English

A floating tension leg platform offshore wind turbine is shown in the figure. The mooring lines are under tension due to the buoyancy force acting on the platform. Wave action and ocean currents cause vibration in the mooring lines. Neglect damping and assume that the transverse deflection, , of a mooring line can be described by the string equation.

Select all the true statements relating to the string equation (negative marks for incorrect answers - do not guess).

Afrikaans

Die figuur toon 'n drywende windturbine wat in die see geanker word. Daar is trekkragte in die anker kabels agv die dryfbaarheid van die platform. Golwe en seestrome veroorsaak vibrasie in die kabels. Ignoreer demping en aanvaar dat die tranversale verplasing, , van 'n kabel beskryf kan word deur die snaarvergelyking

Kies al die korrekte stellings wat verband hou met die snaarvergelyking (negatiewe punte vir verkeerde antwoorde - moenie raai nie).

Afrikaans

Hierdie nuwe isolator sal beter werk as die ou isolator by frekwensies bo r.

English

This new isolator would work better than the old isolator when operating at frequencies above r. 

Please upload your Simulink and MATLAB files that you used to complete the Assignment

Which of the following descriptions of the response, , are correct when the following initial conditions are imposed? There may be more than one correct answer.

Derive the mass and stiffness matrix of the three degree of freedom system and calculate the natural frequencies using MATLAB. 

What is the mode shape matrix, , of the system?

The diagram below represents a three degree of freedom system, with the following equation of motion:

Where is the mass matrix and  is the stiffness matrix.

Assume that  kg,  kg,  N/m,  N/m and  N/m.

What line(s) of MATLAB code can be used to calculate the eigenvalues and mode shapes of the system from the mass and stiffness matrix?

Hint: The output must be a diagonal matrix, , containing the eigenvalues and an orthogonal matrix, , holding the mode shapes in its columns. There may be more than one correct answer.