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.

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 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

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.

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

Flexural Vibration Band Gap in a Periodic Fluid-Conveying Pipe System Based on the Timoshenko Beam Theory

2011 ◽  
Vol 133 (1) ◽  
Author(s):  
Dianlong Yu ◽  
Jihong Wen ◽  
Honggang Zhao ◽  
Yaozong Liu ◽  
Xisen Wen
Keyword(s):  
Finite Element Method ◽  
Band Gap ◽  
Timoshenko Beam ◽  
Beam Theory ◽  
Flexural Vibration ◽  
Timoshenko Beam Theory ◽  
Flexural Wave ◽  
Vibration Band ◽  
Frequency Range ◽  
Pipe System

The flexural vibration band gap in a periodic fluid-conveying pipe system is studied based on the Timoshenko beam theory. The band structure of the flexural wave is calculated with a transfer matrix method to investigate the gap frequency range. The effects of the rotary inertia and shear deformation on the gap frequency range are considered. The frequency response of finite periodic pipe is calculated with a finite element method to validate the gap frequency ranges.

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