7/24/2019 Impuls 2

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80 DYNAMICS OF STRUCTURES

FIGURE 5-6

Displacement-response spectra (shock spectra) for three types of impulse.

Rectangular

TriangularHalf sine wave

2.4

2.0

1.6

1.2

0.8

0.4

0

Maximumresponseratio

Rmax

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Ratiot1

T=

Impulse duration

Period

t1T for various forms of impulsive loading. Such plots, shown in Fig. 5-6 for the

three forms of loading treated above, are commonly known as displacement-response

spectra, or merely as response spectra. Generally plots like these can be used to

predict with adequate accuracy the maximum effect to be expected from a given type

of impulsive loading acting on a simple structure.

These response spectra also serve to indicate the response of the structure to

an acceleration pulse applied to its base. If the applied base acceleration is vg(t),

it produces an effective impulsive loading peff=m vg(t) [see Eq. (2-17)]. If the

maximum base acceleration is denoted byvg0, the maximum effective impulsive load

isp0,max= m vg0. The maximum response ratio can now be expressed as

Rmax=

vmax

mvg0k

(5-16)

in which only the absolute magnitude is generally of interest. Alternatively, this

maximum response ratio can be written in the form

Rmax= vtmax

vg0

(5-17)

wherevtmaxis the maximum total acceleration of the mass. This follows from the fact

that in an undamped system, the product of the mass and the total acceleration must