Parametric vibration analyses of eccentric rotational ring-shaped periodic structures
A dynamic model with time-varying excitation of eccentric rotating structures was established based on Hamilton principle to solve the parametric vibration problem of eccentric rotational ring-shaped periodic structures.The influences of topological structures with different supports and parameter combinations on natural frequency splitting were analyzed.Floquét theory was used to calculate the instability regions for different parameters,and the relationship between the natural frequency splitting and the instability regions was revealed.In addition,the influences of wavenumbers,intergroup angle,and the angle between the radius and rotary supports of grouping topology on the stability were analyzed,based on which a method for improving stability was proposed.The results showed that natural frequencies splitting and the parameter excitation arose when the topology of the rotary supports and wavenumbers met some specific relationships.The parametric instability mainly appeared at the natural frequency and their linear combinations.The instability regions changed periodically with the intergroup angle,and the angle between the radius and rotary supports had different influences on each instability region.
eccentric rotational ring-shaped periodic structuresrotational supportsparametric vibrationnatural frequency splittingparametric stability
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