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NONLINEAR VIBRATIONS OF DISCRETE DISSIPATIVE SYSTEMS
Abstract
A significant amount of structural mechanics' problems is associated with structures working under dynamic loading conditions; however the majority of the existing methods of the solution of dynamic tasks simplifies slightly parameters of model which describes a real building structure. As a rule, a uniform damping model is selected or internal friction is not considered. Number of degrees of freedom is limited; dimensions of the distributed masses are often neglected. External actions are simulated simplistically: system's response to a single (usually instant) impulse is investigated, more complex loadings (groups of impulses) are being studied for a single-degree-of-freedom model. Model of behavior of construction material is simplified: nonlinear elastic and plastic properties are not considered. The suggested mathematical models allow implementing the computational scheme of nonlinear time analysis of discrete dissipative systems under complex dynamic loadings. The entire calculation process is divided into time intervals, the dynamic parameters of the system are invariable within a specific interval. Consequently, at every specific time interval the movement equations are integrated according to linear solution scheme. Thus, the problem of forming of nonlinear system's response is reduced to the similar operations of repetitive various quasi-linear solutions which written down analytically as Duhamel integral. This approach is available for practical application due to clear algorithm. Vibrations of three-storey frame with columns made of purely elastic-plastic material under action of group of impulses were investigated to illustrate the efficiency of the time analysis method.
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