Periodic Surface Design for Boosting Low-Order Modal Frequencies in Cylindrical Shells

Inspired by corrugated bellows, this study proposes a novel design strategy for doubly clamped cylindrical shells to enhance low-order modal frequencies through periodic surface design. First, three types of periodic surfaces are designed by emulating the geometric characteristics of bellows. Subsequently, the governing differential equations for free vibration of cylindrical shells with periodic surfaces are derived by using the energy variation method combined with the Gauss–Fourier expansion. Finally, the computational efficiency of the model is enhanced by the Gauss–Legendre quadrature, and its accuracy is verified through finite element analysis. Numerical results demonstrate that while maintaining a near-constant total volume of the shell, the enhancement effect induced by the periodic surface exhibits parameter-sensitive intervals. Within these intervals, significant enhancement of low-order modal frequencies can be achieved through different periodic surface shapes.