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Sheet 3 Page 1
Imperial College of Science, Technology & Medicine
Department of Aeronautics
Second Year
Structural Mechanics and Dynamics
Tutorial Sheet 3
Section a – Theory Development
1. It is common practice to estimate the effect of a suddenly applied loading on a
structure by doubling the static deflections and stresses to allow for dynamic effects.
Considering the undamped single degree of freedom system
)
(
R
kr
r
m
τ
=
+
±
±
subject to the step load shown in figure 1 then use the convolution integral to find the
displacement response and the time variation of the spring force. Discuss the
relevance of the 2*static approximation.
R(
τ
)
Time
τ
R
o
Fig 1
2. An undamped single degree of freedom system has the equation of motion
ωτ
=
+
sin
R
kr
r
m
0
±
±
If the excitation frequency is the resonant frequency of the system,
m
k
2
=
ω
, then the
steady state solution gives an infinite response. Use the convolution integral to
investigate how the response increases with time and show that an infinite response is
only achieved after an infinite time.
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This note was uploaded on 03/24/2010 for the course AE A.213 taught by Professor S.pinhoandm.aliabadi during the Winter '09 term at Imperial College.
 Winter '09
 S.PinhoandM.Aliabadi

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