
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
Figure 29: Definition of positiv ...