

High Speed ◽

Surface Profile ◽

Quantitative Agreement ◽

Fringe Field ◽

Profile Measurement ◽

Sensing Element ◽

Process Measurement ◽

Static Profile ◽

Process Measurements ◽

Surface Profile Measurement

The use of fringe-field capacitive sensing for surface profile measurement during the turning process is described. Measurements of the local surface height are inferred from variations in a fringe electric field induced between the sensing element and the workpiece. The surface profile is determined from high-speed scanning of the sensing element across the surface. The technique is particularly well-suited to the relatively harsh environment of in-process measurement. We have implemented a system in which profile measurements are made continuously, in real-time, and immediately adjacent to the cutting tool. The results of tests conducted to determine the accuracy and sensitivity of this capacitive profilometer are presented. In-process measurements of surfaces generated by turning with roughness in the range of 0.3 to 4.0 μm were made. Comparisons with static profile measurements made using standard stylus instrumentation are presented, and show quantitative agreement.

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Tension of Conductor Under Concentrated Loads

Journal of Applied Mechanics ◽

10.1115/1.2897017 ◽

1995 ◽

Vol 62 (3) ◽

pp. 802-809 ◽

Cited By ~ 13

Author(s):

P. Yu ◽

P. S. Wong ◽

F. Kaempffer

Keyword(s):

Transmission Lines ◽

Dimensional Space ◽

Three Dimensional ◽

Concentrated Loads ◽

Analysis And Design ◽

Distribution Lines ◽

Practical Engineering ◽

Static Profile ◽

Transmission And Distribution ◽

Three Dimensional Space

A common difficulty in the analysis and design of transmission and distribution lines is to determine a conductor’s tension and its static profile under concentrated loads. For relatively small concentrated loads (such as detuning pendulums on transmission lines), approximation methods may give good predictions. For large concentrated loads (such as fallen trees on distribution lines), however, exact solutions must be found. This paper presents methodologies to compute conductor tension and static profile in three-dimensional space using both approximate and exact solution procedures under concentrated loads with different boundary conditions. Practical engineering examples from galloping control of transmission lines and mechanical coordination of distribution lines are given to demonstrate the applicability of the theory.

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