Study Of Dynamic Characteristics Of Composite Chain Of Beads Under Vertical Vibration

Granular material, as a research field of physics, has attracted many interests recently. Because of its own strong nonlinearity, granular material has a lot of unique and interesting phenomenon. Under certain conditions, it may behave like solid, liquid or gas. As the basic model of granular material, one-dimensional chain of beads has also attracted a lot of scientists. Especially about the propagation of acoustic energy, many valuable results have been stated.First in this paper, there's the numerical simulation of propagation of solitary wave in a chain of beads. In a one-dimensional granular chain, beads interact with each other under Hertz law. When an instant excitation is applied to one end, the energy will propagate through the chain in the form of a solitary wave. By numerically calculating the dynamic equations obtained by Hertz law, simulation of this type of solitary wave can be conducted. In this paper there's also the simulation of influence of elastic coefficients on solitary wave propagation. The results are compared with those of mass. And the conclusion is that the influence of mass is more decisive. There's also discussion on how to add dissipation to Hertz law equations. Based on the concept of restitution coefficient of "hard-sphere model" dissipation coefficient is proposed. The value of dissipation coefficient can be obtained by trying different values in differential equations. The revised Hertz law equation is more accurate and more suitable for simulating chains under continuous vibration. Following in this paper are the experimental researches on the dynamic properties of composite chain of beads under continuous vibration. Copper and aluminum beads, which have great differences on mechanic parameters, are chosen to form a two-section composite chain. The motion of the chain, phase-shift, mean dilation and displacement of center of mass, are recorded and analyzed. In experiments, the behavior of "heavy-light" chain is quite similar to that of chain constituted by single-type "hard" beads. It will transit from condensation to fluidization as excitation acceleration increases. But "light-heavy" chain is similar to chain of single-type "soft" beads, which transits from condensation to clusterization without fluidizing. By calculating the energy situation of two arrangements under same excitation, the differences are found. At high excitation accelerations, there's less energy in "light-heavy" chain than in "heavy-light" chain. The effect of interface is considered as cause of differences between energy and dynamic properties. This discovery might be used for vibration-isolation with granular materials.There are also discussions on the wave propagation in fluidized "heavy-light" chain in this paper. With second-order polynomial data fitting of peak values in average displacement-time curves, velocities of wave propagation can be obtained. In the heavy chain section, velocities are similar under different frequencies and are close to a constant, while in the light chain section, they are various. At low frequencies, velocities in the light section are close to a constant, similar to those in heavy section, but at high frequencies, they have an initial instant increase and then decrease with time. The higher the frequency is, the higher the initial velocity is.