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

Abstract

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.