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.

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.

scholarly journals Column Stiffness Requirements for Diagonally Stiffened Steel Plate Shear Walls

2020 ◽  
Vol 9 (5) ◽  
pp. 101-109
Keyword(s):  
Aspect Ratio ◽  
Steel Plate ◽  
Numerical Models ◽  
Shear Walls ◽  
Shear Capacity ◽  
Thickness Ratio ◽  
Steel Plate Shear Wall ◽  
Out Of Plane ◽  
The Impact ◽  
Stiffened Steel

Various numerical models of diagonally stiffened steel plate shear wall were tested under push-over loads to study the required stiffness of columns of diagonally stiffened SPSWs. This research presents a parametric study to explore the influence of varying the infill panel’s thickness, width, and height and the number of floors on the stiffness of the edge columns, and to propose expressions to predict the column’s in-plane stiffness and area required for preliminary design. Different SPSWs were modeled with a range of several stories, an aspect ratio, and height to thickness ratio, respectively, of (n=3-7), (Lp /hp=1-2), and (λ=200-400). The results indicated that the number of floors (n) has a great effect on the wall’s shear capacity. A greater number of floors lead to buckling in columns and early failure of the system, and subsequently, an increase in the column’s rigidity is required. Moreover, an equation is proposed to calculate the value of ωh required for sufficient inertia of the column. Higher the drift is, lower the shear capacity of the wall is, particularly for walls with a larger aspect ratio (Lp /hp > 1.5), and smaller height to thickness ratio (λ < 400). It is proposed that the columns’ out-of-plane stiffness divided by its in-plane stiffness to be equal or greater than 0.4. An equation is also proposed to predict the required columns’ rx substantial to assure that the columns can resist the impact of the tension field and the plate achieves full yield strength.

scholarly journals Out-of-Plane Vibration of Curved Uniform and Tapered Beams with Additional Mass

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Hamdi Alper Özyiğit ◽  
Mehmet Yetmez ◽  
Utku Uzun
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Variable Cross ◽  
Additional Mass ◽  
Inertia Effects ◽  
Tapered Beam ◽  
Out Of Plane ◽  
Good Agreement

As there is a gap in literature about out-of-plane vibrations of curved and variable cross-sectioned beams, the aim of this study is to analyze the free out-of-plane vibrations of curved beams which are symmetrically and nonsymmetrically tapered. Out-of-plane free vibration of curved uniform and tapered beams with additional mass is also investigated. Finite element method is used for all analyses. Curvature type is assumed to be circular. For the different boundary conditions, natural frequencies of both symmetrical and unsymmetrical tapered beams are given together with that of uniform tapered beam. Bending, torsional, and rotary inertia effects are considered with respect to no-shear effect. Variations of natural frequencies with additional mass and the mass location are examined. Results are given in tabular form. It is concluded that (i) for the uniform tapered beam there is a good agreement between the results of this study and that of literature and (ii) for the symmetrical curved tapered beam there is also a good agreement between the results of this study and that of a finite element model by using MSC.Marc. Results of out-of-plane free vibration of symmetrically tapered beams for specified boundary conditions are addressed.

scholarly journals Impact of Pretreatment of the Bulk Starting Material on the Efficiency of Liquid Phase Exfoliation of WS2

Nanomaterials ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 1072
Author(s):  
Steffen Ott ◽  
Melanie Lakmann ◽  
Claudia Backes
Keyword(s):  
Liquid Phase ◽  
Quantum Yield ◽  
Aspect Ratio ◽  
Optical Quality ◽  
Starting Material ◽  
Binding Strength ◽  
Photoluminescence Quantum Yield ◽  
Out Of Plane ◽  
Liquid Phase Exfoliation ◽  
Pretreatment Conditions

Liquid phase exfoliation (LPE) is widely used to produce colloidal dispersions of nanomaterials, in particular two-dimensional nanosheets. The degree of exfoliation, i.e., the length to thickness aspect ratio was shown to be intrinsically limited by the ratio of in-plane to out-of-plane binding strength. In this work, we investigate whether simple pretreatment of the starting material can be used to change the in-plane to out-of-plane binding strength through mild intercalation to improve the sample quality in sonication-assisted LPE. Five different pretreatment conditions of WS2 were tested and the dispersions size-selected through centrifugation. From optical spectroscopy (extinction, Raman, photoluminescence), information on nanosheet dimension (average lateral size, layer number, monolayer size) and optical quality (relative photoluminescence quantum yield) was extracted. We find that the pretreatment has a minor impact on the length/thickness aspect ratio, but that photoluminescence quantum yield can be increased in particular using mild sonication conditions. We attribute this to the successful exfoliation of nanosheets with a lower degree of basal plane defectiveness. This work emphasizes the complexity of the exfoliation process and suggests that the role of defects has to be considered for a comprehensive picture.

NUMERICAL AND EXPERIMENTAL STUDY ON FREE VIBRATION OF DELAMINATED WOVEN FIBER GLASS/EPOXY COMPOSITE PLATES

2012 ◽  
Vol 12 (02) ◽  
pp. 377-394 ◽  
Author(s):  
J. MOHANTY ◽  
S. K. SAHU ◽  
P. K. PARHI
Keyword(s):  
Experimental Study ◽  
Aspect Ratio ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Numerical Study ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Fiber Glass ◽  
Number Of Layers

This paper presents a combined experimental and numerical study of free vibration of industry-driven woven fiber glass/epoxy (G/E) composite plates with delamination. Using the first-order shear deformation theory, an eight-noded two-dimensional quadratic isoparametric element was developed, which has five degrees of freedom per node. In the experimental study, the influence of various parameters such as the delamination size, boundary conditions, fiber orientations, number of layers, and aspect ratio on the natural frequencies of delaminated composite plates are investigated. Comparison of the numerical results with experimental ones shows good agreement. Fundamental natural frequencies are found to decrease with the increase in the delamination size and fiber orientation and increases with the increase in the number of layers and aspect ratio of delaminated composite plates. The natural frequency of the delaminated composite plate varies significantly for different boundary conditions.

Estimation of Seismic Energy Dissipation for Steel Slit Shear Walls Considering Out-of-Plane Buckling

2021 ◽  
Author(s):  
Yiming Ma ◽  
Liusheng He ◽  
Ming Li
Keyword(s):  
Energy Dissipation ◽  
Shear Walls ◽  
Seismic Energy ◽  
Thickness Ratio ◽  
Design Parameters ◽  
Test Results ◽  
Loading Test ◽  
Aspect Ratios ◽  
Out Of Plane ◽  
Energy Dissipation Capacity

Steel slit shear walls (SSSWs), made by cutting slits in steel plates, are increasingly adopted in seismic design of buildings for energy dissipation. This paper estimates the seismic energy dissipation capacity of SSSWs considering out-of-plane buckling. In the experimental study, three SSSW specimens were designed with different width-thickness ratios and aspect ratios and tested under quasi-static cyclic loading. Test results showed that the width-thickness ratio of the links dominated the occurrence of out-of-plane buckling, which produced pinching in the hysteresis and thus reduced the energy dissipation capacity. Out-of-plane buckling occurred earlier for the links with a larger width-thickness ratio, and vice versa. Refined finite element model was built for the SSSW specimens, and validated by the test results. The concept of average pinching parameter was proposed to quantify the degree of pinching in the hysteresis. Through the parametric analysis, an equation was derived to estimate the average pinching parameter of the SSSWs with different design parameters. A new method for estimating the energy dissipation of the SSSWs considering out-of-plane buckling was proposed, by which the predicted energy dissipation agreed well with the test results.

Vibrations of an Intermediately Supported U-Bend Tube

1975 ◽  
Vol 97 (1) ◽  
pp. 23-32 ◽  
Author(s):  
L. S. S. Lee
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Experimental Tests ◽  
Bending Stiffness ◽  
Stiffness Ratio ◽  
Plane Vibration ◽  
Straight Beam ◽  
Out Of Plane ◽  
Straight Segments ◽  
Good Agreement

Vibrations of an intermediately supported U-bend tube fall into two independent classes as an incomplete ring of single span does, namely, the in-plane vibration and the coupled twist-bending out-of-plane vibration. Natural frequencies may be expressed in terms of a coefficient p which depends on the stiffness ratio k, the ratio of lengths of spans, and the supporting conditions. The effect of the torsional flexibility of a curved bar acts to release the bending stiffness of a straight beam and hence decrease the natural frequency. Some conclusions for an incomplete ring of single span may not be equally well applicable to the U-tube case due to the effects of intermediate supports and the presence of the supporting straight segments. Results of the analytical predictions and the experimental tests of an intermediately supported U-tube are in good agreement.

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.

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