Dynamics of Machines - Part II - IFS.pdf

1.10 Project 0 – Identification of Model Parameters (An Example)
GOAL – With the first project the student will face a practical problem of the real life: how
to properly choose the coefficients of linear differential equations of second order, aiming at
achieving a reliable mathematical model, which can predict the machine dynamics?
(a) (b)
Figure 36: (a) Offshore platform http : //www.civl.port.ac.uk/comp−prog/offshore−platforms;
(b) Laboratory prototype composed of one concentrated mass (foundation and rotor) attached
to four flexible beams – An equivalent model of 1 D.O.F. system for analyzing the platform’s
linear vibration in the horizontal direction.
To represent the 2D-movements of the offshore platform shown in figure 36(a) a laboratory
prototype was built, as it can be seen in figure 36(b). This simplified test rig is composed of one
concentrated mass (foundation and rotor) attached to four flexible beams. An equivalent model
of 1 D.O.F. system can be created with the purpose of analyzing the platform’s linear vibration
in the horizontal direction.
m0 2.108 [kg] platform mass
L0 0.205 [m] beam length
b0 0.025 [m] beam width
h0 0.001 [m] beam thickness
E 1.9 · 10 11 [N/m 2 ] steel elastic modulus
Table 5: Main parameters of the test rig (platform)
1. Create a mechanical model of one-degree-of-freedom for describing the horizontal vibration
of the test rig. Use Newton’s law and equivalent coefficients of mass m [Kg], viscous
damping d [N/(m/s)] and linear stiffness k [N/m].
2. There are two different ways of experimentally obtaining the forced vibration response
of the platform in the frequency domain, i.e. its frequency response functions FRF(ω),
namely by means of H1(ω) and H2(ω) functions. Detail about how to experimentally
obtain H1(ω) and H2(ω) will be given in the second part of manuscript. Anyway, for now,
it is important to relate such experimental functions to the frequency response functions
61