The impulse imparted by a blast wave to a freestanding solid plate is studied analytically and numerically focusing on the case in which nonlinear compressibility effects in the fluid are important, as is the case for explosions in air. The analysis furnishes, in effect, an extension of Taylor’s pioneering contribution to the understanding of the influence of fluid-structure interaction (FSI) on the blast loading of structures [The Scientific Papers of Sir Geoffrey Ingram Taylor, edited by G. K. Batchelor (Cambridge University Press, Cambridge, 1963), Vol. III, pp. 287–303] to the nonlinear range. The limiting cases of extremely heavy and extremely light plates are explored analytically for arbitrary blast intensity, from where it is concluded that a modified nondimensional parameter representing the mass of compressed fluid relative to the mass of the plate governs the FSI. The intermediate asymptotic FSI regime is studied using a numerical method based on a Lagrangian formulation of the Euler equations of compressible flow and conventional shock-capturing techniques. Based on the analytical and numerical results, an approximate formula describing the entire range of relevant FSI conditions is proposed. The main conclusion of this work is that nonlinear fluid compressibility further enhances the beneficial effects of FSI in reducing the impulse transmitted to the structure. More specifically, it is found that transmitted impulse reductions due to FSI when compared to those obtained ignoring FSI effects are more significant than in the acoustic limit. This result can be advantageously exploited in the design and optimization of structures with increased blast resistance.
The problem of uniform shocks interacting with free-standing plates is studied analytically and numerically for arbitrary shock intensity and plate mass. The analysis is of interest in the design and interpretation of fluid–structure interaction (FSI) experiments in shock tubes. In contrast to previous work corresponding to the case of incident blast profiles of exponential distribution, all asymptotic limits obtained here are exact. The contributions include the extension of Taylor’s FSI analysis for acoustic waves, the exact analysis of the asymptotic limits of very heavy and very light plates for arbitrary shock intensity, and a general formula for the transmitted impulse in the intermediate plate mass range. One of the implications is that the impulse transmitted to the plate can be expressed univocally in terms of a single nondimensional compressible FSI parameter.
A numerical method is used to compute the flow field corresponding to blast waves of different incident profiles propagating in air and impinging on free-standing plates.The method is suitable for the consideration of compressibility effects in the fluid and their influence on the plate dynamics. The history of the pressure experienced by the plate is extracted from numerical simulations for arbitrary blast strengths and plate masses and used to infer the impulse per unit area transmitted to the plate. The numerical results complement some recent analytical solutions in the intermediate range of plate masses and arbitrary blast intensities where exact solutions are not available. The resulting beneficial effect of the fluid-structure interaction (FSI) in reducing transmitted impulse in the presence of compressibility effects is discussed.In particular, it is shown that in order to take advantage of the impulse reduction provided by the FSI effect, large plate displacements are required which, in effect, Preprint submitted to Elsevier Science 23 July 2008 may limit the practical applicability of exploiting FSI effects in the design of blastmitigating systems.
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