In this paper, a mathematical model for determining the longitudinal and transverse forces (reactions) of an arched elastomeric shock absorber when it is loaded along two axes (compression and transverse displacement of the supporting surfaces) is proposing. The reactions are presented as the sum of independent forces created by its two elastomeric walls. The webs are considered as beams that work in compression, bending and transverse shear, and can also lose stability. The model is phenomenological in nature. The structure of the model is such that in the case of pure compression of the shock absorber, the expression for the static axial reaction automatically satisfies the experimental static force characteristics of compression, which are given in the technical literature. The results of comparing the calculated data obtained by the developed model with the results of calculations in the Ansys Workbench 18.1 finite element analysis package are presented. In the region of deformations until the appearance of additional contact surfaces during buckling, a good agreement is observed. The developed analytical model of an arched elastomeric shock absorber can be used in calculations that require high speed (low computational complexity), in particular, for simulation modeling of systems in various software systems, such as Simulink.

Elastomeric shock absorbers are used in various technical fields to protect equipment from impacts. Elastomers made in an arched shape have complex nonlinear force characteristics due to large deformations, loss of stability of working elements and closing of surfaces. In this regard, obtaining the power characteristics of arched elastomeric shock absorbers is a complex computational problem. It is noteworthy that, in the literature, these characteristics are given only for the case of normal compression. However, when assessing the possibility of using a shock-absorbing system based on arched elastomeric shock absorbers, it is necessary to take into account their lateral force. The study proposes to solve the problem of determining the elastic force characteristics of a shock absorber while operating in the normal and lateral directions in the system of finite element analysis in a flat formulation. Analytical expressions are obtained for the normal and transverse static reactions of the shock absorber under simultaneous loading in the normal and transverse directions. Analytic expressions can be used to simulate complex shock-absorbing systems with a large number of such shock absorbers.