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Journal Article•DOI•

A dynamic rotating blade model at an arbitrary stagger angle based on classical plate theory and the Hamilton's principle

04 Mar 2013-Journal of Sound and Vibration (Academic Press Inc.)-Vol. 332, Iss: 5, pp 1355-1371
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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Journal Article•DOI•
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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Journal Article•DOI•
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

Journal Article•DOI•
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

Journal Article•DOI•
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

Journal Article•DOI•
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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Book•
01 Jan 2000
TL;DR: This paper presents a meta-analyses of Chebyshev differentiation matrices using the DFT and FFT as a guide to solving fourth-order grid problems.
Abstract: Preface 1 Differentiation matrices 2 Unbounded grids: the semidiscrete Fourier transform 3 Periodic grids: the DFT and FFT 4 Smoothness and spectral accuracy 5 Polynomial interpolation and clustered grids 6 Chebyshev differentiation matrices 7 Boundary value problems 8 Chebyshev series and the FFT 9 Eigenvalues and pseudospectra 10 Time-stepping and stability regions 11 Polar coordinates 12 Integrals and quadrature formulas 13 More about boundary conditions 14 Fourth-order problems Afterword Bibliography Index

3,696 citations

Book•
01 Jan 1973
TL;DR: In this article, the authors consider bending waves, which are a special combination of compressional and shear waves, and for some special cases (quasi-) longitudinal waves and torsional waves also have to be considered.
Abstract: Although sound waves in structures cannot be heard directly, and only be felt at low frequencies, they play an important role in noise control, because many sound signals are generated or transmitted in structures before they are radiated into the surrounding medium. In several respects sound waves in structures and sound waves in gases or liquids are similar, there are, however, also fundamental differences, which are due to the fact that solids have a certain shear stiffness, wheras gases or liquids show practically none. As a consequence acoustic energy can be transported not only by the normal compressional waves but also by shear waves and many combinations of compressional (sometimes loosely called longitudinal) and shear waves . For noise control purposes bending waves (which are a special combination of compressional and shear waves) are of primary importance; for some special cases (quasi-) longitudinal waves and torsional waves also have to be considered.

1,085 citations

Journal Article•DOI•
TL;DR: In this paper, the authors consider bending waves, which are a special combination of compressional and shear waves, and for some special cases (quasi-) longitudinal waves and torsional waves also have to be considered.
Abstract: Although sound waves in structures cannot be heard directly, and only be felt at low frequencies, they play an important role in noise control, because many sound signals are generated or transmitted in structures before they are radiated into the surrounding medium. In several respects sound waves in structures and sound waves in gases or liquids are similar, there are, however, also fundamental differences, which are due to the fact that solids have a certain shear stiffness, wheras gases or liquids show practically none. As a consequence acoustic energy can be transported not only by the normal compressional waves but also by shear waves and many combinations of compressional (sometimes loosely called longitudinal) and shear waves . For noise control purposes bending waves (which are a special combination of compressional and shear waves) are of primary importance; for some special cases (quasi-) longitudinal waves and torsional waves also have to be considered.

934 citations

Journal Article•DOI•
TL;DR: A software suite consisting of 17 MATLAB functions for solving differential equations by the spectral collocation (i.e., pseudospectral) method is presented and it is demonstrated how to use the package for solving eigenvalue, boundary value, and initial value problems arising in the fields of special functions, quantum mechanics, nonlinear waves, and hydrodynamic stability.
Abstract: A software suite consisting of 17 MATLAB functions for solving differential equations by the spectral collocation (i.e., pseudospectral) method is presented. It includes functions for computing derivatives of arbitrary order corresponding to Chebyshev, Hermite, Laguerre, Fourier, and sinc interpolants. Auxiliary functions are included for incorporating boundary conditions, performing interpolation using barycentric formulas, and computing roots of orthogonal polynomials. It is demonstrated how to use the package for solving eigenvalue, boundary value, and initial value problems arising in the fields of special functions, quantum mechanics, nonlinear waves, and hydrodynamic stability.

876 citations

01 Feb 1957
TL;DR: In this article, the differential equations of motion for the lateral and torsional deformations of twisted rotating beams are developed for application to helicopter rotor and propeller blades, and the generality is such that previous theories involving various simplifications are contained as subcases to the theory presented in this paper.
Abstract: The differential equations of motion for the lateral and torsional deformations of twisted rotating beams are developed for application to helicopter rotor and propeller blades. No assumption is made regarding the coincidence of the neutral, elastic, and mass axes, and the generality is such that previous theories involving various simplifications are contained as subcases to the theory presented in this paper. Special attention is given the terms which are not included in previous theories. These terms are largely coupling-type terms associated with the centrifugal forces. Methods of solution of the equations of motion are indicated by selected examples.

281 citations