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1. (a) Sketch frequency-response curves for a damped single degree of freedom system subjected to a harmonic excitation under three different damping ratios. The system has a natural frequency of ωn while the forcing frequency of the excitation is ω. Explain the relation of static and dynamic deformation responses for
(i) ω/ωn << 1
(ii) ω/ωn >> 1
(iii) ω/ωn = 1
Also state whether the dynamic response is controlled by the mass, stiffness or damping of the system for each case.
(b) A single degree of freedom building system is excited by a sinusoidal force as shown in Figure 1. Assume that the girder is rigid whereas the columns are flexible to the lateral deformation but rigid in the vertical direction. Use E = 30 GPa, I = 60 x 106 mm4 and 5 % damping and neglect the mass of columns. Determine
(i) The steady state amplitude of vibration,
(ii) The maximum shear force in the column,
(iii) The maximum bending moment.
On the Moodle site just below the assignment you will find data from a slow sine sweep test conducted on a car on a "four-post" road simulator for the frequency range 0 to 20 Hz in
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