Page 50 - Dynamic Loading and Design of Structures
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Figure 2.5 DLF for constant load F(t)=F1.
any time instant to the displacement produced by static application of the load F(t)=F as
1
(2.9)
A simple substitution of eqn (2.8) in eqn (2.9) gives
(2.10)
The DLF is dimensionless and measures the amount by which the dynamic displacement in
the SDOF system exceeds its equivalent static one. Figure 2.5 plots the DLF for the suddenly
applied and maintained load case, where doubling of the response is observed at certain time
instances.
2.2.1.3 Forced vibrations for various forcing functions
(a) General solution by superposition of impulses
The general closed form solution can be obtained by synthesis of the SDOF system response
to a series of impulses. Assume that the system is at rest and then acted upon by a constant
force F with instantaneous time duration td. The mass of the oscillator will experience an
instantaneous acceleration
(2.11)
which in turn produces an instantaneous velocity
(2.12)
where I is the impulse defined as force times duration.
All dynamic loads can be considered as a sequence of impulses of varying magnitude. Thus,
force F(τat time τand for the ensuing time instant td imparts an initial velocity to the SDOF
)
oscillator of the following type:
