Stagger Angle Dependence of Inertial and Elastic Coupling in Bladed Disks

1984 ◽  
Vol 106 (2) ◽  
pp. 181-188 ◽  
Author(s):  
E. F. Crawley ◽  
D. R. Mokadam
Keyword(s):  
Strong Dependence ◽  
Analysis Data ◽  
Body Motion ◽  
Analytical Models ◽  
Mode Shapes ◽  
Elastic Coupling ◽  
Flexible Shaft ◽  
Mass Ratios ◽  
Out Of Plane ◽  
Stagger Angle

The natural frequencies and mode shapes of nonrotating blade-disk-shaft systems have been experimentally and analytically investigated. Two mechanisms of blade motion coupling by the disk and shaft were investigated: inertial coupling by the rigid body motion of the disk on a flexible shaft; and out-of-plane elastic coupling due to disk flexure. A Ritz analysis was carried out which identifies the non-dimensional frequency and mass ratios which govern the blade-disk-shaft coupling. The mass ratios depend directly on the effective blade stagger angle. Estimates of these parameters were made for three typical rotors. Two experiments were performed which model these typical rotors. A single set of well-tuned flat blades was mounted on two different disks, one flexible and one rigid, which were in turn mounted on a flexible shaft. The blade-disk attachments were designed to allow for variations in the blade stagger angles. Experimental results show excellent agreement with simple analytical models derived by Ritz analysis. Data are reported in terms of nondimensional parameters. The results clearly show the strong dependence of the system coupling on the blade stagger angle and the blade-disk frequency and mass ratios.

The Influences of Stagger and Pretwist Angles of Blades on Coupling Vibration in Shaft-Disk-Blade Systems

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Hassan Heydari ◽  
Amir Khorram ◽  
Laya Afzalipour
Keyword(s):  
Aspect Ratio ◽  
Natural Frequencies ◽  
Thickness Ratio ◽  
Lagrangian Approach ◽  
Coupling Vibration ◽  
Flexible Shaft ◽  
Blade Thickness ◽  
Out Of Plane ◽  
Coupling Pattern ◽  
Stagger Angle

Abstract The influences of stagger angle (α) and pretwist angle (βL) of blades on the coupling vibration among shaft bending and blade bending in a shaft-disk-blade (SDB) system are investigated using a Lagrangian approach in combination with the assumed modes method (AMM). The disk is rigid, and the flexible shaft is supported with two rigid bearings. It is shown that α and βL have variable effects on the coupling vibration because their influences can be increased, reduced, or even completely eliminated for different values of disk location (λ), blade thickness ratio (δ), and blade aspect ratio (γ). To study the coupling vibration in an SDB system, consideration of λ, δ, and γ are very important because those can alter the coupling magnitude, the coupling pattern as well as the predominant modes. Nevertheless, previous researches rarely take into account these parameters. Moreover, in the present work, to investigate the natural frequencies and critical speeds versus λ, δ, and γ, new diagrams are introduced. Also, the relation between the in-plane and out-of-plane motions of the blades with the coupling vibration is precisely analyzed.

Influence of Geometric Imperfections on Vibrational Frequencies of Thin Rings

1975 ◽  
Vol 97 (4) ◽  
pp. 1199-1203
Author(s):  
Joseph R. Gartner ◽  
Shrikant T. Bhat
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Rectangular Cross Section ◽  
Circular Ring ◽  
Body Motion ◽  
Mode Shapes ◽  
Geometric Imperfections ◽  
Modal Coupling ◽  
Truncated Fourier Series ◽  
Energy Formulation

A relatively thin—thickness to radius ratio—circular ring with rectangular cross section has been investigated to numerically evaluate the effect of eccentricity on the in plane bending natural frequencies and mode shapes. The assumed boundary conditions correspond to a ring freely supported in space such that it is free to translate and rotate with rigid body motion. A truncated Fourier series solution is assumed in an energy formulation to obtain numerical approximations of the eigenvalues and the corresponding eigenvectors for different eccentricities. Extensional and inextensional models for both Flu¨gge and Love-Timoshenko ring models were considered with two thickness to radius ratios. Results show different rates of decrease in the magnitudes of the natural frequencies for different mode configurations. Existence of closely spaced frequencies along with modal coupling are noticeable at 50 percent eccentricity.

scholarly journals Substitution Rates Under Stabilizing Selection

Genetics ◽  
1987 ◽  
Vol 116 (3) ◽  
pp. 479-486
Author(s):  
Alan Hastings
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Quantitative Traits ◽  
Strong Dependence ◽  
Phenotypic Selection ◽  
Analytical Models ◽  
Stabilizing Selection ◽  
Substitution Rates ◽  
Quantitative Characters ◽  
Selection For

ABSTRACT Allelic substitutions under stabilizing phenotypic selection on quantitative traits are studied in Monte Carlo simulations of 8 and 16 loci. The results are compared and contrasted to analytical models based on work of M. Kimura for two and "infinite" loci. Selection strengths of S = 4Nes approximately four (which correspond to reasonable strengths of selection for quantitative characters) can retard substitution rates tenfold relative to rates under neutrality. An important finding is a strong dependence of per locus substitution rates on the number of loci.

scholarly journals Applications of the Advanced Radiative Transfer Modeling System (ARMS) to Characterize the Performance of Fengyun–4A/AGRI

2021 ◽  
Vol 13 (16) ◽  
pp. 3120
Author(s):  
Fei Tang ◽  
Xiaoyong Zhuge ◽  
Mingjian Zeng ◽  
Xin Li ◽  
Peiming Dong ◽  
...  
Keyword(s):  
Radiative Transfer ◽  
Strong Dependence ◽  
Final Analysis ◽  
Analysis Data ◽  
Water Vapor Absorption ◽  
Absorption Bands ◽  
Geostationary Meteorological Satellite ◽  
Environmental Prediction ◽  
Radiative Transfer Modeling ◽  
Ir Bands

This study applies the Advanced Radiative Transfer Modeling System (ARMS), which was developed to accelerate the uses of Fengyun satellite data in weather, climate, and environmental applications in China, to characterize the biases of seven infrared (IR) bands of the Advanced Geosynchronous Radiation Imager (AGRI) onboard the Chinese geostationary meteorological satellite, Fengyun–4A. The AGRI data are quality controlled to eliminate the observations affected by clouds and contaminated by stray lights during the mid–night from 1600 to 1800 UTC during spring and autumn. The mean biases, computed from AGRI IR observations and ARMS simulations from the National Center for Environmental Prediction (NCEP) Final analysis data (FNL) as input, are within −0.7–1.1 K (0.12–0.75 K) for all seven IR bands over the oceans (land) under clear–sky conditions. The biases show seasonal variation in spatial distributions at bands 11–13, as well as a strong dependence on scene temperatures at bands 8–14 and on satellite zenith angles at absorption bands 9, 10, and 14. The discrepancies between biases estimated using FNL and the European Center for Medium–Range Weather Forecasts Reanalysis–5 (ERA5) are also discussed. The biases from water vapor absorption bands 9 and 10, estimated using ERA5 over ocean, are smaller than those from FNL. Such discrepancies arise from the fact that the FNL data are colder (wetter) than the ERA5 in the middle troposphere (upper–troposphere).

In-Plane Vibration Modes of Arbitrarily Thick Disks

1997 ◽  
Author(s):  
Kevin I. Tzou ◽  
Jonathan A. Wickert ◽  
Adnan Akay
Keyword(s):  
Natural Frequencies ◽  
Arbitrary Dimension ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Three Dimensional Model ◽  
Bending Vibration ◽  
Annular Disk ◽  
Out Of Plane ◽  
Plane Bending

Abstract The three-dimensional vibration of an arbitrarily thick annular disk is investigated for two classes of boundary conditions: all surfaces traction-free, and all free except for the clamped inner radius. These two models represent limiting cases of such common engineering components as automotive and aircraft disk brakes, for which existing models focus on out-of-plane bending vibration. For a disk of significant thickness, vibration modes in which motion occurs within the disk’s equilibrium plane can play a substantial role in setting its dynamic response. Laboratory experiments demonstrate that in-plane modes exist at frequencies comparable to those of out-of-plane bending even for thickness-to-diameter ratios as small as 10−1. The equations for three-dimensional motion are discretized through the Ritz technique, yielding natural frequencies and mode shapes for coupled axial, radial, and circumferential deformations. This treatment is applicable to “disks” of arbitrary dimension, and encompasses classical models for plates, bars, cylinders, rings, and shells. The solutions so obtained converge in the limiting cases to the values expected from the classical theories, and to ones that account for shear deformation and rotary inertia. The three-dimensional model demonstrates that for geometries within the technologically-important range, the natural frequencies of certain in- and out-of-plane modes can be close to one another, or even identically repeated.

Updating of Non-Conservative Systems Using Inverse Methods

1997 ◽  
Author(s):  
Ladislav Starek ◽  
Milos Musil ◽  
Daniel J. Inman
Keyword(s):  
Analytical Model ◽  
Degrees Of Freedom ◽  
Ad Hoc ◽  
Natural Frequencies ◽  
Eigenvalue Problems ◽  
Model Updating ◽  
Analytical Models ◽  
Mode Shapes ◽  
Element Analysis ◽  
Modal Data

Abstract Several incompatibilities exist between analytical models and experimentally obtained data for many systems. In particular finite element analysis (FEA) modeling often produces analytical modal data that does not agree with measured modal data from experimental modal analysis (EMA). These two methods account for the majority of activity in vibration modeling used in industry. The existence of these discrepancies has spanned the discipline of model updating as summarized in the review articles by Inman (1990), Imregun (1991), and Friswell (1995). In this situation the analytical model is characterized by a large number of degrees of freedom (and hence modes), ad hoc damping mechanisms and real eigenvectors (mode shapes). The FEM model produces a mass, damping and stiffness matrix which is numerically solved for modal data consisting of natural frequencies, mode shapes and damping ratios. Common practice is to compare this analytically generated modal data with natural frequencies, mode shapes and damping ratios obtained from EMA. The EMA data is characterized by a small number of modes, incomplete and complex mode shapes and non proportional damping. It is very common in practice for this experimentally obtained modal data to be in minor disagreement with the analytically derived modal data. The point of view taken is that the analytical model is in error and must be refined or corrected based on experimented data. The approach proposed here is to use the results of inverse eigenvalue problems to develop methods for model updating for damped systems. The inverse problem has been addressed by Lancaster and Maroulas (1987), Starek and Inman (1992,1993,1994,1997) and is summarized for undamped systems in the text by Gladwell (1986). There are many sophisticated model updating methods available. The purpose of this paper is to introduce using inverse eigenvalues calculated as a possible approach to solving the model updating problem. The approach is new and as such many of the practical and important issues of noise, incomplete data, etc. are not yet resolved. Hence, the method introduced here is only useful for low order lumped parameter models of the type used for machines rather than structures. In particular, it will be assumed that the entries and geometry of the lumped components is also known.

Control of Static Shape, Dynamic Oscillation, and Thermally Induced Vibration of Nozzles

2005 ◽  
Vol 128 (3) ◽  
pp. 357-363 ◽  
Author(s):  
D. W. Wang ◽  
H. S. Tzou ◽  
S. M. Arnold ◽  
H.-J. Lee
Keyword(s):  
Finite Element ◽  
Conical Shell ◽  
Shape Control ◽  
Numerical Data ◽  
Analysis Data ◽  
Mode Shapes ◽  
Thermal Excitation ◽  
Thermally Induced ◽  
Control Effectiveness ◽  
And Control

Static shape actuation and dynamic control of nozzles can improve their performance, accuracy, reliability, etc. A new curved laminated piezothermoelastic hexahedral finite element is formulated based on the layerwise constant shear angle theory and it is used for modeling and analysis of piezothermoelastic conical shell structures subjected to control voltages for static shape actuation and dynamically and thermally induced vibration controls. Free vibration characteristics of an elastic truncated conical shell nozzle with fixed-free boundary conditions are studied using the new finite element. Both frequencies and mode shapes are accurately computed and compared favorably with available experimental and other numerical data. This study is then extended to evaluate control effectiveness of the conical shell with laminated piezoelectric layers. Static shape control is achieved by an applied electric potential. Vibration sensing and control are carried out using the negative velocity control scheme. Control of thermal excitation is also investigated. Analysis data suggest that the dynamic behavior and control characteristics of conical shells are quite complicated due to the coupled membrane and bending effects participating in the responses. To improve control effectiveness, segmentation and/or shaping of sensor and actuator layers need to be further investigated.

Numerical and Experimental Assessment of the Highway Arch Viaduct

2015 ◽  
Vol 769 ◽  
pp. 252-259
Author(s):  
Jan Bencat ◽  
Maria Stehlikova ◽  
Milan Skarupa
Keyword(s):  
Dynamic Testing ◽  
Highway Bridges ◽  
Structural Condition ◽  
Traffic Load ◽  
Analytical Models ◽  
Mode Shapes ◽  
Bridge Structure ◽  
Modal Damping ◽  
Bridge Structures ◽  
And Performance

Full–scale dynamic testing of bridge structures can provide valuable information on the service behavior and performance of structures. With the growing interest in the structural condition of highway bridges, dynamic testing can be used as a tool for assessing the integrity of bridges. From the measured dynamic response, induced by instructed passing trucks, modal parameters (natural frequencies, mode shapes and modal damping values) and system parameters (stiffness, mass and damping matrices) are obtained. These identified parameters can then be used to characterize and monitor the service of the bridge structure in the future. Analytical models of the structure can also be validated using these parameters [1,2]. The paper presents a procedure for estimating the traffic load bearing capacity of the steel arch highway viaduct Bridge Structure 205 (DC1–9, 755 m) constructed on Highway D1 in Nord Slovakia (Fig. 1) over the natural hollow basin via dynamic tests of the viaduct structures.

scholarly journals Exact strip postbuckling analysis of composite plates under compression and shear

2019 ◽  
Vol 123 (1263) ◽  
pp. 658-677
Author(s):  
K. Zhao ◽  
D. Kennedy ◽  
C.A. Featherston
Keyword(s):  
Finite Element ◽  
Composite Plates ◽  
Mode Shapes ◽  
Computational Time ◽  
Shear Load ◽  
Element Analysis ◽  
Lagrangian Multipliers ◽  
Buckling Loads ◽  
Finite Strip ◽  
Out Of Plane

ABSTRACTStiffened wing and fuselage panels often have a postbuckling reserve of strength, enabling them to carry loads far in excess of their critical buckling loads. Therefore allowing for postbuckling in design can reduce their weight, hence reducing fuel consumption and environmental impact. The present paper extends the postbuckling analysis in the exact strip software VICONOPT to more accurately reflect the skewed mode shapes arising from shear load and anisotropy. Such mode shapes are represented by a series of sinusoidal responses with different half-wavelengths which are coupled together using Lagrangian multipliers to enforce the boundary conditions. In postbuckling analysis the in-plane deflections involve responses with additional half-wavelengths which are absent from the out-of-plane deflection series. Numerical results are presented and compared with finite element analysis for validation. The present analysis gives close results compared to the finite element and finite strip methods and saves computational time significantly.

Dynamic Characteristics of Tsing Ma Suspension Bridge

1996 ◽  
Vol 1541 (1) ◽  
pp. 43-50 ◽  
Author(s):  
Siu Kui Au ◽  
Neil Mickleborough ◽  
Paul N. Roschke
Keyword(s):  
Analytical Solutions ◽  
Bridge Deck ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Suspension Bridge ◽  
Mode Shapes ◽  
Out Of Plane ◽  
Quantitative Results ◽  
Suspension Cable ◽  
Bending Modes

Numerical simulation was carried out to determine the dynamic properties of the Tsing Ma Suspension Bridge. Both the structure as a whole and individual subcomponents were modeled. Classical analytical solutions for simplified models from the available literature were compared with the results obtained from a finite-element code. Quantitative results for static deflection, natural frequencies, and mode shapes were compared with analytical solutions from linear theory. Out-of-plane modes were shown to be dominant. For in-plane antisymmetric and symmetric bending modes, in which the suspension cable and bridge deck vibrate in the same direction, the natural frequency of the main span of the bridge is determined to be approximately equal to the square root of the sum of the squares of the frequencies of the cable and bridge deck.

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