TY - JOUR
T1 - Free vibration analysis of cracked rotating multi-span Timoshenko beams using differential transform method
TT - تحلیل ارتعاشات آزاد تیرهای تیموشنکوی چند تکه دورانی و دارای ترک با استفاده از روش انتقال دیفرانسیل
JF - mdrsjrns
JO - mdrsjrns
VL - 15
IS - 10
UR - http://mme.modares.ac.ir/article-15-8670-en.html
Y1 - 2016
SP - 173
EP - 182
KW - Rotating multi-spam beam
KW - Timoshenko Beam
KW - Differential transform method
KW - Crack
KW - Natural Frequency
KW - Mode Shape
N2 - Free vibration analysis of a cracked rotating multi-span Timoshenko beam is studied in this article to determine the natural frequencies and mode shapes of this beam. First, the relationships between each two segments are obtained by considering the compatibility requirements in the frame angles and in the cracks. To determine the transformed compatibility requirements, the boundary conditions, and the vibrational equations, the so-called differential transform method (DTM) is used. Then, these equations are performed to determine the natural frequencies. The mode shapes of the beam are determined by using the inverse of differential transform method. The results have been validated against those obtained from Abaqus software for a rotating multi-span beam and the ones obtained from transfer matrix method for a non-rotating case that an appropriate agreement is observed. Finally, the effects of the angle of break, the rotational speed, and the crack location on the natural frequencies are investigated. It is shown that the natural frequencies will be increased by increasing the rotational speed. Also, it is seen that the first natural frequency will be increased by moving the crack location from the cantilever support to free support and the variations of other frequencies are dependent to the crack distance to the vibrational nodes. The validation results show the accuracy of DTM in the process of studying the free vibration of this problem.
M3
ER -