The dynamics of a three-layer dome with a discrete-symmetric lightweight reinforced with ribs under a concentrated impact on its top was studied. The study explores the behavior of a three-layer dome, uniquely designed with discrete, symmetrically placed, lightweight ribs for reinforcement, when subjected to a concentrated impact at its apex. The supporting layers of the dome are made with different thicknesses. Each supporting layer of the dome differs in thickness, offering a complex structure for analysis. In the analysis of the elements of the elastic structure, the Timoshenko model of the theory of shells and rods was used under independent static and kinematic hypotheses for each layer. According to the Hamilton–Ostrogradsky variational principle, the equations of motion of asymmetric three-layer hemispherical shells with a discrete-symmetric lightweight rib-reinforced aggregate under axisymmetric local impulse loading were obtained. An appropriate finite element model of the shell was created, which reflects the relationship between the potential energy of deformations in the body and the potential of applied forces. A detailed finite element model was developed to capture the interplay between the dome’s deformation energy and the force applied, facilitating a nuanced exploration of the dome’s dynamic response. The numerical results of the study of the dynamics of a three-layer elastic structure with asymmetric thickness based on the finite element method were obtained The influence of geometrical and physical–mechanical parameters of asymmetric layers of a spherical dome on its dynamic behavior during a concentrated impact on its top was studied and new mechanical effects were investigated. Through numerical analysis, the dome’s asymmetrical layer thickness and the physical and mechanical characteristics of these layers were examined to determine how they influence the dome’s reaction to concentrated impacts. This investigation reveals novel mechanical behaviors and underscores the significance of geometrical and material properties in the dome’s dynamic performance

研究了具有离散对称轻质加强肋的三层圆顶在顶部集中冲击下的动力学。该研究探讨了三层圆顶的行为，该圆顶采用离散、对称放置、轻质肋骨进行独特设计，用于加固，当其顶点受到集中冲击时。圆顶的支撑层具有不同的厚度。圆顶的每个支撑层厚度不同，为分析提供了复杂的结构。在弹性结构单元的分析中，在每层独立的静力和运动学假设下，使用壳杆理论的铁莫申科模型。根据Hamilton-Ostrogradsky变分原理，得到了带有离散对称轻质肋骨骨料的非对称三层半球壳在轴对称局部脉冲载荷作用下的运动方程。创建了适当的壳体有限元模型，该模型反映了主体变形势能与施加力的势能之间的关系。开发了详细的有限元模型来捕获圆顶的变形能量和所施加的力之间的相互作用，从而有助于对圆顶的动态响应进行细致的探索。获得了基于有限元方法的非对称厚度三层弹性结构动力学研究的数值结果。研究了对其顶部的影响并研究了新的机械效应。通过数值分析，检查了圆顶的不对称层厚度以及这些层的物理和机械特性，以确定它们如何影响圆顶对集中冲击的反应。这项研究揭示了新颖的机械行为，并强调了几何和材料特性在圆顶动态性能中的重要性