Effects of Warping and Pretwist on Torsional Vibration of Rotating Beams

1984 ◽  
Vol 51 (4) ◽  
pp. 913-920 ◽  
Author(s):  
K. R. V. Kaza ◽  
R. E. Kielb
Keyword(s):  
Aspect Ratio ◽  
Torsional Vibration ◽  
Equations Of Motion ◽  
Turbine Blades ◽  
Mode Shapes ◽  
Compressor Blades ◽  
Rotating Beams ◽  
Special Cases ◽  
Torsional Frequency ◽  
Compressor And Turbine Blades

The effect of pretwist and warping on the torsional vibration of short-aspect-ratio rotating beams is examined for application to the modeling of turbofan, turboprop, and compressor blades. The equations of motion and the associated boundary conditions by using both Wagner’s hypothesis and Washizu’s theory are derived and a few minor limitations of the Wagner’s hypothesis, as applied to thick blades, are pointed out and discussed. The equations for several special cases are solved in a closed form. Results are presented indicating the effect of warping, pretwist, and rotation on torsional vibration of beams as aspect ratio is varied. The results show that the structural warping and pretwist terms have a significant effect on torsional frequency and mode shapes of short-aspect-ratio blades whereas the inertial warping terms have negligible effect. Since the torsional frequencies and mode shapes are very important in aeroelastic analyses by using modal methods, the structural warping terms should be included in modeling turbofan, turboprop, compressor, and turbine blades.

Torsional vibration of functionally graded carbon nanotube reinforced conical shells

2018 ◽  
Vol 25 (1) ◽  
pp. 41-52 ◽  
Author(s):  
Yaser Kiani
Keyword(s):  
Torsional Vibration ◽  
Conical Shell ◽  
Volume Fraction ◽  
Differential Quadrature Method ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Coupled Equations ◽  
Parametric Studies ◽  
Torsional Frequency ◽  
Generalized Differential

AbstractThe present study deals with the free torsional vibration of a composite conical shell made of a polymeric matrix reinforced with carbon nanotubes (CNTs). Distribution of CNTs across the thickness of the conical shell may be uniform or functionally graded. Five different cases of functionally graded reinforcements are considered. First-order shear deformable shell theory compatible with the Donnell kinematic assumptions is used to establish the motion equations of the shell. These equations are two coupled equations which should be treated as an eigenvalue problem. The generalized differential quadrature method is used to obtain a numerical solution for the torsional frequency parameters and the associated mode shapes of the shell. After validating the results of this study for the cases of isotropic homogeneous cone and annular plates, parametric studies are carried out to analyze the influences of geometrical characteristics of the shell, volume fraction of CNTs, and grading profile of the CNTs. It is shown that volume fraction of CNTs is an important factor with regard to torsional frequencies of the shell; however, grading profile does not change the torsional frequencies significantly.

The Stress Problem of Vibrating Compressor Blades

1955 ◽  
Vol 22 (1) ◽  
pp. 57-64
Author(s):  
Jan R. Schnittger
Keyword(s):  
Turbine Blades ◽  
General Nature ◽  
Compressor Blades ◽  
Stress Problem ◽  
Simplified Analysis ◽  
Compressor And Turbine Blades

Abstract In order to demonstrate the general nature of the actual vibrations of compressor and turbine blades, the author undertakes a simplified analysis in which a single stiff blade, with one translational and one pitching mode, is studied. It is shown that all problems of stress in vibrating compressor blades whether they arise from forced or self-sustained vibrations may be related to the magnitude of finite mechanical or aerodynamic disturbances.

Dynamic Characteristics of Resonant Beams With Passive Thermal Stress Regulators

2018 ◽  
Author(s):  
Tyler Kellar ◽  
Pezhman Hassanpour
Keyword(s):  
Boundary Condition ◽  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Separation Of Variables ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Mode Shapes ◽  
Elastic Boundary ◽  
Special Cases ◽  
Angular Displacements

This paper addresses the dynamic characteristics of a beam with a particular elastic boundary condition. In this elastic boundary condition, the lateral and angular displacements of the beam are coupled through the elastic constraints. The dynamic characteristic, namely natural frequencies and mode shapes of vibrations are frequently encountered in the design and modeling of resonant micro-structures. The governing equations of motion of the beam is derived using Euler-Bernoulli beam theory considering the elastic coupling between the transverse and rotational displacements of the beam’s end. The characteristic equation for the natural frequencies and mode shapes of vibration is derived by applying the method of separation of variables to the governing partial differential equation of motion. The natural frequencies and mode shapes of the system are derived for various combinations of compliance values of the elastic support and are compared with those of several special cases, namely clamped-free, clamped-guided, clamped-pinned and clamped-clamped beams.

Coupled Flexural and Torsional Vibration Analysis of Composite Beams

2019 ◽  
Author(s):  
Ehsan Sarfaraz ◽  
Jeremiah O. Afolabi ◽  
Hamid R. Hamidzadeh
Keyword(s):  
Boundary Conditions ◽  
Torsional Vibration ◽  
Analytical Method ◽  
Composite Beam ◽  
Equations Of Motion ◽  
Closed Form Solution ◽  
Composite Beams ◽  
Form Solution ◽  
Mode Shapes ◽  
Loss Factors

Abstract An analytical method is presented to determine the dynamic response of a coupled flexural and torsional vibration of composite beams. The general governing equations of motion are presented and a closed form solution for free vibration of the composite beam that demonstrates both geometric and material coupling is developed. The proposed solution is used to compute the natural frequencies, modal loss factors, and mode shapes of the composite beam for several modes of the coupled bending and torsional vibrations for any boundary conditions. In this analysis, hysteretic damping for the composite beam is considered and its effects on mode shapes and modal loss factors are determined. In addition, the variation of modal parameters such as bending displacement, bending slope, torsional rotation, shear force, bending moment, and torque along the beam for the first four mode shapes are presented for the clamped-free boundary conditions. Moreover, to verify the validity of the presented analytical method, results for the cases with no damping are compared with the previously established results and good agreement is achieved. The presented results can provide a guideline for selecting appropriate geometries and materials to design composite beams.

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.

Free Vibration of a Thin-Film Inflated Torus

2003 ◽  
Author(s):  
L. Moxey ◽  
H. Hamidzadeh
Keyword(s):  
Thin Film ◽  
Material Properties ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Inner Pressure ◽  
Special Cases ◽  
The Mathematical Model ◽  
Uniform Membrane

In this paper an overview of the mathematical model for an inflated thin-film toroidal structure is provided. In particular, attention has been confined to determine the free vibrations of inflated circular toroidal members. The provided solution is based on an improved set of equations of motion for uniform membrane. From which the dependence of natural frequencies on material properties, dimension, mode of vibration, and the inner pressure can be investigated. The validity of the developed models was verified by comparing some of the computed results with those available for special cases. Numerical results for natural frequencies and mode shapes are provided for a specific thin-film inflated torus.

Free Vibrational Characteristics of Pretensioned Cable Roofs

1972 ◽  
Vol 94 (1) ◽  
pp. 31-37 ◽  
Author(s):  
G. N. Bathish
Keyword(s):  
Equilibrium Position ◽  
Equations Of Motion ◽  
Static Equilibrium ◽  
Transverse Load ◽  
Mode Shapes ◽  
Shear Rigidity ◽  
Membrane Theory ◽  
Special Cases ◽  
Vibrational Characteristics ◽  
Nonlinear Membrane

Cable roofs are analyzed using nonlinear membrane theory. The cable network is simulated by an equivalent thin elastic prestressed membrane without shear rigidity. The equations of motion for the vibrating membrane are formulated by considering the static equilibrium position of the membrane as the position of the membrane after it undergoes nonlinear deformation due to uniform transverse load over the projected area of the membrane. The equations of motion are then solved for natural frequencies and associated mode shapes by restricting the analysis to small amplitude vibrations about the static equilibrium position. Two special cases are considered: a flat rectangular membrane, and a membrane that has the shape of a hyperbolic paraboloid surface that is rectangular in plan. Comparisons between linear and nonlinear membrane theory solutions are presented.

scholarly journals Optimization Design of Lattice Structures in Internal Cooling Channel with Variable Aspect Ratio of Gas Turbine Blade

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3954
Author(s):  
Liang Xu ◽  
Qicheng Ruan ◽  
Qingyun Shen ◽  
Lei Xi ◽  
Jianmin Gao ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Aspect Ratio ◽  
Optimization Model ◽  
Lattice Structure ◽  
Turbine Blades ◽  
Internal Cooling ◽  
Cooling Channel ◽  
Cooling Channels ◽  
Mechanical Performances ◽  
Type Lattice

Traditional cooling structures in gas turbines greatly improve the high temperature resistance of turbine blades; however, few cooling structures concern both heat transfer and mechanical performances. A lattice structure (LS) can solve this issue because of its advantages of being lightweight and having high porosity and strength. Although the topology of LS is complex, it can be manufactured with metal 3D printing technology in the future. In this study, an integral optimization model concerning both heat transfer and mechanical performances was presented to design the LS cooling channel with a variable aspect ratio in gas turbine blades. Firstly, some internal cooling channels with the thin walls were built up and a simple raw of five LS cores was taken as an insert or a turbulator in these cooling channels. Secondly, relations between geometric variables (height (H), diameter (D) and inclination angle(ω)) and objectives/functions of this research, including the first-order natural frequency (freq1), equivalent elastic modulus (E), relative density (ρ¯) and Nusselt number (Nu), were established for a pyramid-type lattice structure (PLS) and Kagome-type lattice structure (KLS). Finally, the ISIGHT platform was introduced to construct the frame of the integral optimization model. Two selected optimization problems (Op-I and Op-II) were solved based on the third-order response model with an accuracy of more than 0.97, and optimization results were analyzed. The results showed that the change of Nu and freq1 had the highest overall sensitivity Op-I and Op-II, respectively, and the change of D and H had the highest single sensitivity for Nu and freq1, respectively. Compared to the initial LS, the LS of Op-I increased Nu and E by 24.1% and 29.8%, respectively, and decreased ρ¯ by 71%; the LS of Op-II increased Nu and E by 30.8% and 45.2%, respectively, and slightly increased ρ¯; the LS of both Op-I and Op-II decreased freq1 by 27.9% and 19.3%, respectively. These results suggested that the heat transfer, load bearing and lightweight performances of the LS were greatly improved by the optimization model (except for the lightweight performance for the optimal LS of Op-II, which became slightly worse), while it failed to improve vibration performance of the optimal LS.

scholarly journals Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket

2020 ◽  
Vol 25 (2) ◽  
pp. 29
Author(s):  
Desmond Adair ◽  
Aigul Nagimova ◽  
Martin Jaeger
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Algebraic Equations ◽  
Structural Vibrations ◽  
Unknown Parameters ◽  
One Dimensional ◽  
Vibration Problems ◽  
Nonuniform Beam

The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton’s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam.

Analysis of Material Coating for Damping in Beam Structures

2010 ◽  
Vol 442 ◽  
pp. 202-210
Author(s):  
S.H. Raza ◽  
M.A. Malik ◽  
W. Akram
Keyword(s):  
Turbine Blades ◽  
Beam Theory ◽  
Industrial Applications ◽  
Theory Model ◽  
Design Tool ◽  
Coating Material ◽  
Mode Shapes ◽  
Turbine Engines ◽  
Gas Turbine Engines ◽  
Finite Element Procedure

Vibratory stresses are the main cause of material failure in aerospace/mechanical structures and machine components. Failure also occurs due to these vibratory stresses in gas turbine engines and rotating machinery components while operating at resonant frequency. A magnetomechanical coating material is used as a very effective method for damping of these stresses. Vibratory stress damping in components like turbine blades through magnetomechanical coating material is well known in literature. However, the geometric correlations for the varying coated beam are not well established. We have utilized a cantilever beam as the basic geometry for this investigation to establish a correlation for varying coating. Beam theory is applied as a mathematical model for obtaining the mode shapes for the beam. A finite element procedure is performed to acquire the data and this data is then correlated with beam theory model for initial verification. This data is further evaluated to form the required model for calculating thickness of coating for a beam. The resulting parametric correlation is verified through comparison with the already published experimental data available in literature. This correlation can be used as a design tool for suppression of vibratory stresses in industrial applications.

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