ME5635 - Dynamics of Petroleum Structures - Engineering Assignment Help

Assignment Task

A1. A structure can be modelled as a three degree of freedom system shown in Figure A1, where the masses and stiffnesses are defined as: 1 m kg = 5.0 2 m kg = 6.0 1 m kg = 7.0 1 4000.0 N k m = 2 4000.0 N k m = 3 4000.0 N k m = 4 4000.0 N k m = The natural frequencies and corresponding eigenvectors for the system are defined as:

a) With the aid of simple sketches, describe each of the three modes of vibration.

b) Determine modal, modal mass and modal stiffness matrices for this system.

c) Mass m2 is subjected to a harmonic force of amplitude 0 F N =1 at a frequency of 6 Hz. Knowing the overall response of the system will comprise contributions from each natural mode of free vibration, which mode will have the most significant influence on system response and why?

d) Determine the response of the system to the loading decribed in part (c) for the case where damping is negligible. Only consider the response from the mode having the greatest influence.

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