خصوصیات لرزش یک تیغه لمینیت کامپوزیت چرخشی
Abstract
1- Introduction
2- Mathematical formulation
3- Numerical results
4- Conclusion
References
Abstract
A new dynamic model based on the shell theory is presented to investigate the vibration behavior of a rotating composite laminated blade with a pre-twisted angle. The effects of the Coriolis and centrifugal forces due to the rotation motion of the blade are considered in the formulation. Based on the Rayleigh-Ritz method and continuous algebraic polynomial functions satisfying the boundary conditions of a cantilever, the natural frequencies and mode shapes of a rotating pre-twisted blade are obtained. The convergence analysis is performed and the accuracy of the proposed model is verified by comparing the non-dimensional frequencies obtained by the present method with those in literature. The frequency loci veering and crossing phenomena along with the corresponding mode shape variations are presented and discussed in detail. A comprehensive parameter investigation of the effects of aspect ratio, pre-twisted angle, stagger angle, rotation velocity and hub radius on variations of the modal characteristics of the blade is conducted. It is demonstrated through the results of this paper that the developed model is effective to evaluate the dynamic behavior of rotating pre-twisted blades, which would be useful for improvement in design and optimization of the material and geometry dimension of the blades.
Introduction
Rotating structures are widely used as key components in various engineering applications, such as blades of turbines, helicopters and aircraft engines. The vibration or modal characteristics of blades change significantly when the structures undergo overall motions. For example, centrifugal inertia forces lead to the stretching of the structures and increase their bending stiffness, while Coriolis effects produce vibration couplings between different vibration modes and generate complex vibration mode shapes [1]. Analytical or semi-analytical methods are desirable to understand and identify the dynamic properties of blades with good accuracy at low computational costs. Beam models have extensively been adopted to analyze the dynamic response of a rotating blade in many literatures. Such idealization could provide accurate dynamic characteristics for most rotating structures. For example, Yao et al. [2,3] treated a rotating blade as a pre-twisted, presetting and thin-walled rotating cantilever beam under varying rotating speed. The nonlinear dynamic responses of the rotating blade under high-temperature supersonic gas flow was investigated. Lee et al. [4,5] studied the free vibration of a beam rotating at a constant angular velocity. They revealed the effects of the setting angle on the natural frequencies of pre-twisted beams. Liu and Ren [6] analyzed the dynamic characteristics of a wind turbine rotor blade by regarding it as a composite anisotropic thin-walled closed-section beam. Yoo et al. [7] used the Rayleigh-Ritz method to study the vibration characteristics of a rotating pre-twisted blade with a concentrated mass. Librescu et al. [8–10] investigated the modeling and free vibration of pre-twisted rotating blades made of functionally graded materials (FGMs) and operating in a high-temperature field. The blade is modeled as a thin-walled beam that incorporates the pre-twisted effects. Lin and Chen [11] investigated the stability problem of spinning pre-twisted sandwich beams subjected to periodic axial load. Other previous studies [12,13] primarily dealt with the free vibration characteristics of twisted rotating beams, which also included the effect of transverse shear and rotary inertia. Hajianmaleki and Qatu [14,15] presented a review of composite beam modeling approach for analyzing anisotropic blades.