VIBRATION MECHANICS OF A SEMI-CYLINDRICAL CUSHION WITH INERTIAL PROPERTIES

 In the present study, the free and forced vibrations of an inertial semi-cylindrical cushion are investigated. A dynamic model is considered, in which the motion of the cushion is described by the Lamé equations in terms of displacements. To solve the posed problem, the natural frequencies and mode shapes are determined, as well as the normal displacements of points on the semi-cylindrical cushion under various boundary conditions. Particular attention is paid to the influence of inertial properties and material parameters, such as density, elastic modulus, and Poisson’s ratio, on the frequency characteristics of the system. The obtained results allow the identification of patterns in the variation of vibration amplitudes and frequencies depending on the geometric and material parameters of the cushion. Characteristic dependencies are constructed to illustrate the effect of inertial parameters on the dynamic behavior of the semi-cylindrical structure. A comparative analysis of theoretical results and numerical calculations is carried out, confirming the validity of the proposed model. The findings can be applied in the design and optimization of structures operating under vibrational loads, as well as in the development of vibration isolation and damping system components. This study contributes to the achievement of the Sustainable Development Goal 9 (Industry, Innovation and Infrastructure) by providing insights for safer, more durable, and optimized engineering structures.