Analysis of Three-Dimensional Coupled Vibration of Thin Shallow Spherical Shells Using Modified Kirchhoff–Love Thin Shell Theory

A modified Kirchhoff–Love thin shell theory that accounts for the in-plane displacements of the shell and the transverse shear stress is proposed to explore the three-dimensional coupled vibration behavior of thin shallow spherical shells. The viability of the proposed theory is established after contrasting the resonant frequencies of three thin shallow spherical shells with various polar angles with the solutions obtained from classical Reissner thin shell theory and finite element method simulations under both free and clamped boundary conditions. The validated theory is then employed to predict the out-of-plane and in-plane modes of thin shallow shells under free boundary conditions. The predictions matched well with the experimental results measured utilizing an amplitude-fluctuation electronic speckle pattern interferometer with macro-fiber composite actuators.