FREE VIBRATIONS OF SHEAR DEFORMABLE CIRCULAR CURVED BEAMS RESTING ON ELASTIC FOUNDATIONS

2002 ◽  
Vol 02 (01) ◽  
pp. 77-97 ◽  
Author(s):  
BYOUNG KOO LEE ◽  
SANG JIN OH ◽  
KWANG KYOU PARK
Keyword(s):  
Shear Deformation ◽  
Natural Frequencies ◽  
Free Vibrations ◽  
Rotary Inertia ◽  
Transverse Shear Deformation ◽  
Curved Beams ◽  
System Parameters ◽  
Elastic Foundations ◽  
Out Of Plane ◽  
Shear Deformable

The governing differential equations for the out-of-plane, free vibration of circular curved beams resting on elastic foundations are derived and solved numerically. The formulation takes into consideration the effects of rotary inertia and transverse shear deformation. The lowest three natural frequencies are calculated for beams with hinged–hinged, hinged-clamped, and clamped–clamped end constraints. The effects of various system parameters as well as rotary inertia and shear deformation on the natural frequencies are investigated.

Whirling of Composite-Material Driveshafts Including Bending-Twisting Coupling and Transverse Shear Deformation

1993 ◽  
Author(s):  
Charles W. Bert ◽  
Chun-Do Kim
Keyword(s):  
Composite Material ◽  
Shear Deformation ◽  
Timoshenko Beam ◽  
Transverse Shear ◽  
Critical Speed ◽  
Numerical Results ◽  
Transverse Shear Deformation ◽  
First Order ◽  
Shear Deformable

Abstract A simplified theory for predicting the first-order critical speed of a shear deformable, composite-material driveshaft is presented. The shaft is modeled as a Bresse-Timoshenko beam generalized to include bending-twisting coupling. Numerical results are compared with those for both thin and thick walled shell theories and generalized Bernoulli-Euler theory.

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.

A Procedure for the Inclusion of Transverse Shear Deformation in a Beam Element Based on the Absolute Nodal Coordinate Formulation

2007 ◽  
Author(s):  
Aki Mikkola ◽  
Oleg Dmitrochenko ◽  
Marko Matikainen
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Absolute Nodal Coordinate Formulation ◽  
Beam Element ◽  
Transverse Shear Deformation ◽  
High Frequencies ◽  
Absolute Nodal Coordinate ◽  
Numerical Performance ◽  
The Absolute ◽  
Shear Deformable

In this study, a procedure to account for transverse shear deformation in the absolute nodal coordinate formulation is presented. In the absolute nodal coordinate formulation, shear deformation is usually defined by employing the slope vectors in the element transverse direction. This leads to the description of deformation modes that are, in practical problems, associated with high frequencies. These high frequencies, in turn, complicate the time integration procedure burdening numerical performance. In this study, the description of transverse shear deformation is accounted for in a two-dimensional beam element based on the absolute nodal coordinate formulation without the use of transverse slope vectors. In the introduced shear deformable beam element, slope vectors are replaced by vectors that describe the rotation of the beam cross-section. This procedure represents a simple enhancement that does not decrease the accuracy or numerical performance of elements based on the absolute nodal coordinate formulation. Numerical results are presented in order to demonstrate the accuracy of the introduced element in static and dynamic cases. The numerical results obtained using the introduced element agree with the results obtained using previously proposed shear deformable beam elements.

Effect of Slenderness Ratio on the Natural Frequencies of Pre-Twisted Cantilever Beams of Uniform Rectangular Cross-Section

1971 ◽  
Vol 13 (1) ◽  
pp. 51-59 ◽  
Author(s):  
B. Dawson ◽  
N. G. Ghosh ◽  
W. Carnegie
Keyword(s):  
Differential Equations ◽  
Shear Deformation ◽  
Cross Section ◽  
Natural Frequencies ◽  
Rectangular Cross Section ◽  
Slenderness Ratio ◽  
Twist Angle ◽  
Equations Of Motion ◽  
Rotary Inertia ◽  
Cantilever Beams

This paper is concerned with the vibrational characteristics of pre-twisted cantilever beams of uniform rectangular cross-section allowing for shear deformation and rotary inertia. A method of solution of the differential equations of motion allowing for shear deformation and rotary inertia is presented which is an extension of the method introduced by Dawson (1)§ for the solution of the differential equations of motion of pre-twisted beams neglecting shear and rotary inertia effects. The natural frequencies for the first five modes of vibration are obtained for beams of various breadth to depth ratios and lengths ranging from 3 to 20 in and pre-twist angle in the range 0–90°. The results are compared with those obtained by an alternative method (2), where available, and also to experimental results.

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