The single degree of freedom (SDOF) system that you studied under free vibration in Assignment #3 - Laboratory Component has been subjected to a strong ground motion. The acceleration at the base (excitation) and the acceleration at the roof (response) of the SDOF system was recorded with sampling rate 50 Hz (50 samples per second, or dt= 0.02 seconds). The file ElCentro.txt includes the two columns of acceleration data. The first column lists the acceleration at the base of the SDOF system. The second column lists the acceleration at the roof of the SDOF system. (a) Plot the time histories of the recorded accelerations at the base and at the roof of the SDOF system. (b) Compute the acceleration, velocity and displacement time histories of the roof of the SDOF system subjected to the recorded base acceleration using the Central Difference method. Plot the accel- eration, velocity and displacement time histories. Plot the restoring force, the damping force, and the inertia force time histories. Compare the recorded acceleration time history at the roof of the SDOF with the acceleration that you computed using the numerical method. (c) Compute the acceleration, velocity and displacement time histories of the roof of the SDOF system subjected to the recorded base acceleration using the Newmark method for β = 1/6 (linear acceleration). Plot the acceleration, velocity and displacement time histories. Plot the restoring force, the damping force, and the inertia force time histories. Compare the recorded acceleration time history at the roof of the SDOF with the acceleration that you computed using the numerical method. (d) Compute the acceleration, velocity and displacement time histories of the roof of the SDOF system subjected to the recorded base acceleration using the Newmark method for β = 1/4 (average acceleration). Plot the acceleration, velocity and displacement time histories. Plot the restoring force, the damping force, and the inertia force time histories. Compare the recorded acceleration time history at the roof of the SDOF with the acceleration that you computed using the numerical method
The single degree of freedom (SDOF) system that you studied under free vibration in Assignment #3 - Laboratory Component has been subjected to a strong ground motion. The acceleration at the base (excitation) and the acceleration at the roof (response) of the SDOF system was recorded with sampling rate 50 Hz (50 samples per second, or dt= 0.02 seconds). The file ElCentro.txt includes the two columns of acceleration data. The first column lists the acceleration at the base of the SDOF system. The second column lists the acceleration at the roof of the SDOF system. (a) Plot the time histories of the recorded accelerations at the base and at the roof of the SDOF system. (b) Compute the acceleration, velocity and displacement time histories of the roof of the SDOF system subjected to the recorded base acceleration using the Central Difference method. Plot the accel- eration, velocity and displacement time histories. Plot the restoring force, the damping force, and the inertia force time histories. Compare the recorded acceleration time history at the roof of the SDOF with the acceleration that you computed using the numerical method. (c) Compute the acceleration, velocity and displacement time histories of the roof of the SDOF system subjected to the recorded base acceleration using the Newmark method for β = 1/6 (linear acceleration). Plot the acceleration, velocity and displacement time histories. Plot the restoring force, the damping force, and the inertia force time histories. Compare the recorded acceleration time history at the roof of the SDOF with the acceleration that you computed using the numerical method. (d) Compute the acceleration, velocity and displacement time histories of the roof of the SDOF system subjected to the recorded base acceleration using the Newmark method for β = 1/4 (average acceleration). Plot the acceleration, velocity and displacement time histories. Plot the restoring force, the damping force, and the inertia force time histories. Compare the recorded acceleration time history at the roof of the SDOF with the acceleration that you computed using the numerical method
Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)
5th Edition
ISBN:9781305084766
Author:Saeed Moaveni
Publisher:Saeed Moaveni
Chapter18: Mathematics In Engineering
Section18.3: Nonlinear Models
Problem 1BYG
Related questions
Question
The single degree of freedom (SDOF) system that you studied under free vibration in Assignment #3
- Laboratory Component has been subjected to a strong ground motion. The acceleration at the base
(excitation) and the acceleration at the roof (response) of the SDOF system was recorded with sampling
rate 50 Hz (50 samples per second, or dt= 0.02 seconds). The file ElCentro.txt includes the two columns
of acceleration data. The first column lists the acceleration at the base of the SDOF system. The second
column lists the acceleration at the roof of the SDOF system.
(a) Plot the time histories of the recorded accelerations at the base and at the roof of the SDOF system.
(b) Compute the acceleration, velocity and displacement time histories of the roof of the SDOF system
subjected to the recorded base acceleration using the Central Difference method. Plot the accel-
eration, velocity and displacement time histories. Plot the restoring force, the damping force, and the
inertia force time histories. Compare the recorded acceleration time history at the roof of the SDOF
with the acceleration that you computed using the numerical method.
(c) Compute the acceleration, velocity and displacement time histories of the roof of the SDOF system
subjected to the recorded base acceleration using the Newmark method for β = 1/6 (linear
acceleration). Plot the acceleration, velocity and displacement time histories. Plot the restoring
force, the damping force, and the inertia force time histories. Compare the recorded acceleration time
history at the roof of the SDOF with the acceleration that you computed using the numerical method.
(d) Compute the acceleration, velocity and displacement time histories of the roof of the SDOF system
subjected to the recorded base acceleration using the Newmark method for β = 1/4 (average
acceleration). Plot the acceleration, velocity and displacement time histories. Plot the restoring
force, the damping force, and the inertia force time histories. Compare the recorded acceleration time
history at the roof of the SDOF with the acceleration that you computed using the numerical method
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