Common effects of the rotary inertia and shear deformation on the out-of-plane natural frequencies of composite circular bars

2001 ◽  
Vol 32 (8) ◽  
pp. 687-695 ◽  
Author(s):  
Vebil Yıldırım
Keyword(s):  
Shear Deformation ◽  
Natural Frequencies ◽  
Rotary Inertia ◽  
Out Of Plane

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.

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.

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.

Natural frequencies of composite beams with a variable fiber volume fraction including rotary inertia and shear deformation

2009 ◽  
Vol 30 (6) ◽  
pp. 717-726 ◽  
Author(s):  
Y. Bedjilili ◽  
A. Tounsi ◽  
H. M. Berrabah ◽  
I. Mechab ◽  
E. A. Adda Bedia ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Fiber Volume Fraction ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Composite Beams ◽  
Rotary Inertia ◽  
Fiber Volume

A Parametric Study on the Free Vibration of Noncylindrical Helical Springs

1998 ◽  
Vol 65 (1) ◽  
pp. 157-163 ◽  
Author(s):  
V. Yıldırım
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Parametric Study ◽  
Natural Frequencies ◽  
Rotary Inertia ◽  
Helical Springs ◽  
Wide Range ◽  
Stiffness Method

In the work based on the stiffness method reported in this paper, considering the rotary inertia, the axial and shear deformation terms, the natural frequencies of conical, barrel and hyperboloidal-type helical springs fixed at both ends are calculated. The results are presented in dimensionless graphical forms for the six lowest natural frequencies of all types of noncylindrical helices for a wide range of vibrational parameters which influence the natural frequencies. A discussion about the effects of vibrational parameters on the natural frequencies is also presented.

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