The maximum principle of Pontryagin and emergency seismic load

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Rubric:     Theoretical and experimental studies   
Annotation:
The work proposes the methods for determining special and emergency seismic loads and emergency calculation situations required in accordance with the current legislation. It is refined the previously proposed way of describing the structure movements with the help of nonlinear ordinary differential equations and the existence of stable limit cycles for them, leading to the appearance of stationary periodic solutions-self-oscillations. It is shown that the task of selecting a special (emergency) seismic action is reduced to the task of optimal speed, when the transition from one extreme position of the structure to another with external seismic action takes place in a minimum time. A proposal was made to apply special (emergency) harmonic seismic actions with a special frequency close to the natural oscillation frequency of the structure as a maximum design earthquake in seismic regions. Emergency seismic horizontal loads are allocated as loads that create an emergency situation. An algorithm for determining the special frequency of emergency seismic actions is presented. It is based on the comparison of the maximum displacements of structures arising from beats and self-oscillations.