A dynamic rotating blade model at an arbitrary stagger angle based on classical plate theory and the Hamilton's principle
TL;DR: In this paper, a dynamic model based on classical plate theory is presented to investigate the vibration behavior of a rotating blade at an arbitrary stagger angle and rotation speed, and the Hamilton's principle is applied to the model.
About: This article is published in Journal of Sound and Vibration.The article was published on 2013-03-04. It has received 58 citations till now. The article focuses on the topics: Hamilton's principle & Plate theory.
Citations
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TL;DR: In this article, a novel dynamic model for a pretwisted rotating compressor blade mounted at an arbitrary stagger angle using general shell theory and including the rotational velocity is developed to study the eigenfrequencies and damping properties of the pre-strained rotating blade.
67 citations
Cites background from "A dynamic rotating blade model at a..."
...Rotating straight plates mounted at an arbitrary stagger angle are studied in [12, 13, 14, 15, 16], where several significant design parameters are varied and both modal and transient analyses are performed....
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TL;DR: In this paper, a rotating cantilever sandwich-plate model with a pre-twisted and pre-set angle has been developed to investigate the vibrational behavior of an aero-engine turbine blade with thermal barrier coating (TBC) layers.
Abstract: A rotating cantilever sandwich-plate model with a pre-twisted and pre-set angle has been developed to investigate the vibrational behavior of an aero-engine turbine blade with thermal barrier coating (TBC) layers. The classic von Karman plate theory and the first-order shear deformation theory are applied to derive the energy equations of the rotating TBC blade, in which the geometric shapes, the work ambient temperature, and the TBC material properties are considered. The Chebyshev-Ritz method is used to obtain the nature frequency of the rotating TBC blade. For static frequency and modal analysis, the finite-element method (FEM) is also applied to compare and validate the results from the Chebyshev-Ritz method. A good agreement is found among these kinds of methods. For dynamic frequency, the results are analyzed in detail concerning the influence of system parameters such as the thickness of the TBC layer, the working temperature, and the pre-twisted and pre-set angle. Finally, the Campbell diagram is demonstrated to analyze the resonance property of the cantilever sandwich TBC blade model.
47 citations
TL;DR: In this paper, a rotating pretwisted cylindrical shell model with a presetting angle is established to investigate nonlinear dynamic responses of the aero-engine compressor blade.
Abstract: A rotating pretwisted cylindrical shell model with a presetting angle is established to investigate nonlinear dynamic responses of the aero-engine compressor blade. The centrifugal force and the Coriolis force are considered in the model. The aerodynamic pressure is obtained by the first-order piston theory. The strain–displacement relationship is derived by the Green strain tensor. Based on the first-order shear deformation theory and the isotropic constitutive law, nonlinear partial differential governing equations are derived by using the Hamilton principle. Discarding the Coriolis force effect, Galerkin approach is utilized to reduce nonlinear partial differential governing equations into a two-degree-of-freedom nonlinear system. According to nonlinear ordinary differential equations, numerical simulations are performed to explore nonlinear transient dynamic responses of the system under the effect of the single point excitation and nonlinear steady-state dynamic responses of the system under the effect of the uniform distribution excitation. The effects of the excitation parameter, damping coefficient, rotating speed, presetting angle and pretwist angle on nonlinear dynamic responses of the system are fully discussed.
45 citations
TL;DR: In this article, 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, where the effects of the Coriolis and centrifugal forces due to the rotation motion of the blade are considered in the formulation.
45 citations
TL;DR: In this paper, a new vibration model for the rotating blade which is treated as a cantilever pre-twisted panel with initial exponential function type geometric imperfection is provided by using the shallow shell theory in which the torsion is considered but the two radii of curvatures are zero.
43 citations
References
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TL;DR: In this article, a geometric nonlinear formulation is developed for dynamic stiffening of a rectangular plate undergoing large overall motions, which takes into account the stiffening terms, are derived based on the virtual power principle.
16 citations
TL;DR: A pseudo-spectral approach to 2D vibrational problems arising in linear elasticity is considerede using differentiation matrices and it is shown that it is necessary to apply an additional "pole" condition to deal with ther=0 coordinate singularity arising in the case of a 2D disc.
Abstract: A pseudo-spectral approach to 2D vibrational problems arising in linear elasticity is considerede using differentiation matrices. The governing partial differential equations and associated boundary conditions on regular domains can be translated into matrix eigenvalue problems. Accurate results are obtained to the precision expected in spectral-type methods. However, we show that it is necessary to apply an additional “pole” condition to deal with ther=0 coordinate singularity arising in the case of a 2D disc.
14 citations
TL;DR: In this paper, a modeling method for the modal analysis of cantilever plates undergoing accelerated in-plane motion is presented, where Von Karman strain measures are employed to derive the inplane and the lateral equations of motion.
14 citations
TL;DR: In this article, a modeling method employing multiple reference frames for dynamic equilibrium and modal analyses of rotating structures is presented, and the superiority of the proposed modeling method over the single reference frame modeling method is verified with numerical examples.
9 citations
TL;DR: In this paper, a nonlinear dynamic model of a thin rectangular plate attached to a moving rigid was established by employing the general Hamilton's variational principle, and it was proved theoretically that both phenomena of dynamic stiffening and dynamic softening can occur in the plate when the rigid undergoes different large overall motions including overall translational and rotary motions.
Abstract: A nonlinear dynamic model of a thin rectangular plate attached to a moving rigid was established by employing the general Hamilton’s variational principle. Based on the new model, it is proved theoretically that both phenomena of dynamic stiffening and dynamic softening can occur in the plate when the rigid undergoes different large overall motions including overall translational and rotary motions. It was also proved that dynamic softening effect even can make the trivial equilibrium of the plate lose its stability through bifurcation. Assumed modes method was employed to validate the theoretical result and analyze the approximately critical bifurcation value and the postbuckling equilibria.
9 citations