Vibration Analysis of Shallow Shells with General Surfaces Expressed by Cubic Polynomial Function

抄録

This study proposes an analytical method to deal with free vibration of shallow shells with generally curved surfaces expressed in terms of cubic polynomial functions. Such shell structures with variable curvature are recently found in automobile and other design-oriented structural applications. In the analysis an interpolating function of the third order is introduced to represent the required surface shape and the corresponding curvature is derived as a function of the position. The obtained curvature is substituted into the total potential energy of the shell, and the analytical procedure is shown to derive a frequency equation by the Ritz method. Numerical examples demonstrate that the vibration of shallow shells with various curved surfaces can be analyzed by the present method, and the effects of varying the coefficients of the cubic function in geometric expression are clarified on the natural frequencies and mode shapes.