Vibration Characteristics of Pre-twisted Blades of Asymmetrical Aerofoil Cross-Section

1971 ◽  
Vol 22 (3) ◽  
pp. 257-273 ◽  
Author(s):  
W. Carnegie ◽  
B. Dawson
Keyword(s):  
Natural Frequency ◽  
Cross Section ◽  
Natural Frequencies ◽  
Twist Angle ◽  
The Other ◽  
Mode Shapes ◽  
Inertia Effects ◽  
Theoretical Frequency ◽  
Frequency Ratios ◽  
Theoretical Results

SummaryThe natural frequencies and mode shapes of vibration of cantilever aerofoil cross-section blades of pre-twist angle in the range 0 to 90 degrees are obtained. The beams are 152·4 mm long and the width / thickness ratio is such that they may be regarded as slender. Theoretical frequency ratios and mode shapes of vibration, neglecting shear and rotary inertia effects, are obtained for two sets of beams, one with clockwise pre-twist relative to the root cross-section and the other with anti-clockwise pre-twist. The effect of variation in the value of the centre-of-flexure coordinates upon the natural frequency ratios and mode shapes of vibration is investigated. The theoretical results are compared to corresponding experimental results.

Theoretical and Experimental Vibration Analyses of Trapezoidal and Sinusoidal Corrugated Plates

2012 ◽  
Author(s):  
Adil Yucel ◽  
Alaeddin Arpaci
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Analysis Technique ◽  
Surface Models ◽  
Section Profile ◽  
Corrugated Plates ◽  
Cross Section Profile ◽  
Manufacturing Parameters ◽  
Theoretical Results

In this study, dynamic behaviour of trapezoidal and sinusoidal corrugated plates which are widely used in the fields of space, aviation, automotive, construction and shipbuilding have been analyzed. 330 different surface models varying according to corrugation height and number have been created for these plates which have various manufacturing parameters. At this stage, the number of analyses is 660. These models have been analyzed for different boundary conditions and modal analyses to obtain natural frequencies and mode shapes have been conducted using finite element method. In addition, changes in the trapezoidal cross-section profile have also been investigated by analyzing 38 different plates with varying cross-section profiles. Examining these results, the effects of corrugation height and number on natural frequencies and mode shapes have been determined. As a result of the study a total of 368 drawings were prepared and 736 analyses were performed. Besides, the theoretical results have been verified using the experimental modal analysis technique for some selected models which are being manufactured in the market.

Modal Analysis of Annular Plate with Crack and its Effect on Natural Frequency

2015 ◽  
Vol 813-814 ◽  
pp. 910-914 ◽  
Author(s):  
R. Pramod ◽  
M.E. Shashi Kumar ◽  
S. Mohan Kumar
Keyword(s):  
Natural Frequency ◽  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Annular Plate ◽  
Structural Member ◽  
Vibration Modes ◽  
Static And Dynamic Characteristics ◽  
Annular Plates ◽  
Theoretical Frequency ◽  
Theoretical Results

The study of the dynamic behavior of annular plates with circumferential cracks can find many applications in several machine components such as flywheels, clutch plates, compact discs etc. A crack on a structural member introduces a local increase of flexibility in that region then; this affects the static and dynamic characteristics. The effects of cracks on the dynamic characteristics of structures, especially on the natural frequencies and modes, were extensively studied. In this study, the natural frequencies of annular plates with circumferential cracks are investigated by using finite element method. The cracks were non-propagating and open. The annular plate with different cracks was subjected to different boundary conditions and final variation in the natural frequency was obtained, which was compared with the theoretical frequency and the change in the natural frequency was studied. The results of this study with improved elements are compared with the theoretical results in the literature. It is observed that the location and the number of cracks have various effects on the natural frequencies related to the vibration modes.

Modal Curves of Pre-Twisted Beams of Rectangular Cross-Section

1969 ◽  
Vol 11 (1) ◽  
pp. 1-13 ◽  
Author(s):  
B. Dawson ◽  
W. Carnegie
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Twist Angle ◽  
Ritz Method ◽  
Transformation Method ◽  
Mode Shapes ◽  
Modes Of Vibration ◽  
Vibrational Characteristics ◽  
Theoretical Results ◽  
Good Agreement

An important aspect of the theoretical study of the vibrational characteristics of turbine and compressor blading is the prediction of the modal curves from which the stresses along the length of the blading can be determined. The accurate prediction of the modal curves allowing for such factors as pre-twist, camber, size of cross-section, centrifugal tensile effects, aerodynamic effects, etc., is still not possible. However, a better understanding of the effects of some of these parameters can be obtained by a study of the modal curves of relatively simple idealized models. In this work the theoretical mode shapes of vibration of pre-twisted rectangular cross-section beams for various width to depth ratios and pre-twist angle in the range 0-90° are examined. The theoretical results are obtained by the transformation method given by Carnegie, Dawson and Thomas (1)† and the accuracy of these results is verified by comparison with results obtained by Dawson (2) using the Ritz method. The theoretical results are compared to modal curves determined experimentally and good agreement is shown between them. A physical explanation of the effects of the pre-twist angle upon the modal curves is given for the first three modes of vibration.

Multi-crack detection in general cross-section swept wings based on natural frequency changes

2020 ◽  
pp. 107754632096401
Author(s):  
Fatemeh Barzegar ◽  
Saeedreza Mohebpour ◽  
Hekmat Alighanbari
Keyword(s):  
Mathematical Model ◽  
Natural Frequency ◽  
Cross Section ◽  
Crack Detection ◽  
Natural Frequencies ◽  
Detection Method ◽  
Mode Shapes ◽  
Modal Strain Energy ◽  
Torsional Mode ◽  
Frequency Changes

In this article, a multi-crack detection method, which is based on natural frequency changes and the concept of modal strain energy, is for the first time developed for the general cross-section swept tapered wings under coupled bending-torsional vibration and applied to the solid and thin-walled airfoil cross-section wings. The presented method is able to handle the problems with an unknown number of cracks and predicts the number of existent cracks, their locations and depths by optimization of an appropriate objective function. The stress intensity factors of airfoil-shaped crack surfaces are obtained using an approximation method. Inputs of the detection method are natural frequencies of uncracked and cracked wings which are calculated by using a mathematical model and finite element method software ANSYS, respectively, and validated by comparison with former research studies. In the mathematical model, the Rayleigh–Ritz method is used to calculate the coupled bending-torsional mode shapes of the uncracked wing and their corresponding natural frequencies. Results demonstrate that the proposed method has precisely predicted the number, locations and depths of cracks in all case studies.

scholarly journals Effects of Elliptical Hole on the Correlation of Natural Frequency with Buckling Load of Basalt Laminates Composite Plates

2020 ◽  
Vol 27 (1) ◽  
pp. 216-225
Author(s):  
Buntheng Chhorn ◽  
WooYoung Jung
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Basalt Fiber ◽  
Orientation Angle ◽  
Elliptical Hole ◽  
Composite Plates ◽  
Buckling Load ◽  
Mode Shapes ◽  
Geometric Ratio

AbstractRecently, basalt fiber reinforced polymer (BFRP) is acknowledged as an outstanding material for the strengthening of existing concrete structure, especially it was being used in marine vehicles, aerospace, automotive and nuclear engineering. Most of the structures were subjected to severe dynamic loading during their service life that may induce vibration of the structures. However, free vibration studied on the basalt laminates composite plates with elliptical cut-out and correlation of natural frequency with buckling load has been very limited. Therefore, effects of the elliptical hole on the natural frequency of basalt/epoxy composite plates was performed in this study. Effects of stacking sequence (θ), elliptical hole inclination (ϕ), hole geometric ratio (a/b) and position of the elliptical hole were considered. The numerical modeling of free vibration analysis was based on the mechanical properties of BFRP obtained from the experiment. The natural frequencies as well as mode shapes of basalt laminates composite plates were numerically determined using the commercial program software (ABAQUS). Then, the determination of correlation of natural frequencies with buckling load was carried out. Results showed that elliptical hole inclination and fiber orientation angle induced the inverse proportion between natural frequency and buckling load.

Vibration of Beams with a Single Delamination under Axial Loading

2011 ◽  
Vol 675-677 ◽  
pp. 477-480
Author(s):  
Dong Wei Shu
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Analytical Solutions ◽  
Axial Load ◽  
Natural Frequencies ◽  
Axial Loading ◽  
Composite Beams ◽  
Mode Shapes ◽  
Equilibrium Conditions ◽  
Monotonic Relation

In this work analytical solutions are developed to study the free vibration of composite beams under axial loading. The beam with a single delamination is modeled as four interconnected Euler-Bernoulli beams using the delamination as their boundary. The continuity and the equilibrium conditions are satisfied between the adjoining beams. The studies show that the sizes and the locations of the delaminations significantly influence the natural frequencies and mode shapes of the beam. A monotonic relation between the natural frequency and the axial load is predicted.

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.

A Note on the Lowest Natural Frequency of a Square Plate Point-Supported at the Corners

1962 ◽  
Vol 66 (616) ◽  
pp. 240-241 ◽  
Author(s):  
C. L. Kirk
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Present Note ◽  
Flexural Vibration ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Electronic Digital Computer ◽  
Isotropic Plates ◽  
Four Corners ◽  
Square Plate

Recently Cox and Boxer determined natural frequencies and mode shapes of flexural vibration of uniform rectangular isotropic plates, that have free edges and pinpoint supports at the four corners. In their analysis, they obtain approximate solutions of the differential equation through the use of finite difference expressions and an electronic digital computer. In the present note, the frequency expression and mode shape for a square plate, vibrating at the lowest natural frequency, are determined by considerations of energy. The values obtained are compared with those given in reference.

scholarly journals Phononic Band Gap and Free Vibration Analysis of Fluid-Conveying Pipes with Periodically Varying Cross-Section

2021 ◽  
Vol 11 (21) ◽  
pp. 10485
Author(s):  
Hao Yu ◽  
Feng Liang ◽  
Yu Qian ◽  
Jun-Jie Gong ◽  
Yao Chen ◽  
...  
Keyword(s):  
Free Vibration ◽  
Band Gap ◽  
Cross Section ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Critical Parameters ◽  
Mode Shapes ◽  
Beam Model ◽  
The Impact ◽  
Fluid Conveying Pipes

Phononic crystals (PCs) are a novel class of artificial periodic structure, and their band gap (BG) attributes provide a new technical approach for vibration reduction in piping systems. In this paper, the vibration suppression performance and natural properties of fluid-conveying pipes with periodically varying cross-section are investigated. The flexural wave equation of substructure pipes is established based on the classical beam model and traveling wave property. The spectral element method (SEM) is developed for semi-analytical solutions, the accuracy of which is confirmed by comparison with the available literature and the widely used transfer matrix method (TMM). The BG distribution and frequency response of the periodic pipe are attained, and the natural frequencies and mode shapes are also obtained. The effects of some critical parameters are discussed. It is revealed that the BG of the present pipe system is fundamentally induced by the geometrical difference of the substructure cross-section, and it is also related to the substructure length and fluid–structure interaction (FSI). The number of cells does not contribute to the BG region, while it has significant effects on the amplitude attenuation, higher order natural frequencies and mode shapes. The impact of FSI is more evident for the pipes with smaller numbers of cells. Moreover, compared with the conventional TMM, the present SEM is demonstrated more effective for comprehensive analysis of BG characteristics and free vibration of PC dynamical structures.

scholarly journals Vibrational Analysis on Hemp and Okra Fibres Mixed Glass Fiber Polyester Composite

2021 ◽  
Vol 8 (11) ◽  
pp. 55-62
Author(s):  
Putti Venkata Siva Teja ◽  
Badatala Ooha ◽  
Kondeti Sravanth
Keyword(s):  
Glass Fiber ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Fiber Composite ◽  
Fem Analysis ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Machine Component ◽  
Free System ◽  
Glass Fiber Composite

In transverse vibrations the element moves to and fro in a direction perpendicular to the direction of the advance of the wave. To determine the vibration characteristics i.e., natural frequencies and mode shapes, modal analysis is a process for a structure or a machine component while is being designed. In real life, aero planes, missiles, rockets, space vehicles, satellites, sub marines etc are modeled as free-free mechanical systems. In this paper an attempt was made to compare natural frequency for two composite materials- ladies finger with Glass fiber composite and Hemp with Glass fiber composite by taking as cantilever beams. The cantilever beam which is fixed at one end is vibrated to obtain the natural frequency, mode shapes at four different modes. A simple low cost demonstration experiment is performed in this paper by using common apparatus in order to compare theoretical, numerical (FEM analysis) profiles of two free-free thin two rectangular composite beams of dimensions 305*49.5* 7 in mm. Keywords: Natural frequencies, Mode shapes, Vibration characteristics, Ladies finger fiber, Hemp fiber, Glass fiber, FEM analysis, Free-Free system.

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