Vibration Analysis of Laminated Shallow Shells with Non-uniform Curvature

Abstract

Although there are a large number of technical papers on vibration of shallow shells, all the previous papers have dealt with shallow shells with uniform curvature to avoid difficulty arising in the variable curvature analysis. Recent products, however, require various surface designs of thin panels from the viewpoint of industrial design, for example, in the fender and door panel designs of commercial vehicles. The present study proposes an analytical method to deal with vibration of shallow shells with non-uniform curvature. An interpolating function is introduced to represent the required surface shape and the corresponding curvature is derived as a function of the position (x, y). The obtained curvature is substituted into the total potential energy of the shell, and the process is shown to derive a frequency equation in the Ritz method. Numerical examples show the effects of non-uniform curvature on the natural frequencies and mode shapes.