Modelling of the Dynamic System: (contd...)
If we assume velocity proportional control algorithm, the active strain becomes proportional to the transverse velocity of the beam , the symbol ‘.’ denotes differentiation with respect to time, the constant of proportionality C is function of electro/magneto-mechanical constant(d), and controller gain (f).
In the case of magnetostrictive material, , where the coil constant is given by
|
(28.6) |
where, nc is the total number of coil-turns, rc – effective length of magnetizing coil and wc – effective width of magnetizing coil.
Thus, stress at any layer may now be written as
)] |
(28.6) |
Using the Hamilton's principle, the governing equations of motion may be derived as
) |
(28.7) |
with the following boundary conditions:
i) either or
ii) either or
Initial conditions in time will also be prescribed along with. |
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Figure 28.3: Distributed control of a composite beam |