Aleksander Kornecki (1920-1985)
● TITLE: An application of Galerkin's method to non-self-adjoint equation
● AUTHORS: Kornecki, A.
● SOURCE: Israel Journal of Technology, V. 9, pp. 189-194 (1971).
● LANGUAGE: English.
● ABSTRACT: The critical velocity of fluid flow in a cantilever tube is evaluated by applying Galerkin's method to a model type analysis. The rate of convergence of the method appears to depend on the mass ratio of the pipe and the fluid. Comparison with the results obtained by Galerkin's method for the problem of membrane flutter in a supersonic flow permits some general conclusions to be drawn concerning the title problem.

● 14 references

● COMMENT:
Pipe conveying fluid is a member in a group of similar problems called follower forces, because the direction of the load force is changed because of the strain/bending that is caused by this load force while being exerted on the structure. This Kornecki's paper (1971) is the first paper discussing and solving a follower force problem, preceding others' works on follower forces by about 25 years. Kornecki's last paper (1986) also deals with the same problem and still precedes others' works on follower forces by about 10 years.
Another practical follower force problem is testing a rocket held on a ground structure. Here too the load force exerted by the rocket bends the structure, causing change of the tilt of the rocket, that is a change in the direction of load force. The follower force problem while testing a rocket held on a ground structure became important for rockets launched to space.
Other similar problems are the bending of the turbine shafts, and the problem of an axial load torque exerted on rotating shaft by a propeller. These follower force problems are not considered formally as follower forces problems, (although they are follower force problems,) because the rotation and precessions involved make these problems even more complicated. Bousso (1963) was the first to solve the backward precession in turbines, reported in
Den-Hartog's book (1956), as well as the problem of an axial force caused by a load torque of a rotating propeller, exerted on a rotating shaft. Bousso (1963) showed that the bending of the rotating shaft causes a difference in the directions of the driving torque and the load torque, giving a perpendicular resultant force, which acts on the turbine or the rotor, causing precessions. Other publications before 1986, discussing and solving these problems are Bousso's book (1965), and papers and theses by
Ben-Amots (1969), Bousso (1972), Ben-Amots (1975), Ben-Amots (1976),
Porat (1980), Cohen (1982), Cohen and Porat (1984) and Cohen and Porat (1985).



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