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ME 413 Systems Dynamics & Control (Semester 131)
Lab Project: Design and Selection of Tuned Mass Damper Device
(Teamwork: 2-3 members, Report: due in week 14, Presentation: due in week 15)*
Tuned mass dampers (TMD) have been widely used for vibration control in mechanical
engineering systems. A TMD is a device consisting of a mass, a spring, and a damper that is
attached to a structure in order to reduce the dynamic response of the structure. The
frequency of the TMD is tuned to a particular structural frequency so that when that frequency
is excited, the TMD will resonate out of phase with the structural motion. Energy is dissipated
by the TMD inertia force acting on the structure.
Problem Description
A rotating machine, such as turbines or compressors, is vibrating and transmitting large forces
to the ground. This vibration might be due to shock or unbalanced mass of the rotor.
Considering the vibration in vertical direction only, the machine can be represented as a single
degree of freedom system having mass M, stiffness K and damper B, subjected to a force,
shown in Figure 1. The harmonic force F is due to rotating unbalance when rotating at speed N
(see Table 1). A tuned mass damper device is to be mounted on the machine in order to reduce
the dynamic response (the TMD has mass m, spring coefficient k and damping coefficient b. Two
newly designs were proposed for the TMD devices, as shown in Figure 2. Your task, as an
engineer, is to evaluate the performance of each system in order to select the best
configuration.
K
y
B
M
(a)
F = mf e ω2
sin(ωt)
Figure 1: (a) Machine supported by a spring and damper.
ME 413 Systems Dynamics & Control (Semester 131)
Undamped System Analysis
As an initial analysis, use the model for the undamped machine system with vibration
absorber (Figure 2a, with b = B = 0), draw FBD, find EOM, and solve for the steady-state solution
y(t) due to harmonic forces. Show the amplitude as a function of force frequency, i.e. frequency
response. Comment on how the secondary mass and spring are affecting the response of the
machine. What are the optimum values for the mass and spring of vibration absorber?
Damped System Analysis
Including the damper in the vibrational systems is more realistic idealization of the machine.
Therefore, for the damped system, Figure 2, draw the FBD, find EOM, and solve for the steadystate
response y(t) as function of force frequency (frequency response). Hint: for the values of
m and k of the TMD, you could use the results of the undamped system as your initial
parameter. Simulate the motion of the damped machine for different values of mass, stiffness
and damping coefficients (m, k and b) of the TMD. Compare the amplitudes of the damped
machine for the two configurations shown in Figure 2. Show how the TMD is affecting the
dynamic response of the machine and suggest optimum values to obtain the minimum
response. Formulate a procedure for selection the optimum design values for the TMD.
Time Response
Plot the displacement response versus time (total solution) of the mass M, for several
parameters of TMD due to impulse force. Compare the response for the system with damped
TMD to the system without damping. Does TMD improve the time response of the machine due
to shock input (impulse force)? Comment on the results.
Selection of TMD
Based on the previous analysis, one TMD configuration from those shown in Figure 2 has to be
selected. Describe which design would provide better suppressing of the machine vibration,
justify your answer by comparing the response for both TMD systems. Show your final selection
of the TMD device mass, spring and damper parameters.
Notes:
In order to avoid heavy weight on the machine, the mass of the TMD device cannot be more
than 10% of the total mass of the machine, i.e. m ≤ 0.10 M.
ME 413 Systems Dynamics & Control (Semester 131)
In the report, include all equations, transfer functions and simulations.
Each group will be assigned specific parameter for the machine by the lab instructor.
Table 1: Data for the Mass, spring and damper of the machine and the rotational speed of the rotor.
Group # Machine mass
M (kg)
Spring
constant
K (N/m)
Damping
constant B
(N.s/m)
Rotational
speed N (rpm)
Mass
unbalance
mf . e (kg.m)
1 100 8400000 3000 2760 2
2 150 8650000 3000 2290 2
3 200 9900000 3000 2120 2
4 250 8950000 3000 1800 2
5 300 9100000 5000 1660 2
6 350 9200000 5000 1550 2
7 400 9350000 5000 1460 2
8 450 9500000 5000 1385 2
9 500 9650000 5000 1325 2
10 550 9800000 5000 1275 2
* This project is teamwork of 2-3 members. A technical report, Word processed, must be
submitted in week 14, followed by a Power Point presentation in week 15. The grade
distribution for the Lab project is: Report 4% + Presentation 2% = Total 6%.
