Vibrations of Tapered Timoshenko Beams in Terms of Static Timoshenko Beam Functions

In this paper, the free vibrations of a wide range of tapered Timoshenko beams are investigated. The cross section of the beam varies continuously and the variation is described by a power function of the coordinate along the neutral axis of the beam. The static Timoshenko beam functions, which are the complete solutions of a tapered Timoshenko beam under a Taylor series of static load, are developed, respectively, as the basis functions of the flexural displacement and the angle of rotation due to bending. The Rayleigh-Ritz method is applied to derive the eigenfrequency equation of the tapered Timoshenko beam. Unlike conventional basis functions which are independent of the cross-sectional variation of the beam, these static Timoshenko beam functions vary in accordance with the cross-sectional variation of the beam so that higher accuracy and more rapid convergence have been obtained. Some numerical results are presented for both truncated and sharp-ended Timoshenko beams. On the basis of convergence study and comparison with available results in the literature it is shown that the first few eigenfrequencies can be given with quite good accuracy by using a small number of terms of the static Timoshenko beam functions. Finally, some valuable results are presented systematically.

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An accurate solution method for the vibration analysis of Timoshenko beams with general elastic supports

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406214558675 ◽

2014 ◽

Vol 229 (13) ◽

pp. 2327-2340 ◽

Cited By ~ 21

Author(s):

Dongyan Shi ◽

Qingshan Wang ◽

Xianjie Shi ◽

Fuzhan Pang

Keyword(s):

Boundary Conditions ◽

Series Expansion ◽

Solution Method ◽

Free Vibrations ◽

Accurate Solution ◽

Fourier Series Expansion ◽

Timoshenko Beams ◽

End Points ◽

Solution Algorithms ◽

Wide Range

In this investigation, an accurate solution method is presented for the free vibrations of Timoshenko beams with general elastic restraints at the end points, a class of problems which are rarely attempted in the literatures. Unlike in most existing studies where solutions are often developed for a particular type of boundary conditions, the current method can be generally applied to a wide range of boundary conditions with no need of modifying solution algorithms and procedures. Under the current framework, the displacement and rotation functions are generally sought, regardless of boundary conditions, as an improved trigonometric series in which several supplementary functions introduced to remove the potential discontinuities with the displacement components and its derivatives at the end points and accelerated the series expansion. Mathematically, the current Fourier series expansion is an exact solution for a class of problems with the Timoshenko beam such that both the governing equations and the boundary conditions simultaneously satisfy any specified degree of accuracy. The effectiveness and reliability of the presented solution are demonstrated by comparing the present results with those results published in literatures and finite element method data, and numerous new results for beams with elastic boundary restraints is presented, which may serve as benchmark solution for future researches.

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High-Speed Ice Friction Experiments under Lab Conditions: On the Influence of Speed and Normal Force

ISRN Tribology ◽

10.5402/2013/703202 ◽

2013 ◽

Vol 2013 ◽

pp. 1-6 ◽

Cited By ~ 7

Author(s):

Matthias Scherge ◽

Roman Böttcher ◽

Mike Richter ◽

Udo Gurgel

Keyword(s):

Coefficient Of Friction ◽

High Speed ◽

Aerodynamic Drag ◽

Limiting Factors ◽

Maximum Speed ◽

Cross Sectional ◽

Sliding Speed ◽

Ice Friction ◽

Wide Range ◽

The Cross

Using a high-speed tribometer, coefficients of friction for bobsled runners were measured over a wide range of loads and speeds. Between 2.8 m/s and 28 m/s (equal to 10 km/h and 100 km/h), the measured coefficients of friction showed a linear decrease with increasing speed. The experiments revealed ultra-low friction coefficients of less than 0.01 after exceeding a sliding speed of about 20 m/s. At maximum speed of 28 m/s, the average coefficient of friction was 0.007. The experiments help to bridge the gap between numerous low-speed friction tests by other groups and tests performed with bobsleds on real tracks. It was shown that the friction data obtained by other groups and our measurements can be approximated by a single master curve. This curve exhibits the largest decrease in friction up to a sliding speed of about 3 m/s. The further increase in speed generates only a small decrease in friction. In addition, friction decreases with increasing load. The decrease stops when ice wear becomes effective. The load point of constant friction depends on the cross-sectional radius of the runner. The larger the radius is, the higher the load is, before the ice shows signs of fracture. It turned out that besides aerodynamic drag (not considered in this work), ice friction is one of the main speed-limiting factors. In terms of runner geometry, a flat contact of runner and ice ensures the lowest friction. The rocker radius of the runner is of greater importance for a low coefficient of friction than the cross-sectional radius.

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Exact Characteristic Equations in Closed-Form for Vibration of Completely Free Timoshenko Beams

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455415500789 ◽

2016 ◽

Vol 16 (10) ◽

pp. 1550078 ◽

Cited By ~ 3

Author(s):

Jae-Hoon Kang

Keyword(s):

Exact Solution ◽

Closed Form ◽

Timoshenko Beam ◽

Ritz Method ◽

Timoshenko Beams ◽

Characteristic Equations ◽

Shear Modes ◽

Bending Modes ◽

The One ◽

Thickness Shear

Huang 1 presented first in 1961 the characteristic equations and normal mode equations for all six common types of simple, finite Timoshenko beams in closed-form. Unfortunately, there exist several errors, not typographical, in the frequency in the characteristic equations for a Timoshenko beam free at both ends. In this paper, the exact characteristic equations in closed-form for completely free Timoshenko beams are derived based on Ref. 1. In order to justify the solutions obtained by amending herein Huang’s equations, both the closed-form exact solution and the one obtained by the Ritz method will be adopted as the references. Using the characteristic equations derived by Huang 1 , we can obtain only frequencies for the flexural modes, while using the closed-form exact method and Ritz method, we can obtain frequencies for the thickness-shear modes, as well as for the bending modes. The purpose of the present study is to identify the errors in Ref. 1, correct them, and provide some numerical results.

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Determination the Modes Characteristics in the Complex Cross-Section Waveguides

International Journal of Circuits, Systems and Signal Processing ◽

10.46300/9106.2020.14.138 ◽

2021 ◽

Vol 14 ◽

pp. 1103-1106

Author(s):

Mohammed Yousef AL-Gawagzeh

Keyword(s):

Optical Fiber ◽

Cross Section ◽

Wavelength Range ◽

Arbitrary Number ◽

Bessel Functions ◽

Ritz Method ◽

Single Mode ◽

Cross Sectional ◽

The Cross ◽

Sectional Shape

In this research the Expressions that determine the eigenfunctions and modes eigenvalues in waveguides with a composite sectorial cross-section are obtained. The possibility of characteristics changing for eigenvalues by changing the parameters that characterizing the cross-sectional shape was studied. The field modes of waveguide based on Ritz method was analyzed.it was determined the characteristics of the quasi – H_mn modes in a cruciform sector waveguide, and quasi – H_mn modes in a composite sector waveguide with an arbitrary number of sectors.it was also shown the advantage of using the cross-section waveguide in single mode optical fiber wavelength range. The eigenvalues (χ) and the normalized coefficients (a )for quasi – H_mn modes in terms of Bessel functions (Q_m,P_m ) and their combinations was obtained.

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Structural innovation in state variables and expected stock returns

Managerial Finance ◽

10.1108/mf-02-2020-0076 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Prodosh E. Simlai

Keyword(s):

Risk Factors ◽

Stock Returns ◽

Systematic Risk ◽

Expected Returns ◽

State Variables ◽

Cross Sectional ◽

Content Type ◽

Wide Range ◽

The Cross ◽

Structural Innovation

PurposeThe purpose of this study is to investigate whether the surprise components of systematic risk, which are useful in forecasting future investment opportunities, help explain the cross-section of average returns associated with portfolios sorted on size, book-to-market and accruals. This study also aims to examine the mispricing attributes of the size, value and accrual effects by investigating the relative economic relevance of aggregate risk factors, which are related to exogenous shocks in state variables, in the cross-sectional returns of triple-sorted portfolios.Design/methodology/approachThis study uses innovations of systematic risk, which affect the cash flows and risk-adjusted discount rates of all firms in an economy and determines the expected returns of portfolios based on firm characteristics. This study uses independent sorts based on size, book-to-market and total accruals – all of which are measured at the firm level – and construct three-dimensional test portfolios. For unobserved innovations, this study estimates a triangular structural vector autoregressive system and obtain the exogenous innovations in state variables. The author uses Fama-MacBeth two-pass cross-sectional regressions and examines whether the structural innovations explain a significant part of the cross-sectional variation in the average returns of the test portfolios.FindingsThis study finds that variations in expected returns of testing assets are determined by differences in the underlying assets’ exposure to systematic risk innovation. The empirical evidence also shows that exogenous innovation in Fama-French (FF) risk factors leaves out important cross-sectional information about expected returns, and additionally, the FF-factor betas have lower cross-sectional power than the proxy for innovation betas. The cross-sectional differences in the test portfolios’ sensitivity to instruments such as the short-term Treasury bill rate and term spread survive the presence of FF-factor betas.Originality/valueIn contrast to the existing literature, this study uses structural innovations that are uncorrelated and thus exogenous in nature. The author creates test portfolios that display a wide range of average returns and are unlikely to show spurious variability in risk exposures. Unlike the existing research, where size, value and accrual anomalies have been analyzed in isolation, this study examine these pricing patterns jointly, focusing on the possible contributing role of structural innovation in economy-wide predictor variables. To the best of the author’s knowledge, this paper is the first attempt to link the sensitivity of portfolios sorted on size, book-to-market and accruals to exogenous structural innovation.

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Nonlinear In-Plane Stability of Deep Parabolic Arches Using Geometrically Exact Beam Theory

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455418500062 ◽

2018 ◽

Vol 18 (01) ◽

pp. 1850006 ◽

Cited By ~ 7

Author(s):

Aditya Sabale ◽

K. V. Nagendra Gopal

Keyword(s):

Continuation Method ◽

Constitutive Law ◽

Exponential Map ◽

Cross Sectional ◽

Concentrated Load ◽

Wide Range ◽

Geometrically Exact Beam ◽

Rod Model ◽

Post Buckling ◽

The Cross

In this paper, we investigate the in-plane stability and post-buckling response of deep parabolic arches with high slenderness ratios subjected to a concentrated load on the apex, using the finite element implementation of a geometrically exact rod model and the cylindrical version of the arc-length continuation method enabled with pivot-monitored branch-switching. The rod model used here includes geometrically exact kinematics of the cross-section, exact kinetics, and a linear elastic constitutive law; and advantageously employs quaternion parameters to treat the cross-sectional rotations and to compute the exponential map in the configurational update of rotations. The evolution of the Frenet frame along the centroidal curve is used to determine the initial curvature of the rod. Three sets of boundary conditions, i.e. fixed–fixed (FF), fixed–pinned (FP) and pinned–pinned (PP), are considered, and arches with a wide range of rise-to-span ratios are analyzed for each set. Complete post-buckling response has been derived for all cases. The results reveal that although all the PP arches and all the FF arches (with the exception of FF arches with rise-to-span ratio less than 0.3) considered in this study buckle via bifurcation, the nature of stability of the different solution branches in the post-buckling regime differs from case to case. All FP slender parabolic arches exhibit limit-point buckling, again with several markedly different post-buckling behaviors. Also, some arches in the FF and PP case are shown to exhibit a clear bistable behavior in the post-buckled state.

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On the cross-sectional shape of the cellulose crystallites in the tunicate Halocynthia papillosa

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100160388 ◽

1990 ◽

Vol 48 (3) ◽

pp. 566-567

Author(s):

J.-F. Revol ◽

Y. Van Daele ◽

F. Gaill

Keyword(s):

Contrast Imaging ◽

Animal Kingdom ◽

Bright Field ◽

Field Mode ◽

Cross Sectional ◽

Ultrathin Sections ◽

The Cross ◽

Sectional Shape ◽

Valonia Ventricosa ◽

C Nmr

The only form of cellulose which could unequivocally be ascribed to the animal kingdom is the tunicin that occurs in the tests of the tunicates. Recently, high-resolution solid-state l3C NMR revealed that tunicin belongs to the Iβ form of cellulose as opposed to the Iα form found in Valonia and bacterial celluloses. The high perfection of the tunicin crystallites led us to study its crosssectional shape and to compare it with the shape of those in Valonia ventricosa (V.v.), the goal being to relate the cross-section of cellulose crystallites with the two allomorphs Iα and Iβ.In the present work the source of tunicin was the test of the ascidian Halocvnthia papillosa (H.p.). Diffraction contrast imaging in the bright field mode was applied on ultrathin sections of the V.v. cell wall and H.p. test with cellulose crystallites perpendicular to the plane of the sections. The electron microscope, a Philips 400T, was operated at 120 kV in a low intensity beam condition.

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A New Anomaly: The Cross-Sectional Profitability of Technical Analysis

CFA Digest ◽

10.2469/dig.v44.n8.17 ◽

2014 ◽

Vol 44 (8) ◽

Author(s):

Butt Man-Kit

Keyword(s):

Technical Analysis ◽

Cross Sectional ◽

The Cross

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A Cross Sectional Survey of Chicken Astroviruses Antibody in Broiler and Sonali (Cross-Bred) Chickens in Selected Areas in Bangladesh

Macedonian Veterinary Review ◽

10.2478/macvetrev-2020-0016 ◽

2020 ◽

Vol 43 (1) ◽

pp. 75-80

Author(s):

Md Zulfekar Ali ◽

Mohammad Moktader Moula ◽

Zafar Ahmed Bhuiyan ◽

Muhammad Tariq Javed

Keyword(s):

Age Groups ◽

Winter Season ◽

Cross Sectional Survey ◽

Cross Sectional ◽

Blood Samples ◽

Elisa Kit ◽

Published Report ◽

Poultry Birds ◽

Wide Range ◽

Group B

AbstractChicken astroviruses (CAstV) are enteric viruses of poultry causing gastroenteritis, malabsorption, gout and white chick disease commonly known as runting-stunting syndrome (RSS). It can affect the wide range of poultry birds, especially chicken, turkey and duck worldwide. To our best knowledge there is no published report on presence of antibodies against CAstV in Bangladesh. Therefore, the study aimed to detect the presence of CAstV antibodies in broilers and sonali chickens (a cross-bread) in Bangladesh through a cross-sectional survey. A total of 454 blood samples from 66 flocks of broiler (n=343) and sonali chickens (n=111) of different ages were obtained during 2017 from four districts. The birds were healthy but were not vaccinated against CAstV. The samples were tested for specific antibodies against CAstV Group B by using commercially available ELISA kit. Overall, 16.74% (76/454) samples and 34.84% (23/66) flocks were positive for CAstV antibodies. The seroprevalence of CAstV was significantly (p=0.001) higher in sonali chickens (36.96%) than broiler (10.20%), while it was significantly higher (p=0.001) in birds of Bogura district (36.94%) than the other three districts. Regarding the age groups, seroprevalence was insignificantly (p=0.192) higher in sonali chicken before laying age (45%) than during laying age (27.45%). Regarding the seasons, CAstV infection was prevalent significantly (p=0.001) higher in winter season. Thus, the present study indicated the presence of CAstV in poultry in Bangladesh, so further studies are required to find out the magnitude of the problem in the country.

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