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 paper, a quasi-three-dimensional (quasi-3D) dynamic model for rotating pre-twisted functionally graded (FG) blades based on the three-dimensional elasticity shell theory and Carrera unified formulation is provided.
15Â citations
TL;DR: In this article, the free vibration analysis of rotating orthotropic cantilever plates attached with an arbitrary stagger angle to a hub is studied, which leads to improvement in design and appropriate optimization of the material and geometry in this class of problems.
Abstract: This manuscript is concerned with the free vibration analysis of rotating orthotropic cantilever plates attached with an arbitrary stagger angle to a hub. The general governing equations which include both the centrifugal inertia forces and Coriolis effects are derived using Hamilton’s principle. The results are obtained using extended Kantorovich method and extended Galerkin method which are compared with each other, and available data in the literature and in good agreements are observed. A very detailed study of the influence of varying stiffness ratio, rotation speed, stagger angle, hub radius ratio and aspect ratio on the dynamic characteristics is conducted. These investigations provide complementary results, which leads to improvement in design and appropriate optimization of the material and geometry in this class of problems. The observation of the results shows that the crossing/veering phenomenon is influenced by the stiffness ratio, stagger angle and hub radius ratio. It is found that the centrifugal stiffening rate in the spanwise bending modes is constant, while in the torsion mode is changeable. The plate with the lower stiffness ratio has the higher centrifugal stiffening rate.
13Â citations
TL;DR: In this article, a weak-form formulation for three-dimensional vibration analysis of rotating pre-twisted cylindrical isotropic and functionally graded (FG) shell panels is first developed.
12Â citations
TL;DR: In this article , a weak-form formulation for three-dimensional vibration analysis of rotating pre-twisted cylindrical isotropic and functionally graded (FG) shell panels is first developed.
12Â citations
TL;DR: In this paper, free vibration and buckling analyses of functionally graded blades with variable thickness subjected to mechanical and thermal loading using isogeometric analysis as a power-firm blade were presented.
Abstract: This article presents free vibration and buckling analyses of functionally graded blades with variable thickness subjected to mechanical and thermal loading using isogeometric analysis as a powerfu...
11Â citations
Cites methods from "A dynamic rotating blade model at a..."
...(Sun et al., 2013; Xiao and Chen, 2006) based on the classical plate theory (CPT) and first-order shear deformation theory (FSDT) (Hashemi et al....
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...Email: setoodeh@sutech.ac.ir (Sun et al., 2013; Xiao and Chen, 2006) based on the classical plate theory (CPT) and first-order shear deformation theory (FSDT) (Hashemi et al., 2009)....
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References
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01 Jan 2000TL;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
3,696Â citations
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01 Jan 1973TL;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.
1,085Â citations
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.
934Â citations
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.
876Â 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.
281Â citations