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
More filters
TL;DR: In this article, an improvement of the Absolute Nodal Coordinate Formulation (ANCF) is carried out for modal analysis of rotating plates in order to solve transient dynamics problems and the results obtained from the presented method are validated by comparison with available results from literature and commercial software ANSYS.
Abstract: Dynamics analysis of a rotating plate with a setting angle is presented in this study by using the Absolute Nodal Coordinate Formulation (ANCF). The setting angle has a significant influence on distribution of the centrifugal force so that rotating plates can be twisted. However, the rotation-induced torsion deformation has not been discussed in existing literature and the existing approaches are not always appropriate both in transient and modal analysis for this subject. An improvement of the ANCF which is very suitable to solve transient dynamics problems is carried out for modal analysis of rotating plates in this paper. The results obtained from the presented method are validated by comparison with available results from literature and commercial software ANSYS which exhibits a good agreement. The results in different cases indicate that the torsion deformations of rotating plates not only exist in the transient dynamics but also affect significantly the modal characteristics. Incidentally, the effect of setting angle on torsion deformation, frequencies and mode shapes is discussed by parametric analysis .
20Â citations
TL;DR: In this paper, the super-harmonic resonances combined with 2:1 internal resonance of a rotating blade subjected to strong gas pressure were investigated, and the steady-state response of the rotating blade was calculated via the method of multiple scales.
Abstract: The present work investigates the super-harmonic resonances combined with 2:1 internal resonance of a rotating blade subjected to strong gas pressure. The dynamic model includes the effect of the initial curved axis of the blade induced by the thermal gradient. The dimensionless gas excitation amplitude is assumed to be the same magnitude of the dimensionless vibration displacement. The vibration of the blade in the plane of rotation and the plane perpendicular to it are described by a set of coupled ordinary differential equations with quadratic and cubic nonlinearities. The steady-state response of the rotating blade is calculated via the method of multiple scales. The stabilities of the steady-state responses are determined via Lyapunov theory. Parametric studies are performed to clarify the influences of system parameters on dynamic response and unstable regions. The various typical phenomena including jump, hysteresis and saturation are observed in the dynamic model. The stable and unstable regions of the solution are analyzed in the plane of external detuning parameter and excitation amplitude. The evaluation of the blade dynamic response is revealed in the unstable region. The theoretical results obtained via the method of multiple scales coincide with the numerical solutions.
18Â citations
TL;DR: In this paper, the vibration characteristics of the rotating pretwist functionally graded (FG) sandwich blades operating in the thermal environment are studied for the first time, where the FG sandwich blade is composed of a single metallic core combined with two FG surface layers and is assumed to be in a steady state temperature field.
16Â citations
TL;DR: Based on the three-dimensional heat conduction theory, von Karman equation and laminated plate theory, the threedimensional steady thermodynamic behavior for a double-layer (coating/FGM) plate subjected to a local heat source and harmonic load is investigated in this paper.
16Â citations
TL;DR: In this article, a numerical shallow conical shell model is proposed, and the displacement fields of the shell model are described via the first-order shear deformation theory, considering the rotating speed, the governing equation of the rotating pre-twisted laminated conical shells is derived, and then solved using the meshless kp-Ritz method.
16Â citations
References
More filters
Book•
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
Book•
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