Response to a pulse load

Question 1

explosions

Answer 1

-fast chemical reactions that produce transient pressure waves

-detonation
*instantaneous shock wave
*impulse of 1-1000 bar
*duration of micro s to milliseconds
*-ve portion at 0.1P

-deflagration
*no wave finite time before peak load is reached
*upto 4 bar
*duration of ms-1s

Question 2

pressure waves

Answer 2

-shocked or unshocked
-fast moving compressed air thats driven by expanding gases
-deforms objects by applying a dynamic blast load

Question 3

pulse load examples

Answer 3

-explosions
-mass hit by fast moving object
*creates an acceleration and increase in mass
*treated as free vibrations after

Question 4

analysis methods

Answer 4

-elastic analysis but can only be used in blasts
-pressure impulse diagrams can be produced from simple energy balance considerations
*takes into account plasticity
*not assessed

Question 5

impulses

Answer 5

-short duration relative to the natural f

-as duration tends to zero
*P –> inf, Dirac delta function
*I = integral of P dt –>1 so the velocity just after it will be 1/m
** I is the change in momentum and the velocity before the impulse is zero
** displacement either side of the impule is zero

-motion is free and undamped after t=tau

Question 6

general loading

Answer 6

u(t) = P0.omega0/K times the integral of P(tau)/P0 . sin(omega0(t-tau)) d.tau

u(t) = P0/K . F(t) for an undamped system

Question 7

response spectra

Answer 7

3 regions of the u_max/(P0/k) - t1/T graph:
-impulsive small t1/T < 0.4
-quasi-static for large t1/T > 40
-dynamic

Impulsive asymptote:
-equate KE with strain E since the structure will be given a velocity
-small duration therefore little deformation

Quasi-static asymptote:
-equate work done by load to strain energy
-usually about 2 which is generally used when inertia isnt important

*both written in terms of u_max/(P0/k)

Question 8

modal analysis example

Answer 8

-for short duration pulses damping is ignored since peak response occurs in the first cycle

Mn = sum over i phi_in^2.mi
Kn = omega_j^2.Mn
Pn(t) = phi_n.P

-mirroring the solution for an arbitrary load in u(t)

qn(t) = P_n0/Kn . Fn(t)
*Fn(t) is the dynamic amplification factor

Question 9

displacement response

Answer 9

-given in natural coords
-max is found using the response spectra to get the max vale of the amplification factor
-upper bound by adding the mag. of each disp.
-root-sum-square can also be used to estimate