Vibration mechanics of a semi-cylindrical cushion with inertial properties

This study investigates the free and forced vibrations of an inertial semi-cylindrical cushion using the Lamé displacement–based formulation and the Hamilton-Ostrogradsky variational principle. Natural frequencies, vibration modes, and normal displacements were obtained for different boundary conditions. Special attention was given to the influence of inertial and elastic parameters, including density, Young’s modulus, Poisson’s ratio, and foundation inertia. Analytical relations describing the variation of vibration amplitudes and frequencies with respect to geometric and material characteristics were derived. A comparative analysis between the analytical solution and a 3D finite element model developed in ABAQUS demonstrated strong agreement, confirming the accuracy of the proposed formulation. The results provide practical guidelines for optimizing vibration-isolation elements and improve the design of structures exposed to dynamic loads. The study contributes to Sustainable Development Goal 9 by supporting the development of safer and more durable infrastructure components.