1) In the figure, a singledegreesystem with a tunedmass damper (TMD)is given.of freedomkawwwwWritedownthemequationsk motion of the systemby using Newton'softheMethodforfreevibrationThe parameters of thestructure are as follows:m= 1000 kgk= 120000 N/mc= 1000 Ns/mµ= 0.225The properties of TMD are found according to thefolloequations of Den Hartog:mass ratio, u =kWa.optfoet-1+u2m w d.opt8(1 + u)mka -wiLopt ma

TMD (Tuned Mass Damper) inverter can be used in civil structures. It is a mechanical device of…

Answered: 1) In the figure, a single degree of…

1) In the figure, a single degree of freedom system with a tuned mass damper (TMD) is given. ka Write down the m equations k motion of the system by using Newton's of the Method for free vibration

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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Concept explainers

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.

Question

1) In the figure, a single
degree
system with a tuned
mass damper (TMD)
is given.
of freedom
ka
wwww
Write
down
the
m
equations
k motion of the system
by using Newton's
of
the
Method
for
free
vibration
The parameters of the
structure are as follows:
m= 1000 kg
k= 120000 N/m
c= 1000 Ns/m
µ= 0.225
The properties of TMD are found according to the
follo
equations of Den Hartog:
mass ratio, u =
k
Wa.opt
foet-
1+u
2m w d.opt
8(1 + u)
m
ka -wi
Lopt ma

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