Nonlinear random vibration of vibroimpact systems

Date of Award




Degree Name

Doctor of Philosophy (Ph.D.)


Mechanical Engineering

First Committee Member

Daniil. V. Iourtchenko, Committee Chair


Vibroimpact system is a mechanical system in which certain masses may collide with others or with rigid barriers during their oscillations. It has been used in a variety of construction and mining devices, as well as in power engineering, ocean engineering and nuclear engineering. It is a specific class of nonlinear systems, with a differential equation of motion being supplemented by an impact condition. Since the instants of impact are not given in advance, but are governed by the system's motion, vibroimpact systems may exhibit a strongly nonlinear behavior. Analysis of stochastic vibroimpact systems with inelastic impact, i.e., with velocity jumps, faces significant difficulties. The systems are usually analyzed approximately by the quasi-conservative averaging method and in order to apply this method, the impact condition should be incorporated into the system's equation of motion. This method is limited to small velocity jumps, which is impractical since in most applications, the restitution coefficient of the barrier lies between 0.2 and 0.8. Besides, an analytical expression may be derived only for a system with a barrier located at the system's equilibrium position. Other cases, including systems with two barriers, must be treated numerically in order to obtain a normalized, stationary probability density function.The only alternative technique, capable of predicting analytically mean response energy of a vibroimpact system with substantial impact losses, is the Direct Energy Balance method. The Direct Energy Balance method can be used to study vibroimpact systems with a one-sided barrier, shifted from the system's equilibrium position and vibroimpact systems with two-sided, symmetric barriers. Mean energy and mean square response can be derived for different cases of vibroimpact systems using this method. Comparison of Direct Energy Balance results with numerical simulation results has shown high accuracy of analytical predictions. Two important characteristics of a vibroimpact system, Probability Density Function and Power Spectral Density, have been obtained numerically; results of Direct Energy Balance method were used where appropriate. Numerical simulation was used to investigate behavior of two-degree-of-freedom vibroimpact systems. It has been shown that the mean energy of such systems, similar to single-degree-of-freedom vibroimpact systems, is linearly proportional to coefficient of impact energy losses.


Engineering, Mechanical

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