This document is a summary of a PhD coursework examination on structural dynamics. The exam has 3 questions to choose from. Question I involves deriving equations for normal modes of vibration for a SDOF system with given mass and stiffness. Question II involves deriving and solving the equation of motion for an un-damped SDOF system subjected to harmonic loading. Question III covers shape function selection, damping types, and Raleigh's method. Question IV requires short notes on power spectra, Fourier spectra, and response spectra. The candidate is Gadha Venugopal and the exam duration is 3 hours with a maximum of 40 marks.

1. PhD course work second internal examination
School of Engineering, Cochin University
Structural Dynamics
Candidate: Gadha Venugopal
Duration : 3hours Max. Marks: 40
I a) Derive the equation of normality and orthogonality principle
b) Obtain frequencies and modes of vibration. Assume m = 5 x 104
kg,
k= 5 x 104
kN/cm.
OR
II a) Derive equation of motion for un-damped SDOF system.
b) A machine of weight 1750 kg is mounted on fixed end steel beam as
shown in figure. A piston that moves up and down in the machine
produces a harmonic force of magnitude Fo=31.75kN and frequency
ω=60rad/s. Neglecting the weight of the beam and assuming 10% of
the critical damping. Determine
a) The amplitude of motion of the machine
b) the force transmitted to the beam supports and
c) the corresponding phase angle.
E=206GPa and I=4995cm4
.
III a) Explain about shape function selection.
b) Compare the decay curves for various types of damping
c) Explain Raleigh’s method.
OR
IV Write short notes on
a) Power spectra
b) Fourier spectra
c) Response spectra
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0.5m
m
2m
2k
2k
2k
2m 2m