Abstract This study addresses the design of geometric and material distortion scale models for the free vibration of large thin-walled shallow spherical shells. By applying similarity transformations to the frequency equation and natural frequency solutions of clamped shallow spherical shells, we derive the similarity conditions for free vibration and the scaling law for natural frequencies. Numerical simulations verify the accuracy of the frequency formula, similarity conditions, and scaling laws for natural frequencies of shallow spherical shells under various rise-to-thickness ratios. The research findings demonstrate that the theoretical frequency formula is consistent with the simulation results for shallow spherical shells under different rise-to-thickness ratios. Models designed according to these similarity conditions, combined with the scaling laws, can accurately predict the natural vibration characteristics of the prototype. The similarity conditions and scaling laws presented in this study can provide valuable references for the design and experimentation of scaling models with thickness and material distortions.
2025, Vol. 46 
