# To model MDOF system using Newtonian or Lagrangian Methods

18 / 01 / 2019 Mechanical engineering

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To model MDOF system using Newtonian or Lagrangian Methods
To use Influence Coefficients to determine stiffness and flexibility matrices
To determine the lowest and highest Un-damped natural frequencies and their associated mode shapes from theory
To determine all Un-damped Natural Frequencies from experiment

Theory:

You will need to derive the equations of motion for this 4 degree of freedom system. You can do this by either Newtonian or Lagrangian method.
You should demonstrate the use of influence coefficients to develop the stiffness and flexibity matrices and confirm by comparison with original system.
You will need to develop a 4x4 characteristic equation and solve using matrix iteration for the highest and lowest modes. You will also determine all modes by either frequency scanning or Holzer`s method - whichever you deem appropriate.
Compare theoretical natural frequencies and mode shapes between theories used.

Experiment (to be done under the supervision of the lecturer or Technical skills specialist)
1: Determine the stiffness of the supports assuming propped cantilevers in bending
2: Determine the masses of the blocks by calculation.
3: Turn on all devices and set a suitable amplification level to give excite the system with visible displacements on each floor. Do not change the input force once started.

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