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Frequency veering of Rotating Metal Porous Twisted Plate with Cantilever Boundary Using Shell Theory

Acta Mechanica Solida Sinica 2022年第2期35卷 282-302页

作者： Y.Y.Liu Y.X.Hao W.Zhang L.T.Liu S.W.Yang Y.T.Cao College of Mechanical Engineering Beijing Information Science and Technology UniversityBeijing 100192China College of Mechanical Engineering Beijing University of TechnologyBeijing 100124China

The Frequency veering of a metal porous rotating cantilever twisted plate with twist angle and stagger angle is investigated.Metal porous materials may have the characteristics of gradient or uniform distribution along the thickness direction.Based on the classical shell theory,considering the influence of centrifugal force produced by high-speed rotation,the free vibration equations of a rotating cantilever twisted plate are derived.Through the polynomial function and Rayleigh-Ritz method,the natural frequencies and mode shapes of the metal porous cantilever twisted plate in both static and rotating states are derived.The accuracy of the present theory and calculation results is confirmed by a comparison between them and the results available from the literature and those obtained from Abaqus.The influences of the thickness ratio,porosity,twist angle,stagger angle and rotational velocity on the Frequency veering and mode shape shift of the rotating cantilever twisted plate with porous material under three different distributions are analyzed.It should be mentioned that the Frequency veering accompanied by mode shape shift occurs in both static and dynamic states.

关键词： Frequency veering Rotating twisted plate Cantilever boundary Metal porous

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Natural vibration of cantilever porous twisted plate with variable thickness in different directions

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Defence Technology(防务技术) 2023年第9期27卷 200-216页

作者： Y.X.Hao Y.Y.Liu W.Zhang L.T.Liu K.C.Sun S.W.Yang College of Mechanical Engineering Beijing Information Science and Technology UniversityBeijing100192PR China College of Mechanical Engineering Beijing University of TechnologyBeijing100124PR China

In this paper,the blade is assumed to be a rotating variable thickness cantilever twisted plate structure,and the natural vibrations of variable thickness cantilever twisted plate made of metal porous material are studied.It is assumed that the thickness of the plate changes along spanwise direction and chordwise direction,respectively,and it changes in both directions.The classical thin shell theory,the first and second fundamental forms of surface and von Karman geometric relationship are employed to derive the total potential energy and kinetic energy of the cantilever twisted plate,in which the centrifugal force potential due to high rotational speed is included.Then,according to the Rayleigh-Ritz procedure and applying the polynomial functions which satisfy the cantilever boundary conditions,the dynamic system expressed by equations of motion is reduced to an eigenvalue problem.By numerical simulation,the frequency curves and the mode shapes of the twisted plate can be obtained to reveal the internal connection between natural vibration and the parameters.A series of comparison studies are performed to verify the accuracy of the present formulation and calculations,in which compared data come from experimental,finite element method and theoretical calculation,respectively.The influence of pre-twist angle,three different forms of thickness taper ratio and rotational speed on natural vibration,mode exchange and Frequency veering phenomenon of the system is discussed in detail.In addition,the approach proposed here can efficiently extract analytical expressions of mode functions for rotating variable thickness cantilever twisted plate structures.

关键词： Porous cantilever twisted plate Variable thickness Natural vibration Frequency veering Mode exchange

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