Natural frequencies of a pre-twisted blade in a centrifugal force field

doi:10.1016/J.JSV.2010.12.017

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Natural frequencies of a pre-twisted blade in a centrifugal force field

Journal Article•DOI•

Natural frequencies of a pre-twisted blade in a centrifugal force field

Sunil K. Sinha¹, Kevin E. Turner¹•Institutions (1)

General Electric¹

23 May 2011-Journal of Sound and Vibration (Academic Press)-Vol. 330, Iss: 11, pp 2655-2681

TL;DR: In this paper, the authors derived the partial differential equation of motion for the transverse deflection of a rotating pre-twisted plate by considering it as a plate of an equivalent rectangular cross-section subjected to a quasi-static load due to a centrifugal force field.

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About: This article is published in Journal of Sound and Vibration.The article was published on 2011-05-23. It has received 106 citations till now. The article focuses on the topics: Bending of plates & Centrifugal force.

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Journal Article•DOI•

Free vibration of rotating pretwisted functionally graded composite cylindrical panel reinforced with graphene platelets

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Y. Niu¹, Wen Zhang¹, X.Y. Guo¹•Institutions (1)

Beijing University of Technology¹

01 Sep 2019-European Journal of Mechanics A-solids

TL;DR: In this paper, the free vibrations of the rotating pretwisted functionally graded (FG) composite cylindrical panels reinforced with the graphene platelets (GPLs) were investigated by considering the cantilever boundary conditions.

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Abstract: This paper investigates the free vibrations of the rotating pretwisted functionally graded (FG) composite cylindrical panels reinforced with the graphene platelets (GPLs) by considering the cantilever boundary conditions. The weight fraction of the graphene platelets in each ply may be different, which leads to the layer-wise functionally graded composite cylindrical panels reinforced with the GPLs. The effective Young's modulus is calculated by the modified Halpin-Tsai model. The effective Poisson's ratio and mass density are derived by the rule of the mixture. The strain-displacement relationship is acquired by the Green strain tensor. Based on the first-order shear deformation theory, Chebyshev-Ritz method is used to obtain the natural frequencies of the rotating pretwisted functionally graded composite cylindrical panel reinforced with the GPLs. The natural frequencies are discussed by considering different material and geometry parameters of the rotating pretwisted functionally graded composite cylindrical panel reinforced with the GPLs, such as the GPL distribution pattern, the GPL weight fraction, the geometries of the GPLs, the pretwisted angle, the presetting angle and the rotating speed. Several validations are carried out, the numerical results are in good agreement with the results of the literature and ANSYS.

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126 citations

Journal Article•DOI•

Rotordynamic analysis of asymmetric turbofan rotor due to fan blade-loss event with contact-impact rub loads

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Sunil K. Sinha¹•Institutions (1)

General Electric¹

29 Apr 2013-Journal of Sound and Vibration

TL;DR: In this article, the effect of the rotary inertia and gyroscopic moments as a result of both shaft bending as well as staggered blades flexing in-and-out of the plane of the disk was investigated.

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98 citations

Cites background or methods from "Natural frequencies of a pre-twiste..."

...In this formulation, the blade airfoils on the fan–disk are modeled as pre-twisted thin shells [44], which are cantilevered with the clamped-end attached to the top surface of the disk at radius ‘r’....
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...Here, for capturing all relevant blade vibrational modes we have considered n1 number of terms in the span direction and 4 terms of the series in the chord or width direction [44] of the blade....
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...Here in the current formulation, the blade geometry is assumed to be a pre-twisted airfoil [44] which can deform both in the flexural as well as in extensional modes [45]....
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Journal Article•DOI•

Vibration characteristics of rotating pretwisted composite tapered blade with graphene coating layers

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Wen Zhang¹, Y. Niu¹, Kamran Behdinan²•Institutions (2)

Beijing University of Technology¹, University of Toronto²

01 Mar 2020-Aerospace Science and Technology

TL;DR: In this paper, a new dynamic model of the rotating tapered cantilever cylindrical panel with the graphene coating layers is developed to investigate the vibration characteristics of a rotating pretwisted tapered blade.

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83 citations

Journal Article•DOI•

A new dynamic model of rotor-blade systems

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Hui Ma¹, Yang Lu¹, Zhiyuan Wu¹, Xingyu Tai, Hui Li¹, Bangchun Wen¹ - Show less +2 more•Institutions (1)

Northeastern University (China)¹

24 Nov 2015-Journal of Sound and Vibration

TL;DR: In this paper, a new dynamic model of rotor-blade systems is developed considering the lateral and torsional deformations of the shaft, gyroscopic effects of the rotor which consists of shaft and disk, and the centrifugal stiffening, spin softening and Coriolis force of the blades.

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71 citations

Journal Article•DOI•

General shell model for a rotating pretwisted blade

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Jia Sun¹, Ines Lopez Arteaga², Ines Lopez Arteaga¹, Leif Kari¹•Institutions (2)

Royal Institute of Technology¹, Eindhoven University of Technology²

28 Oct 2013-Journal of Sound and Vibration

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.

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67 citations

Cites methods from "Natural frequencies of a pre-twiste..."

...In [20], a thin shell theory is applied to study the dynamic characteristics of a pretwisted rotating blade, where the equations of motion are only dependent on the transverse displacement and the specific mode shape functions are designed to satisfy the first few modes in order to reduce the computational cost due to the...
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References

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Book•

Theory of plates and shells

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Stephen P. Timoshenko, Sergius Woinowsky-Krieger

01 Jan 1959

TL;DR: In this article, the authors describe the bending of long RECTANGULAR PLATES to a cycloidal surface, and the resulting deformation of shels without bending the plates.

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Abstract: CONTENTS: BENDING OF LONG RECTANGULAR PLATES TO A CYLINDRICAL SURFACE PURE BENDING OF PLATES SYMMETRICAL BENDING OF CIRCULAR PLATES SMALL DEFLECTIONS OF LATERALLY LOADED PLATES SIMPLY SUPPORTED RECTANGULAR PLATES RECTANGULAR PLATES WITH VARIOUS EDGE CONDITIONS CONTINUOUS RECTANGULAR PLATES PLATES ON ELASTIC FOUNDATION PLATES OF VARIOUS SHAPES SPECIAL AND APPROXIMATE METHODS IN THEORY OF PLATES BENDING OF ANISTROPIC PLATES BENDING OF PLATES UNDER THE COMBINED ACTION OF LATERAL LOADS AND FORCES IN THE MIDDLE PLANE OF THE PLATE LARGE DEFLECTIONS OF PLATES DEFORMATION OF SHELLS WITHOUT BENDING GENERAL THEORY OF CYLINDRICAL SHELLS SHELLS HAVING THE FORM OF A SURFACE OF REVOLUTION AND LOADED SYMMETRICALLY WITH RESPECT TO THEIR AXIS.

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10,200 citations

"Natural frequencies of a pre-twiste..." refers background or methods in this paper

...(7)–(12) would reduce to the classical rectangular plate equations given in any standard textbook [43] on plate and shell theory....
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...Based upon the classical Kirchoff–von Karman’s plate bending theory [43], the general equation for the flexural motion wðx,y,tÞ in the transverse direction ðz-axisÞ along with the rotary inertia of a flat untwisted rectangular plate with in-plane distributed membrane forces Nx and Ny, respectively, can be derived....
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Book•

Shock and vibration handbook

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Cyril M. Harris, Charles E. Crede, H. M. Trent

01 Jan 1976

TL;DR: The third edition of the Handbook as discussed by the authors provides a wealth of detailed information on all aspects of shock and vibration, including instrumentation and measurements, data analysis and testing, methods of control, solutions to engineering problems and effects of vibration on people.

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Abstract: Professionals who want the most effective techniques for dealing with shock and vibration in a mechanical system have depended on this highly popular Handbook for over 25 years. It's the definitive reference for aerospace engineers, mechanical engineers, civil engineers, acoustical engineers, electrical engineers, plant engineers, product designers, and students. Now completely revised and updated, this new Third Edition contains approximately 50% new or substantially revised material. There's new coverage of modal analysis . . . shock and vibration instrumentation .. . vibration of structures induced by ground motion . . . vibration of structure produced by fluid flow . . . types, characteristics, and applications of isolators . . . condition monitoring of machinery . . . vibration standards, data reduction, testing, and specifications . . . and more. Copiously illustrated and written by 55 top experts in research and development, this giant Handbook brings together in one place a wealth of detailed information on all aspects of shock and vibration, including . . . Shock and vibration fundamentals Instrumentation and measurements Data analysis and testing Methods of control Solutions to engineering problems Equipment design and packaging Effects of vibration on people

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1,346 citations

"Natural frequencies of a pre-twiste..." refers methods in this paper

...The typical plate vibrational modes have been listed by Harris and Crede [47] and are also computed and verified by using a commercial code called ANSYS....
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Journal Article•DOI•

Structural and Dynamic Behavior of Pretwisted Rods and Beams

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Aviv Rosen¹•Institutions (1)

Technion – Israel Institute of Technology¹

01 Dec 1991-Applied Mechanics Reviews

TL;DR: In this paper, a review of the structural and dynamic aspects of pretwisted rods is presented, which is divided into three main subjects: static analysis, dynamic analysis and stability problems.

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Abstract: Because of being important structural elements in many engineering applications on one hand, and presenting inherent complicated coupling effects on the other hand, pretwisted rods have attracted the interest of many researchers. During the years, as a result of engineering breakthroughs, like the introduction of composite materials or operating at very high temperatures, the problems associated with pretwisted rods became more complicated. The present review will present the research during the last fifty years. It will be divided into three main subjects: static analysis, dynamic analysis and stability problems. The review will concentrate on the structural and dynamic aspects of pretwisted rods. Derivations of models and solution techniques will be addressed.

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130 citations

"Natural frequencies of a pre-twiste..." refers background in this paper

...Rosen [2] has presented a comprehensive review of structural and dynamic aspects of pre-twisted beams....
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Journal Article•DOI•

Vibration studies for laminated composite twisted cantilever plates

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Mohamad S. Qatu¹, Arthur W. Leissa²•Institutions (2)

Dresser Industries¹, Ohio State University²

01 Jan 1991-International Journal of Mechanical Sciences

TL;DR: In this article, the first known natural frequencies and mode shapes of the title problem were presented using the Ritz method with algebraic polynomial displacement functions, and convergence studies were made which demonstrate that accurate results were obtained using 144 displacement terms.

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121 citations

"Natural frequencies of a pre-twiste..." refers methods in this paper

...D elasticity results of Leissa and Jacob [1] for most of the twist values except again for some higher modes such as 1EB and 2T types of deformation with very highly twisted configurations of 601....
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...Before establishing the accuracy of one method or another as a benchmark, it is worth quoting the observations made by Leissa and Jacob [1] in their groundbreaking paper with 3-...
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...Comparison of the non-dimensional frequency parameters as computed by the current analytical model shows good correlation with the ANSYS computed results as well as the values reported by Leissa and Jacob [1] using their 3-...
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...For the first time, in 1986, Leissa and Jacob [1] solved the vibrational characteristics of very thick pre-twisted cantilever blades starting with the fundamentals of 3-...
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...Leissa and Jacob [1] were the first ones to investigate the free vibration characteristics of cantilevered twisted beams and plates as a three-dimensional vibration problem....
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Journal Article•DOI•

Development of an exact dynamic stiffness matrix for free vibration analysis of a twisted Timoshenko beam

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J.R. Banerjee¹•Institutions (1)

Northampton Community College¹

06 Feb 2004-Journal of Sound and Vibration

TL;DR: In this paper, an exact dynamic stiffness matrix for a twisted Timoshenko beam is developed in order to investigate its free vibration characteristics, and the resulting stiffness matrix is used with particular reference to the Wittrick-Williams algorithm to compute the natural frequencies and mode shapes of a twisted timoshenko beam with cantilever end condition.

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119 citations