A SDOF system is characterized by a mass m = 1000 kg, a stiffness k = 157.75 kN/m and a damping ratio .3" = 5%. Determine the rst 20 sec...
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A SDOF system is characterized by a mass m = 1000 kg, a stiffness k = 157,75 kN/m and a damping ratio ξ = 5%.

Determine the first 20 sec response of this system to an imposed harmonic force p(t) = p0 sin πt, where p0 = 2000 kN, considering an initial displacement u(0) = 20 cm and an initial velocity (du/dt)t=0 = 1,5 m/sec.

How can I find the first 20 sec response of this system using the Newmark's constant average acceletarion method with the time steps Δt = 0.01 sec, 0.05 sec, 0.1 sec for this system?ques 1.png

ques 1.png

A SDOF system is characterized by a mass m = 1000 kg, a stiffness k = 157.75 kN/m and a
damping ratio .3" = 5%. Determine the first 20 sec response of this system to an imposed harmonic force p(t) = p0 sin 152‘, where p0 = 2000 kN, considering an initial displacement u(0) = 20 cm and an initial velocity (du/dt):=o = 1.5 m/sec:

Top Answer

First write the equation of motion of the system. Then... View the full answer

Newmark 2-11_1.jpg

Newmar K Constant average acceleration method
the method is based on the following equations
O
Now , the system equation of motion is
mutbut ku = P
P = Po Sinit
at time till
will, + bug + kut, =...

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