On the problem of nonlinear dynamics of shell systems influenced by the internal pressure local impulse

Abstract

Purpose. Critical infrastructure facilities, including pipelines and tanks, are an integral part of ensuring the functioning of industrial and civil life support facilities. External factors that may affect their functioning can be both the cause of force majeure and targeted actions by third parties. Therefore, the purpose of this work is to establish a mathematical description of the dynamic behavior of cylindrical shells under the action of a local impulse caused by internal pressure. Methodology. To achieve the goal of the work, the provisions of the nonlinear dynamics of the system of forces are applied, taking into account approximate analytical and asymptotic methods. Results. The results obtained make it possible to describe nonlinear processes caused by local pulses of internal pressure in shell systems, which can be interpolated for use in numerous methods for determining the parameters of the strength and bearing capacity of the corresponding structure, taking into account the physical and mechanical parameters of the materials used and the nature of the force action. Interpolation of the results to similar technical systems will allow scaling the mathematical approach in solving engineering problems. Scientific novelty. The existing dynamic models are mostly represented by simplified calculation models without taking into account the totality of real loads and characteristic design and technological factors. In this paper, it is proposed to take into account the nonlinearity of dynamic processes due to the shape of the impulse action, the power exponent of the nonlinearity of displacements, and the Dirac delta function. This approach is new of scientific and practical significance. Practical significance. The resulting singular inhomogeneous model of interaction in the form of a differential equation with variable coefficients makes it possible to provide numerical simulation of interaction processes with asymptotically approximate results and to establish the parameters of dynamic behavior to impulse action. As a result, it is possible to obtain new technical solutions for shell structures resistant to dynamic impact, which will have improved technical and operational characteristics.