Damped oscillatory motion is one of the most widely studied movements in physics courses. Despite this fact, dry damped oscillatory motion is not commonly discussed in physics textbooks. In this work, we discuss the dry and viscous damped pendulum, in a teaching experiment that can easily be performed by physics or engineering students.
In this study, detonation limits in very small diameter tubes are investigated to further the understanding of the near-limit detonation phenomenon. Three small diameter circular tubes of 1.8 mm, 6.3 mm, and 9.5 mm inner diameters, of 3m length, were used to permit the near-limit detonations to be observed over long distances of 300 to 1500 tube diameters. Mixtures with high argon dilution (stable) and without dilution (unstable) are used for the experiments. For stable mixtures highly diluted with argon for which instabilities are not important and where failure is due to losses only, the limit obtained experimentally is in good agreement in comparison to that computed by the quasi-steady ZND theory with flow divergence or curvature term modeling the boundary layer effects. For unstable detonations suppression of the instabilities of the cellular detonation due to boundary conditions is responsible for the failure of the detonation wave. Different near-limit propagation regimes are also observed, including the spinning and galloping mode. Based on the present experimental results, an attempt is made to study an operational criterion for the propagation limits of stable and unstable detonations.
In this paper, the post-divergence behaviour of fluid-conveying pipes supported at both ends is studied using the complete extensible nonlinear equations of motion. The two coupled nonlinear partial differential equations are discretized via Galerkin’s method and the resulting set of ordinary differential equations is solved by Houbolt’s finite difference method and also using AUTO. Typically, the pipe is stable and retains its original static equilibrium position up to where it loses stability by a supercritical pitchfork bifurcation. By increasing the flow velocity, the amplitude of the buckled position increases, but no secondary instability can be observed thereafter, in agreement with Holmes’ results for his simplified model. The effect of different parameters on the behaviour of the pipe has been studied. By increasing the externally applied tension, or by increasing the gravity parameter, the critical flow velocity for the pitchfork bifurcation increases. The pitchfork bifurcation is subcritical if the nondimensional externally imposed tension, is greater than the nondimensional axial rigidity. The solution in the vicinity of the critical point for this case is confirmed to be subcritical, although the fold and the stable non-trivial solution thereafter could not be seen — perhaps because the model is correct to only third-order of magnitude. Dynamic instabilities may be possible for a pipe hinged at both ends but free to slide axially at the downstream end, according to preliminary results.
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