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Probabilistic Models for Dynamical Systems, 2nd Edition
book

Probabilistic Models for Dynamical Systems, 2nd Edition

by Haym Benaroya, Seon Mi Han, Mark Nagurka
May 2013
Intermediate to advanced content levelIntermediate to advanced
764 pages
6h 43m
English
CRC Press
Content preview from Probabilistic Models for Dynamical Systems, 2nd Edition
8 Continuous System Vibration
Section 8.1: Continuous Systems
8.1. A transverse beam is supported by torsional springs at both ends with each spring having stiffness
k. Find the equation of motion and corresponding boundary conditions.
Solution: The boundary conditions are obtained by drawing a free body diagram. Let us define y be
positive upward and x be coordinate along the beam defined positive to the right. Then, the slope, moment,
and shear are given by
slope = y
moment = EIy

shear = (EIy

)
,
and defined positive as shown in Figure 29. Due to positive slope y
, the torsional spring on the left end
y'
M=EIy''
Q=(EIy'')'
Figure 29: Definition of positiv ...
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Publisher Resources

ISBN: 9781439849897