Fillet effects on hemispherical shell resonators: Analytical insights for enhanced structural integrity

This study investigates the impact of fillet geometry on the dynamic and thermoelastic damping (TED) properties of hemispherical shell resonators, commonly used in composite structural applications. Fillets are often applied to reduce stress concentrations and improve structural integrity, but their influence on the mechanical behavior and thermoelastic quality factor (QTED) of resonators has not been thoroughly examined. An analytical approach is presented to evaluate the free vibration and TED characteristics of filleted hemispherical shells. The model incorporates variations in shell thickness to represent fillet effects and applies the first-order shear deformation theory (FSDT) for theoretical derivation.

Mode shapes are described using a combination of Jacobi polynomials and Fourier series, and the equations of motion are derived using Hamilton's principle and the assumed mode method. The analytical model for the QTED is developed by calculating the dissipated energy and the maximum elastic potential energy of the shell. The accuracy of the model is validated through comparison with existing literature and finite element method (FEM) simulations.

Numerical examples highlight the effect of fillet geometry on the vibration modes and QTED characteristics, offering insights into the optimization of fillet design for improved performance in hemispherical shell resonators.