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9 Forced Vibration of Continuous Systems
9.5 An earth dam 50 m high has on average a width of 90 m. For earth, G =
9 × 10
6 N/m
2 and density 2000 kg/m
3 . The dam is to be treated as a cantilever
shear beam having uniform width of 90 m (μ = 0.833).
Calculate the maximum deflection at the top, if the base is excited by a force
shown in the figure.
Prob. 9.5
9.6 A cantilever beam under the action of a forceP applied at the free end deflects
the end by 30 mm. What will be the amplitude of forced vibration produced
by a pulsating force P sin ω t applied at the free end, if the frequency ω is
equal to half the fundamental frequency of the beam?
9.7 A Simply Supported Beam is Subjected to Pulsating Loads as Shown in the
figure. Find the Amplitude of Forced Vibration at the Middle, if the Frequency
ω is Equal to Half the Fundamental Frequency of the Beam.
Prob. 9.7
Prob. 9.8
9.8 Find the forced vibrations produced in the beam of figure by a distributed
load
p = p o sin
π x
L
sin ωt
9 Forced Vibration of Continuous Systems
9.5 An earth dam 50 m high has on average a width of 90 m. For earth, G =
9 × 10
6 N/m
2 and density 2000 kg/m
3 . The dam is to be treated as a cantilever
shear beam having uniform width of 90 m (μ = 0.833).
Calculate the maximum deflection at the top, if the base is excited by a force
shown in the figure.
Prob. 9.5
9.6 A cantilever beam under the action of a forceP applied at the free end deflects
the end by 30 mm. What will be the amplitude of forced vibration produced
by a pulsating force P sin ω t applied at the free end, if the frequency ω is
equal to half the fundamental frequency of the beam?
9.7 A Simply Supported Beam is Subjected to Pulsating Loads as Shown in the
figure. Find the Amplitude of Forced Vibration at the Middle, if the Frequency
ω is Equal to Half the Fundamental Frequency of the Beam.
Prob. 9.7
Prob. 9.8
9.8 Find the forced vibrations produced in the beam of figure by a distributed
load
p = p o sin
π x
L
sin ωt