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Pressure transients in a cavity due to impulsive loads. (English)
Applied mathematics and computing, Trans. 4th Army Conf., Ithaca/N.Y. 1986, ARO Rep. 87-1, 83-94 (1987).
[For the entire collection see Zbl 0614.00003.] The impact of a mass on a structural plate of a compartment causes plastic and elastic deformations which can give rise to pressure fluctuations of significant magnitude and duration due to the confined nature of the compartment and the low damping forces in the gas. This paper presents a procedure for calculating the pressure transients in an enclosed gas from an impact. The procedure uses a formulation which gives the equations of motion in terms of a scalar momentum potential. This momentum potential is physically interpretable as a pressure impulse. With this formulation the transient pressure behavior of the gas is characterized by a single partial differential equation which is the wave equation in three dimensions. The spatial derivatives are treated by a finite element technique to obtain solutions for an arbitrary geometry of the enclosure. The boundary conditions for the problem are that the normal velocity of the gas is compatible with the prescribed velocity of the enclosure walls. The rate of deformation of the wall resulting from the impact is approximated by modelling the region in the form of two concentric plastic hinges. Since the stress in the hinges must be at the yield value, it is possible to approximate the plastic deformation and hence the time history of the deformation.
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