Shear Coefficients for Timoshenko Beam Theory

2000 ◽  
Vol 68 (1) ◽  
pp. 87-92 ◽  
Author(s):  
J. R. Hutchinson
Keyword(s):  
Cross Sections ◽  
Timoshenko Beam ◽  
Circular Cross Section ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Full Agreement ◽  
Shear Coefficient ◽  
Slender Beams ◽  
The Subject ◽  
New Formula

The Timoshenko beam theory includes the effects of shear deformation and rotary inertia on the vibrations of slender beams. The theory contains a shear coefficient which has been the subject of much previous research. In this paper a new formula for the shear coefficient is derived. For a circular cross section, the resulting shear coefficient that is derived is in full agreement with the value most authors have considered “best.” Shear coefficients for a number of different cross sections are found.

scholarly journals Natural Frequency Characteristics of the Beam with Different Cross Sections Considering the Shear Deformation Induced Rotary Inertia

2020 ◽  
Vol 10 (15) ◽  
pp. 5245
Author(s):  
Chunfeng Wan ◽  
Huachen Jiang ◽  
Liyu Xie ◽  
Caiqian Yang ◽  
Youliang Ding ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Cross Sections ◽  
Timoshenko Beam ◽  
High Frequency ◽  
Natural Frequencies ◽  
Beam Theory ◽  
Equation Of Motion ◽  
Timoshenko Beam Theory ◽  
Rotary Inertia ◽  
Cross Sectional

Based on the classical Timoshenko beam theory, the rotary inertia caused by shear deformation is further considered and then the equation of motion of the Timoshenko beam theory is modified. The dynamic characteristics of this new model, named the modified Timoshenko beam, have been discussed, and the distortion of natural frequencies of Timoshenko beam is improved, especially at high-frequency bands. The effects of different cross-sectional types on natural frequencies of the modified Timoshenko beam are studied, and corresponding simulations have been conducted. The results demonstrate that the modified Timoshenko beam can successfully be applied to all beams of three given cross sections, i.e., rectangular, rectangular hollow, and circular cross sections, subjected to different boundary conditions. The consequence verifies the validity and necessity of the modification.

On the Quest for the Best Timoshenko Shear Coefficient

2003 ◽  
Vol 70 (1) ◽  
pp. 154-157 ◽  
Author(s):  
M. B. Rubin
Keyword(s):  
Correction Factor ◽  
Timoshenko Beam ◽  
Theoretical Basis ◽  
Natural Frequencies ◽  
Beam Theory ◽  
Vibrational Frequencies ◽  
Timoshenko Beam Theory ◽  
Cosserat Theory ◽  
Shear Correction Factor ◽  
Shear Coefficient

Classical Timoshenko beam theory includes a shear correction factor κ which is often used to match natural vibrational frequencies of the beam. In this note, a number of static and dynamic examples are considered which provide a theoretical basis for specifying κ=1. Within the context of Cosserat theory, natural frequencies of the beam can be matched by appropriate specification of the director inertia coefficients with κ=1.

scholarly journals On the Accuracy of the Timoshenko Beam Theory Above the Critical Frequency: Best Shear Coefficient

2016 ◽  
Vol 32 (5) ◽  
pp. 515-518 ◽  
Author(s):  
J. A. Franco-Villafañe ◽  
R. A. Méndez-Sánchez
Keyword(s):  
Experimental Data ◽  
Timoshenko Beam ◽  
Critical Frequency ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Least Square ◽  
Shear Coefficient ◽  
Least Square Fitting

AbstractWe obtain values for the shear coefficient both below and above the critical frequency by comparing the results of the Timoshenko beam theory with experimental data published recently. The best results are obtained, by a least-square fitting, when different values of the shear coefficient are used below and above the critical frequency.

scholarly journals A new method to determine the shear coefficient of Timoshenko beam theory

2011 ◽  
Vol 330 (14) ◽  
pp. 3488-3497 ◽  
Author(s):  
K.T. Chan ◽  
K.F. Lai ◽  
N.G. Stephen ◽  
K. Young
Keyword(s):  
Timoshenko Beam ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
New Method ◽  
Shear Coefficient

Natural Frequencies of Out-of-Plane Vibration of Arcs

1982 ◽  
Vol 49 (4) ◽  
pp. 910-913 ◽  
Author(s):  
T. Irie ◽  
G. Yamada ◽  
K. Tanaka
Keyword(s):  
Boundary Conditions ◽  
Cross Section ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Circular Cross Section ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Plane Vibration ◽  
Out Of Plane

The natural frequencies of out-of-plane vibration based on the Timoshenko beam theory are calculated numerically for uniform arcs of circular cross section under all combination of boundary conditions, and the results are presented in some figures.

ANALYSIS OF AUXETIC BEAMS AS RESONANT FREQUENCY BIOSENSORS

2012 ◽  
Vol 12 (05) ◽  
pp. 1240027 ◽  
Author(s):  
TEIK-CHENG LIM
Keyword(s):  
Shear Deformation ◽  
Cross Sections ◽  
Timoshenko Beam ◽  
Poisson’S Ratio ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Poisson's Ratio ◽  
Bernoulli Beam ◽  
Bernoulli Beam Theory ◽  
Euler Bernoulli Beam

The mechanics of beam vibration is of fundamental importance in understanding the shift of resonant frequency of microcantilever and nanocantilever sensors. Unlike the simpler Euler–Bernoulli beam theory, the Timoshenko beam theory takes into consideration rotational inertia and shear deformation. For the case of microcantilevers and nanocantilevers, the minute size, and hence low mass, means that the topmost deviation from the Euler–Bernoulli beam theory to be expected is shear deformation. This paper considers the extent of shear deformation for varying Poisson's ratio of the beam material, with special emphasis on solids with negative Poisson's ratio, which are also known as auxetic materials. Here, it is shown that the Timoshenko beam theory approaches the Euler–Bernoulli beam theory if the beams are of solid cross-sections and the beam material possess high auxeticity. However, the Timoshenko beam theory is significantly different from the Euler–Bernoulli beam theory for beams in the form of thin-walled tubes regardless of the beam material's Poisson's ratio. It is herein proposed that calculations on beam vibration can be greatly simplified for highly auxetic beams with solid cross-sections due to the small shear correction term in the Timoshenko beam deflection equation.

On the Transverse Vibration of Beams of Rectangular Cross-Section

1986 ◽  
Vol 53 (1) ◽  
pp. 39-44 ◽  
Author(s):  
J. R. Hutchinson ◽  
S. D. Zillmer
Keyword(s):  
Exact Solution ◽  
Cross Section ◽  
Plane Stress ◽  
Timoshenko Beam ◽  
Transverse Vibration ◽  
Rectangular Cross Section ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Shear Coefficient ◽  
Stress Solution

An exact solution for the natural frequencies of transverse vibration of free beams with rectangular cross-section is used as a basis of comparison for the Timoshenko beam theory and a plane stress approximation which is developed herein. The comparisons clearly show the range of applicability of the approximate solutions as well as their accuracy. The choice of a best shear coefficient for use in the Timoshenko beam theory is considered by evaluation of the shear coefficient that would make the Timoshenko beam theory match the exact solution and the plane stress solution. The plane stress solution is shown to provide excellent accuracy within its range of applicability.

Exact Dynamic Analysis of Space Structures Using Timoshenko Beam Theory

AIAA Journal ◽  
2004 ◽  
Vol 42 (4) ◽  
pp. 833-839 ◽  
Author(s):  
Jen-Fang Yu ◽  
Hsin-Chung Lien ◽  
B. P. Wang
Keyword(s):  
Dynamic Analysis ◽  
Timoshenko Beam ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Space Structures

Optimal design of high-g MEMS piezoresistive accelerometer based on Timoshenko beam theory

2017 ◽  
Vol 24 (2) ◽  
pp. 855-867 ◽  
Author(s):  
Feng Liu ◽  
Shiqiao Gao ◽  
Shaohua Niu ◽  
Yan Zhang ◽  
Yanwei Guan ◽  
...  
Keyword(s):  
Optimal Design ◽  
Timoshenko Beam ◽  
Beam Theory ◽  
Timoshenko Beam Theory
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