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The Volume 3, No 1, March 1998

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A Century of Shock and Wave Dynamics

Sir James Lighthill


The recent three-volume history ?Twentieth Century Physics? 1 includes my 118 page Chapter 10. Fluid Dynamics about a field where the 20th century?s first decade saw big breakthroughs in the analysis of nonlinear problems for which the physicist?s standard perturbation methods break down - and which would later be named singular perturbation problems. Besides the 1904 elucidation of boundary-layer structure by Prandtl, these included the 1910 elucidation of shock-wave structure in complementary investigations by Rayleigh and by Taylor. Subsequent advances in shock wave dynamics brought crucial new discoveries on the structure and propagation of weak shocks, and also on shock-wave/boundary-layer interaction, both with major aeronautical implications; along with still harder investigations into the structure and propagation of strong shock waves such as appear in explosions and implosions and also around spacecraft re-entering the earth?s atmosphere. It may, perhaps, be worth noting that questions which remain relatively simple for weak waves, like the nature of reflexion and diffraction by a solid body, raise formidable and intriguing difficulties for strong shock waves. In this introductory paper looking back over a century of shock wave dynamics, I highlight (i) key analytical approaches for both weak and strong shock waves, (ii) beautiful and effective optical methods for use in wind tunnels and shock tubes and (iii) powerful techniques for accurate shock capturing in computational fluid dynamics.

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The Influence of Geometric Imperfections on the Non-linear Dynamical Behaviour of Parametrically Excited Rectangular Plates

M. J. Bugaru


The author reviews recent developments in the non-linear forced and parametric vibrations of rectangular plates. The geometric imperfections of the plate are considered as a new parameter of the system and the problem is solved for one set of boundary-conditions: a simply-supported plate. The solution indicates the involvement of the geometric imperfections on the amplitude of forced vibrations and on the amplitude of parametric vibrations at the principal parametric resonance. In the mean time the interaction between forced vibrations and parametric vibrations is presented as a chaos behaviour. Numerical results reveal the influence of various system parameters and the experimental data verify the analytical solution from a qualitative and a quantitative point of view.

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