The Asymptotic Analysis Of Symmetrical Free Vibration Of Revolution Shell

There exists transition point in the free vibration of revolution shells at some special frequencies. In this case, a particular parallel circle would appear on the surface of revolution shell. At one side of this circle, the vibration style of shell is "bending model". Its surface curls quickly. At the other side of this circle, the vibration style is "membrane model". Its deformation happens just only on the surface of shell. But in the area around this circle, the surface would intumesce. The parallel would move along the shell when frequency changed. This phenomenon can be explained by solve the vibration equation of revolution shell when asymptotic method was used. If the vibration equation is solved by asymptotic matching method which calculate the frequency separately at the two sides of the circle, two mode whose representation are described separately would be gotten. The two modes can be matched around the area of the transition point, and finally, one consecutive mode function which was described separately at two sides of the circle can be given.For decades, there are so many people who want to get a mode function which is uniformly valid in all area, but it is difficult. In 1966, Ross solved the equation of symmetrical free vibration and got six matching solution, but he believed that it is impossible to find a solution which is useful in everywhere. In 1979, Gol'denveizer printed a monography in which the uniformly valid representations of curved solution were published, but the representations of membrane solution were still not found. In 1988, Ruo-jing Zhang published the uniformly valid representation of six solutions for symmetrical free vibration and eight solutions for dissymmetrical free vibration for the first time.To get the uniformly valid representation of vibration mode, Ruo-jing Zhang published three generalized related functions. The fist functions (four) are used to extend the bending solution, the second function is used to extend the singularity membrane solution, and the third is used to extend the common membrane solution (there are 1 in symmetrical free vibration and 3 in dissymmetrical free vibration). They are the foundation of uniformly valid solutions.In this thesis, numerical method was used to calculate the three generalized related functions. The obtained solution is in good agreement with the answers which were solved by Ruo-jing Zhang with asymptotic method. Finally an example was solved by the use of the uniformly valid solutions. The answer was checked by finite element method.