Vibration Characteristics of Low Aspect Ratio Compressor Blades

1971 ◽  
Vol 93 (1) ◽  
pp. 103-112 ◽  
Author(s):  
Ralph Petricone ◽  
Fernando Sisto
Keyword(s):  
Aspect Ratio ◽  
Contact Point ◽  
Twist Angle ◽  
Ritz Method ◽  
Three Dimensional ◽  
Beam Theory ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Compressor Blades ◽  
Low Aspect Ratio

This paper presents the results of a study of the vibration characteristics of low aspect ratio compressor blades. The treatment is based on thin shell theory and the Rayleigh-Ritz method is used to obtain the eigenvectors and eigenvalues. The object is to elucidate those characteristics which are inaccessible using beam theory. Results are presented which show the variation of the natural frequencies and mode shapes with angle of twist, aspect ratio, and angle of inclination of the base of the blade. A three-dimensional plot of the bending mode frequencies versus aspect ratio and twist angle is presented. Although the surfaces describing the variation of frequencies for specific modes do not intersect, there is a point of contact. This contact point is significant in the transition of mode shapes along the frequency surfaces. It is demonstrated that the “stiff-direction” or “in-plane” vibration of the untwisted plate evolves into coupled bending modes as the twist angle increases from zero and that the character of these modes changes in the vicinity of the contact point.

scholarly journals Three-Dimensional Elasticity-Based Solutions for Natural Vibrations of Low Aspect Ratio Compressor Blades

1993 ◽  
Author(s):  
Oliver G. McGee
Keyword(s):  
Aspect Ratio ◽  
Twist Angle ◽  
Ritz Method ◽  
Three Dimensional ◽  
Natural Vibrations ◽  
Compressor Blades ◽  
Low Aspect Ratio ◽  
Plate And Shell ◽  
Convergence Study ◽  
Three Dimensional Elasticity

This paper offers three-dimensional (3-D) vibration frequency solutions for low aspect ratio compressor blades. The Ritz method is used to minimize the 3-D elasticity-based dynamical energies with displacements approximated by mathematically complete polynomials satisfying the clamped boundary conditions exactly. The accuracy of the method is established by a convergence study explicitly showing the influence of solution determinant size. Several tables are presented which show the variation of natural frequencies with twist angle in the presence of skewness of low aspect ratio compressor blades. Results obtained using the present Ritz method are used to elucidate those frequency solutions which are inaccessible using beam, plate and shell theories, since kinematic constraints associated with these theories are eliminated in the present 3-D approach.

Free Vibrations of Thick, Complete Conical Shells of Revolution From a Three-Dimensional Theory

2005 ◽  
Vol 72 (5) ◽  
pp. 797-800 ◽  
Author(s):  
Jae-Hoon Kang ◽  
Arthur W. Leissa
Keyword(s):  
Ritz Method ◽  
Three Dimensional ◽  
Axial Direction ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Vibration Frequencies ◽  
Shells Of Revolution ◽  
Dimensional Theory ◽  
Conical Shells ◽  
Cylindrical Coordinate

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution in which the bottom edges are normal to the midsurface of the shells based upon the circular cylindrical coordinate system using the Ritz method. Comparisons are made between the frequencies and the corresponding mode shapes of the conical shells from the authors' former analysis with bottom edges parallel to the axial direction and the present analysis with the edges normal to shell midsurfaces.

Three-Dimensional Vibration Analysis of Twisted Cylinder With Sectorial Cross Section

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
D. Zhou ◽  
S. H. Lo
Keyword(s):  
Cross Section ◽  
Chebyshev Polynomial ◽  
Numerical Solutions ◽  
Twist Angle ◽  
Ritz Method ◽  
Three Dimensional ◽  
Cylindrical Domain ◽  
Linear Elasticity Theory ◽  
Boundary Functions ◽  
Polynomial Series

The three-dimensional (3D) free vibration of twisted cylinders with sectorial cross section or a radial crack through the height of the cylinder is studied by means of the Chebyshev–Ritz method. The analysis is based on the three-dimensional small strain linear elasticity theory. A simple coordinate transformation is applied to map the twisted cylindrical domain into a normal cylindrical domain. The product of a triplicate Chebyshev polynomial series along with properly defined boundary functions is selected as the admissible functions. An eigenvalue matrix equation can be conveniently derived through a minimization process by the Rayleigh–Ritz method. The boundary functions are devised in such a way that the geometric boundary conditions of the cylinder are automatically satisfied. The excellent property of Chebyshev polynomial series ensures robustness and rapid convergence of the numerical computations. The present study provides a full vibration spectrum for thick twisted cylinders with sectorial cross section, which could not be determined by 1D or 2D models. Highly accurate results presented for the first time are systematically produced, which can serve as a benchmark to calibrate other numerical solutions for twisted cylinders with sectorial cross section. The effects of height-to-radius ratio and twist angle on frequency parameters of cylinders with different subtended angles in the sectorial cross section are discussed in detail.

Calculation of the Rise and Pitch of a Three-Dimensional Low-Aspect-Ratio Flat Ship

1991 ◽  
Vol 35 (04) ◽  
pp. 314-324
Author(s):  
Todd McComb
Keyword(s):  
Aspect Ratio ◽  
Three Dimensional ◽  
Static Case ◽  
Equilibrium Flow ◽  
Low Aspect Ratio ◽  
Fast Speed ◽  
Flow Past

Using low-aspect-ratio flat ship theory, this paper defines a procedure to determine the position of a hull which is in equilibrium at some "fast" speed in terms of a given hull shape for the same hull at rest. This procedure is then used to find the equilibrium flow past a moving ship, when given the shape of the hull at rest. The method is then extended to find the hull configuration at various speeds based on either the configuration in the static case or at some other equilibrium speed, leading to a calculation of drag versus speed. Some general formulas and some simple examples are given.

Improving the Performance of a Turbine With Low Aspect Ratio Stators by Aft-Loading

2004 ◽  
Vol 128 (3) ◽  
pp. 492-499 ◽  
Author(s):  
Graham Pullan ◽  
John Denton ◽  
Eric Curtis
Keyword(s):  
Aspect Ratio ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Loss Reduction ◽  
Low Aspect Ratio ◽  
Surface Pressure Distribution ◽  
Loaded Surface ◽  
Nozzle Guide ◽  
Nozzle Guide Vanes ◽  
Stage Efficiency

Experimental data and numerical simulations are presented from a research turbine with low aspect ratio nozzle guide vanes (NGVs). The combined effects of mechanical and aerodynamic constraints on the NGV create very strong secondary flows. This paper describes three designs of NGV that have been tested in the turbine, using the same rotor row in each case. NGV 2 used three-dimensional design techniques in an attempt to improve the performance of the datum NGV 1 blade, but succeeded only in creating an intense vortex shed from the trailing edge (as previously reported) and lowering the measured stage efficiency by 1.1% points. NGV 3 was produced to avoid the “shed vortex” while adopting a highly aft-loaded surface pressure distribution to reduce the influence of the secondary flows. The stage with NGV 3 had an efficiency 0.5% points greater than that with NGV 1. Detailed comparisons between experiment and computations, including predicted entropy generation rates, are used to highlight the areas where the loss reduction has occurred and hence to quantify the effects of employing highly aft-loaded NGVs.

Free vibration characteristics of delaminated composite pretwisted stiffened cylindrical shell

2017 ◽  
Vol 232 (4) ◽  
pp. 595-611 ◽  
Author(s):  
Mrutyunjay Rout ◽  
Sasank Shekhara Hota ◽  
Amit Karmakar
Keyword(s):  
Free Vibration ◽  
Dynamic Equilibrium ◽  
Twist Angle ◽  
Cylindrical Shells ◽  
Shell Element ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Iteration Algorithm ◽  
Lagrange’S Equation ◽  
Benchmark Solutions

Effects of delamination on free vibration characteristics of laminated stiffened cylindrical shells with pretwist are analyzed by finite element method. The investigation is carried out using an eight-noded quadratic isoparametric shell element, which incorporates the transverse shear deformation and rotary inertia along with a three-noded beam element for the stiffener. The multipoint constraint algorithm has been included to guarantee the compatibility of deformation, equilibrium of resultant forces, and moments at delamination crack tip. The general dynamic equilibrium equation is derived from Lagrange’s equation of motion for moderate rotational speeds for which the Coriolis effect is neglected. The standard eigenvalue problem is solved utilizing QR iteration algorithm. The accuracy of the present formulation is validated with benchmark solutions is available in the literature. The present work concerns about the effects of delamination, fiber orientation, twist angle, stiffener depth-to-shell thickness ratio, and rotational speed on the fundamental frequency of shallow cylindrical shells with stiffener. Representative mode shapes for some typical case of the stiffened shell for different twist angles and rotational speeds are also presented.

The Lift on Wings at Sonic Speeds by Means of an Electrical Resistance Analogue

1956 ◽  
Vol 60 (542) ◽  
pp. 137-139
Author(s):  
P. J. Palmer
Keyword(s):  
Aspect Ratio ◽  
Electrical Resistance ◽  
Close Agreement ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Sonic Velocity ◽  
Dimensional Problem ◽  
Low Aspect Ratio ◽  
Small Incidence ◽  
Low Aspect Ratio Wings

This note shows how a pure resistance analogue can be used to find the lift on low aspect ratio wings travelling, with small incidence, at speeds close to the sonic velocity.The method is applicable to flat, twisted or cambered wings and is simple in operation; the results obtained being in close agreement with those obtained by calculations based on the same theory.The solutions given in this note are essentially those corresponding to the Jones theory, which is applicable to low aspect ratio wings at small incidence, travelling with velocity close to the sonic value. Under these conditions it has been shown that the three-dimensional problem reduces to a series of two-dimensional problems in planes perpendicular to the direction of motion. Thus the wing can be considered as a series of spanwise sections, the solution for each section, in terms of the velocity potential, being considered in turn.

AXISYMMETRIC VIBRATION OF POLAR ORTHOTROPIC CIRCULAR PLATES OF QUADRATICALLY VARYING THICKNESS RESTING ON ELASTIC FOUNDATION

2005 ◽  
Vol 05 (03) ◽  
pp. 387-408 ◽  
Author(s):  
N. BHARDWAJ ◽  
A. P. GUPTA
Keyword(s):  
Elastic Foundation ◽  
Ritz Method ◽  
Three Dimensional ◽  
Normal Modes ◽  
Mode Shapes ◽  
Axisymmetric Vibration ◽  
Circular Plates ◽  
Varying Thickness ◽  
Edge Conditions ◽  
Polar Orthotropic

This paper is concerned with the axisymmetric vibration problem of polar orthotropic circular plates of quadratically varying thickness and resting on an elastic foundation. The problem is solved by using the Rayleigh–Ritz method with boundary characteristic orthonormal polynomials for approximating the deflection function. Numerical results are computed for frequencies, nodal radii and mode shapes. Three-dimensional graphs are also plotted for the first four normal modes of axisymmetric vibration of plates with free, simply-supported and clamped edge conditions for various values of taper, orthotropy and foundation parameters.

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