Parametric elastic vibration analysis method of rotating annular periodic structure

Abstract

A parametric elastic vibration analysis method of a rotating annular periodic structure comprises the steps of building a rigid-elastic coupling dynamic model of the rotating annular periodic structure according to a Hamilton principle under a global stationary coordinate system; introducing coordinate conversion, and converting the dynamic model to a support follow-up coordinate system so that a parametric item in an original equation is eliminated; performing discrete processing on a partial differential constant coefficient dynamic equation under the rotating support follow-up coordinate system by a Galerkin method to obtain an ordinary differential matrix equation; analyzing a characteristic value of the ordinary differential matrix equation by using a classical vibration theory; and respectively analyzing mode characteristic of the rotating annular periodic structure and a dynamic stability rule of parametric elastic vibration by employing an imaginary part and a real part of the characteristic value of the ordinary differential matrix equation. The parametric elastic vibration analysis method can be used for dynamic analysis of rotating machinery, calculation and solution of the mode characteristic of a system, and analysis on the dynamic stability and the dynamic response of the system.

Description

technical field [0001] The invention relates to a vibration analysis method. In particular, it relates to a method for analyzing parametrically excited elastic vibration of a rotating ring periodic structure. Background technique [0002] Rotating annular periodic structural systems widely exist in modern industries, such as ring gears of planetary gear transmission systems, annular stators and rotors of rotating electrical machines, steam turbine blades, inner and outer rings of rolling bearings, etc. Such structures usually consist of rings and rotating loads. Under rotating loads, the ring structure will create vibration and noise problems, especially for high-speed, heavy-duty workplaces. Among various vibration behaviors, parametric vibration has attracted much attention. However, the calculation efficiency and accuracy of traditional analysis techniques for its modal characteristics and dynamic stability problems are low, and there is an urgent need for high-efficie...

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Problems solved by technology

Since the classical vibration theory can only analyze ordinary differential equations analytically, the existing technology cannot directly solve the dynamic equations analytically

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