Numerical and Analytical Approach in Predicting Vibrational Analysis of Metallic Expansion Bellows Under Varying Geometrical Condition

Metal bellows are flexible components that can expand in vacuum or get compressed when subjected to external pressure. Because of their special property of energy absorption and structural displacement accommodation, they find extensive use in applications like bridges, industrial actuators, piping systems, and safety-critical components in aerospace and medical industries. The bellows used in this research are from the product portfolio of Aeroflex Industries Limited (a market leader in flexible flow solutions). Aeroflex Industries Limited provided the design data and physical prototypes for investigation purpose along with the support in project through funding and technical collaborations. This research explores the dynamic performance of metal expansion bellows using a combined analytical-numerical strategy. Three bellows of varying sizes (¼'', 2'', and 12'') having different geometries are under investigation. The examination is carried out for two boundary conditions: (i) both ends are fixed, and (ii) one end is fixed while the other end is free.Natural frequencies of the bellows are calculated with both analytical equations and finite element analysis. The simulated natural frequency is found to converge when the mesh is refined, and optimal frequency values are achieved with particular mesh sizes that trade-off computational efficiency and accuracy. The investigation also compares the maximum deformation felt by each bellow under the aforementioned conditions through numerical simulations. The findings emphasize the role of mesh resolution and boundary constraints on the metal bellows' dynamic response, providing insight useful for design and application in high-performance engineering systems.