INFLUENCE OF DAMPING AND PRESSURE DURATION ON THE STRENGTHS OF STRUCTURES UNDER EXPLOSIVE LOADING

Abstract

The article presents an analysis of the influence of the damping coefficient, the phase of structural vibrations, and the duration of the explosion wave on the magnitude of the dynamic factor. Different methods for determining the dynamic factor depending on these factors are considered. In the literature, the disregard of damping is associated with simplifying calculations. The article demonstrates that in some cases, to save materials, the dynamic factor can be reduced by up to 16%. When considering the actual curvilinear pressure diagram of the explosion wave, the maximum response of the system may occur in the first phase of oscillations. Therefore, it is shown that instantaneous impulse calculation is not always applicable. By considering the damping coefficient (if objectively justified) and the actual curvilinear pressure diagram, materials can be saved by reducing the dynamic factor. It is demonstrated that a more accurate calculation method is direct integration of the equations of motion. However, for multi-mass systems, solving these equations is only possible through numerical methods. In such systems, the vibration frequencies for different modes can significantly differ. Thus, the question arises of which integration step to choose for a more accurate solution, as an optimal step for one frequency may not be suitable for another. In such cases, a better approach is the well-known modal superposition method, which transforms the coupled system of differential equations in physical coordinates into independent differential equations in modal coordinates. These second-order differential equations for a linear oscillator are easily solved in closed form, allowing the derivation of an analytical solution for both linear and curvilinear pressure functions, with or without considering the negative pressure phase. Given that these equations are analytically solvable, the problem of selecting the appropriate integration step is automatically eliminated.