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Some Areas of Development of Methods Structural Mathematical Modeling
Abstract
Mathematical modeling of mechanical oscillatory systems using structural analysis methods is considered. The main focus is on the interpretation of the dynamic interactions of the system elements using structural diagrams, which makes it possible to obtain new results in the theory of vibration technologies, transport dynamics and vibration protection. The main approaches to the transformation of mathematical models into structural analogues are presented, including the use of dynamically equivalent automatic control systems. This allows you to apply frequency analysis and dynamic synthesis methods to solve vibration protection problems. Examples of single-degree-of-freedom mechanical systems include models with springs, dampers, and mass-inertial links. Frequency equations and concepts of dynamic stiffness of elements and the system as a whole are analyzed. Particular attention is paid to resonant vibrations and their effect on the dynamic properties of the system.
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