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Journal ArticleDOI

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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Posted ContentDOI
TL;DR: In this article, the primary resonance and nonlinear vibrations of the functionally graded graphene platelet (FGGP)-reinforced rotating pretwisted composite blade under combined the external and multiple parametric excitations are investigated with three different distribution patterns.
Abstract: The primary resonance and nonlinear vibrations of the functionally graded graphene platelet (FGGP)-reinforced rotating pretwisted composite blade under combined the external and multiple parametric excitations are investigated with three different distribution patterns The FGGP-reinforced rotating pretwisted composite blade is simplified to the rotating pretwisted composite cantilever plate reinforced by the functionally graded graphene platelet It is novel to simplify the leakage of the airflow in the tip clearance to the non-uniform axial excitation The rotating speed of the steady state adding a small periodic perturbation is considered The aerodynamic load subjecting to the surface of the plate is simulated as the transverse excitation Utilizing the first-order shear deformation theory, von Karman nonlinear geometric relationship, Lagrange equation and mode functions satisfying the boundary conditions, three-degree-of-freedom nonlinear ordinary differential equations of motion are derived for the FGGP-reinforced rotating pretwisted composite cantilever plate under combined the external and multiple parametric excitations The primary resonance and nonlinear dynamic behaviors of the FGGP-reinforced rotating pretwisted composite cantilever plate are analyzed by Runge–Kutta method The amplitude–frequency response curves, force–frequency response curves, bifurcation diagrams, maximum Lyapunov exponent, phase portraits, waveforms and Poincare map are obtained to investigate the nonlinear dynamic responses of the FGGP-reinforced rotating pretwisted composite cantilever plate under combined the external and multiple parametric excitations

26 citations

Journal ArticleDOI
TL;DR: In this article, the critical buckling load and dynamic instability of the rotating cantilever cross ply laminate thin walled twisted plate with exponential function type initial geometric imperfection are investigated for the first time.
Abstract: The initial geometric imperfections in manufacturing structure are unavoidable. Critical buckling load and dynamic instability of the rotating cantilever cross ply laminate thin walled twisted plate with exponential function type initial geometric imperfection are investigated for the first time. The mode shapes are obtained by using Rayleigh-Ritz method and shallow shell theory including the influence of rotational speed and imperfection. Based on the Lagrange equations and the obtained mode shape function, motion equations considering the first three modes of the system are derived. The mode shapes, critical loads and dynamic instability obtained in present have been verified by comparing them with other researcher results. The detail studies about the effect of rotating speed, twisted angle, stacking sequence and imperfection factors of the rotating thin walled twisted plate subjected to the in-plane load on the static critical buckling load and dynamic instability are carried out.

23 citations

Journal ArticleDOI
TL;DR: In this paper, a new structural dynamic model for the free vibration characteristic analysis of rotating pretwisted functionally graded (FG) sandwich blades is developed, which is made up of two functionally graded skins and a homogeneous material core.
Abstract: A new structural dynamic model for the free vibration characteristic analysis of rotating pretwisted functionally graded (FG) sandwich blades is developed. The sandwich blade is made up of two functionally graded skins and a homogeneous material core. The thick shell theory is applied to derive the basic equations of motion of the rotating FG sandwich blade by considering the effects of centrifugal and Coriolis forces. The mode shapes are expanded in terms of two-dimensional algebraic polynomials in the Rayleigh–Ritz method, and the static and dynamic natural frequencies of the blade are obtained. The convergence analysis is studied, and the accuracy of the proposed model is verified by comparing with the literature results and ANSYS data. The effects of frequency parameters such as the twist angle, the thickness ratio, the aspect ratio, the layer thickness ratio, the scalar parameter of volume fraction, the stagger angle, and the rotation velocity on the vibration characteristics for pretwist FG sandwich blade are investigated in detail. In addition, the phenomena of frequency locus veering and mode shape exchanging occur in the static and dynamic states. Frequency locus veering is essentially caused by the coupling between different modes.

22 citations


Cites methods from "A dynamic rotating blade model at a..."

  • ...[11] presented a dynamic model based on CLPT, investigated the vibration behavior of a rotating blade by using Hamilton’s principle, and studied the point and distribution forced response using a proportional damping model....

    [...]

Journal ArticleDOI
TL;DR: In this paper, the free vibration analysis of rotating functionally graded (FG) turbo-machinery blades with linear and non-linear variable thickness operating in thermal environment is presented, where the governing equations are extracted by deployment of principle of the virtual work and Hamilton's principle in the context of first-order shear deformation plate theory and the two-dimensional kinematics of the rotating blades.

21 citations

Journal ArticleDOI
TL;DR: In this article, a dynamic model of a rotating variable-thickness pre-twisted blade with elastic constraints is established by using the shallow shell theory, and the effects of Coriolis and centrifugal force due to the rotational motion are considered in the formulation.

21 citations

References
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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 ArticleDOI
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 ArticleDOI
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