FLEXURAL VIBRATION OF DOUBLY-TAPERED CYLINDRICAL SHALLOW SHELLS

An approach based on the principle of energy is proposed to study the free flexural vibration of chordwise doubly-tapered cylindrical shallo w shells. The variations in shell thickness are linear and symmetric. This topic is of practical interest, but one on which no previous work has been conducted. The analysis is performed using an efficient comp utational method based on the Ritz minimum energy approach. The in-pla ne and transverse displacement amplitude functions of the shells are a pproximated by sets of pb-2 shape functions with unknown coefficients. The pb-2 shape functions are basically a set of admissible functions composed of the product of a set of mathematically complete two-dimens ional orthogonal polynomials and a boundary kinematically oriented bas ic function. The basic function is defined by the product of the equat ions of continuous piecewise boundary expressions of the shell planfor m each raised to an appropriate basic power corresponding to a free, s imply supported or clamped edge, respectively. These pb-2 shape functi ons comply with the kinematic boundary conditions of the shells at the outset. Three classes of different shell configurations and boundary conditions are studied with selected mode shapes presented. A study on the ignoring of tangential inertia has shown little effect on the fre quency response. However, the trend reveals a higher effect is evident as the shell curvature increases. The effects of symmetric thickness variation are reflected in the tabulated data, as well as the mode sha pe figures. Since no data for a doubly-tapered cylindrical shallow she ll can be found in the open literature, the results presented in the c urrent study can be used for future reference and comparison.