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A two degree-of-freedom model of suspended cables is studied for forced resonant response. The method of averaging is used to obtain first-order approximations to the response of the system. A bifurcation analysis of the averaged system is performed in the case of 2-to-1 internal resonance. Nonlinear coupled-mode motions are found to bifurcate from single-mode responses and further bifurcate to limit cycle motions via Hopf bifurcations. The limit cycle solutions undergo period doubling bifurcations to chaos.
Ground-borne noise and vibration generated by underground transit system has been recognized as an important environmental problem. This study reviews several of the procedures that have been used to predict ground-borne vibration. The vibration responses are measured at three sites that have different soil qualities. The measured vibration levels are compared with the predicted results by previously used vibration level prediction models. There are some drawbacks to apply these prediction models to selected sites because most of the existing prediction models are primarily based on empirical data and all of them lack of analytical models for the mechanism of ground-borne vibration generation. radiation, and propagation. In this study a numerical method, which is based on explicit differential method, is used to compensate for the shortcomings of existing prediction models. Although numerically computed results are not quantitatively in good agreement with the measured results, the trends are comparable in the sense that vibration level does not decrease monotonically with distance. Also, the site with the deepest tunnel gives the highest vibration level.
To assess downward positions of water spray for the small-scale release of chlorine gas, dispersion coefficients for the Gaussian dispersion model were validated at the small-scale release experiment. And the downwind distances of water spray were assessed with the simulated results. As results, the Gaussian plume model using the Briggs' dispersion coefficient well estimated the dispersed characteristics for small-scale release of chlorine gas. The best adequate downwind position of water spray is the position of the maximum concentration of chlorine at the ground level. And the adequate vertical and horizontal dimensions of water spray consider the maximum width and height of cloud.
Nonlinear vibrations of a beam are studied when it is excited by harmonic forces in one of lateral directions. The physical phenomena of interest here arise when a bending and a torsional mode have nearly the same natural frequencies. The method of averaging is used to analyze the nonlinear interaction between the two modes. It is shown that the beam can respond in the bending mode only or in a mixed-mode. For some combinations of parameter values, the steady-state mixed-mode responses can undergo slowly varying amplitude-modulated motions via Hopf bifurcations. The amplitude-modulated motions can exist over wide frequency interval.
A viscoelastic damper model which has a non-linear spring as an element is studied. The model is useful for expressing the non-linearity of viscoelastic materials. A time integration of constitutive differential equation shows non-linear hysteresis curves which have the qualitatively similar behavior of real viscoelastic materials. Harmonic balance method is used to get an analytic solution of system equations, which gives the frequency response curves. A direct time integration of system equation shows the periodicity of time response of system. The result of time integration shows that the harmonic balance method can be used efficiently. Jump phenomena of system response has been found.