Asymptomatic Solution Of The Thin Shell Equations Containing A Turning Point

Abstract

The subject matter of this report is the vibrating behavior of thin shells of revolution when the generating line has a point of inflection at s*. At this point s*, the curvature changes its sign. We develop from the deformation of a shell of revolution and obtain the natural frequency of vibration using Lord Rayleigh’s method. We make use of the law of conservation of energy, which states that, at equilibrium, the total kinetic energy is equal to the total potential energy. We then equate the kinetic energy, Jy (which is proportional to the square of the natural frequency ù,) to the total potential energy, Jk. To solve the integrals we make use the Laplace’s method and a programme from mathematica and then compare the two results.