A Higher-Order Theory for Vibration Analysis of Curvilinear Thick Shallow Shells with Constrained Boundaries

Abstract

This article presents the vibration analysis of thick doubly curved shallow shells having curvilinear planform. The Gaussian curvature of shell varies from positive (such as spherical) to negative (such as hyperbolic paraboloidal). The boundaries are constrained with either soft-simply supported or fully clamped edges. A higher-order shear deformation theory, which includes transverse shear strain and rotary inertia, is developed to model the vibration characteristics of the shell. The inclusion of Lamé parameters in the present formulation accounts for the presence of shell curvature and yields cubic transverse shear strain distribution in contrast with the existing quadratic expressions. A set of versatile, globally continuous shape functions is adopted in the Ritz numerical procedure to approximate the displacement and rotation fields. A set of new results for a wide range of shell configurations is presented with some selected contour and three-dimensional displacement mode shapes.