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.

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.

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 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 INFLUENCE OF LASER BEAM PROFILE ON LIGHT SCATTERING BY HUMAN SKIN DURING PHOTOMETRY BY ELLIPSOIDAL REFLECTORS

2018 ◽  
Vol 9 (1) ◽  
pp. 56-65 ◽  
Author(s):  
M. A. Bezuglyi ◽  
N. V. Bezuglaya ◽  
S. Kostuk
Keyword(s):  
Monte Carlo Simulation ◽  
Adipose Tissue ◽  
Laser Beam ◽  
Human Skin ◽  
Cross Section ◽  
Beam Profile ◽  
Laser Beam Profile ◽  
Reflected Light ◽  
Section Profile ◽  
Cross Section Profile

The correct accounting of laser emitter parameters for improvement of diagnostic authenticity of methods of optical biomedical diagnostic is important problem for applied biophotonic tasks. The purpose of the current research is estimation of influence of energy distribution profile in transversal section of laser beam on light scattering by human skin layers at photometry by ellipsoidal reflectors.Biomedical photometer with ellipsoidal reflectors for investigation of biological tissue specimens in transmitted and reflected light uses laser probing radiation with infinitely thin, Gauss-type and uniform cross-section profile. Distribution of beams with denoted profiles, which consist of 20 million photons with wavelength 632.8 nm, was modeled by using of Monte-Carlo simulation in human skin layers (corneous layer, epidermis, derma and adipose tissue) of various anatomic thickness and with ellipsoidal reflectors with focal parameter equal to 16.875 mm and eccentricity of 0.66.The modeling results represent that illuminance distribution in zones of photometric imaging is significantly influenced by the laser beam cross-section profile for various thickness of corneous layer and epidermis in transmitted and reflected light, and also derma in reflected light. Illuminance distribution for adipose tissue in reflected and transmitted light, and also derma in transmitted light, practically do not depend of laser beam profile for anatomic thicknesses, which are appropriate for human skin on various sections of body.There are represented results of modified Monte-Carlo simulation method for biomedical photometer with ellipsoidal reflectors during biometry of human skin layers. For highly scattered corneous layer and epidermis the illumination of middle and external rings of photometric images changes depending from the laser beam profile for more than 50 % in transmitted and 30 % in reflected light. For weakly scattering skin layers (derma and adipose layer) the influence of profile can be observed only for derma in reflected layer and is equal not more than 15 %. 

scholarly journals Fusion17 summary talk: windsurfing on a cross section profile

2017 ◽  
Vol 163 ◽  
pp. 00067
Author(s):  
Dieter Ackermann ◽  
Lorenzo Corradi
Keyword(s):  
Cross Section ◽  
Section Profile ◽  
Cross Section Profile ◽  
Summary Talk

Vibration Characteristics of Straight Blades of Asymmetrical Aerofoil Cross-Section

1969 ◽  
Vol 20 (2) ◽  
pp. 178-190 ◽  
Author(s):  
W. Carnegie ◽  
B. Dawson
Keyword(s):  
Analytical Solution ◽  
Cross Section ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Limited Range ◽  
First Order ◽  
Special Cases ◽  
Theoretical Results ◽  
Theoretical Procedure ◽  
Good Agreement

SummaryTheoretical and experimental natural frequencies and modal shapes up to the fifth mode of vibration are given for a straight blade of asymmetrical aerofoil cross-section. The theoretical procedure consists essentially of transforming the differential equations of motion into a set of simultaneous first-order equations and solving them by a step-by-step finite difference procedure. The natural frequency values are compared with results obtained by an analytical solution and with standard solutions for certain special cases. Good agreement is shown to exist between the theoretical results for the various methods presented. The equations of motion are dependent upon the coordinates of the axis of the centre of flexure of the beam relative to the centroidal axis. The effect of variations of the centre of flexure coordinates upon the frequencies and modal shapes is shown for a limited range of coordinate values. Comparison is made between the theoretical natural frequencies and modal shapes and corresponding results obtained by experiment.

Effect of Fiber Orientation on Vibration Characteristic of Composite Laminated Plates

2014 ◽  
Vol 670-671 ◽  
pp. 158-163 ◽  
Author(s):  
Hui Fen Peng ◽  
Cheng Wang ◽  
Peng Wang
Keyword(s):  
Fiber Orientation ◽  
Natural Frequencies ◽  
Structure Design ◽  
Laminated Plates ◽  
Mode Shapes ◽  
Vibration Characteristic ◽  
Composite Laminated Plates ◽  
Practical Engineering ◽  
Lamination Theory ◽  
Theoretical Results

To describe vibration characteristic of composite laminated plates with various fiber orientations, a composite laminated finite element, which follows classical lamination theory, was constructed. In each ply of rectangular composite laminated plates, the fiber orientation changes with respect to the horizontal coordinate. Natural frequencies and mode shapes of composite laminated plates were studied. The first six natural frequencies and mode shapes of composite laminated plates with various fiber orientations are obtained. The accuracy of this composite laminated element is verified by comparing numerical and theoretical results. The results show that the changes of fiber orientation bring a greater degree of flexibility for structure design of composite laminated plates, which can be used to adjust frequencies and mode shapes of composite laminated plates according to practical engineering need.

Support-Condition Analyses of Rotating Beams Under Distributed Imbalance Loading

2011 ◽  
Author(s):  
Kai Jokinen ◽  
Erno Keskinen ◽  
Marko Jorkama ◽  
Wolfgang Seemann
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Cross Section ◽  
Cross Sections ◽  
Natural Frequencies ◽  
Element Model ◽  
Mode Shapes ◽  
Constant Cross Section ◽  
Support Condition ◽  
Beam Elements

In roll balancing the behaviour of the roll can be studied either experimentally with trial weights or, if the roll dimensions are known, analytically by forming a model of the roll to solve response to imbalance. Essential focus in roll balancing is to find the correct amount and placing for the balancing mass or masses. If this selection is done analytically the roll model used in calculations has significant effect to the balancing result. In this paper three different analytic methods are compared. In first method the mode shapes of the roll are defined piece wisely. The roll is divided in to five parts having different cross sections, two shafts, two roll ends and a shell tube of the roll. Two boundary conditions are found for both supports of the roll and four combining equations are written to the interfaces of different roll parts. Totally 20 equations are established to solve the natural frequencies and to form the mode shapes of the non-uniform roll. In second model the flexibility of shafts and the stiffness of the roll ends are added to the support stiffness as serial springs and the roll is modelled as a one flexibly supported beam having constant cross section. Finally the responses to imbalance of previous models are compared to finite element model using beam elements. Benefits and limitations of each three model are then discussed.

On the Cross-Section Structure of the Mitochondrial Cristae-Membrane as Revealed by X-Ray Diffraction

1976 ◽  
Vol 31 (9-10) ◽  
pp. 612-621 ◽  
Author(s):  
W Müller-Klieser ◽  
W Kreutz
Keyword(s):  
Cross Section ◽  
Function Evaluation ◽  
X Ray Diffraction ◽  
X Ray ◽  
Section Profile ◽  
The Cross ◽  
Diffraction Patterns ◽  
Cross Section Profile ◽  
Section Structure ◽  
Q Function

Abstract Mitochondria were isolated using sorbitol and high buffer concentration in the medium. X-ray diffraction patterns arising from the mitochondrial cristae-membrane were recorded in the fully dried state and in two different states in humidity. The Q-function evaluation of these X-ray dif­fraction diagrams resulted in electron density cross-section profiles, which consist of two main peaks of opposite sign and one, respectively two, smaller peaks. The total thickness of the membrane amounts to 120 Å in the dry and 140 Å to 160 Å in the wet state.An interpretation of the cross-section profile is tentatively proposed.

Optimization of cold formed steel cross section profile for timber upgrading

2012 ◽  
Author(s):  
C. González-Bravo ◽  
J. Claver ◽  
R. Alvarez ◽  
R. Domingo
Keyword(s):  
Cross Section ◽  
Section Profile ◽  
Cold Formed Steel ◽  
Cross Section Profile
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