Determine the equation of angular velocity of the beam

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Vibration Analysis of Mechanical Systems Assignment -

In the mechanical system shown in the figure below the bar is uniform and homogeneous of mass 4m. Determine:

1. The kinetic and potential energy of the system as well as the dissipated energy function.

2. The differential equation of motion of the system in matrix format using Lagrange's Equations.

3. The natural frequencies of the system in terms of k and m, and the normal modal matrix.

4. The natural frequencies of the system if k = 1 N/m and m = 1 kg.

5. The equation of motion of the system if dampers are removed, L = 2m, F₁ = 0.1 sinv₁t N, F₂ = 0.2 cosv₂t N, M = 0.2 sinv₃t Nm, v₁ = ω₁/2, v₂ = (ω₁+ω₂)/2, v₃ = (ω₂+ω₃)/2, {x}₀ = {10 0 -20}^Tcm and {x^·}₀ = {0 -10 10}^T cm/s.

Now replace the dampers and assume c = 1 Ns/m. Determine:

6. The equation of motion of the system using the data in Part 5.

7. Determine the equation of angular velocity of the beam.

8. Find the first amplitude of the lumped masses, as well as their corresponding maximum velocities.

9. How much energy does the system lose in one cycle?

Professional presentation of the report.

NOTE: You may use MATLAB for all matrix calculations and solving equations.

Reference no: EM132312203

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5/27/2019 1:31:21 AM

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