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, n_c is the total number of coil-turns, r_c – effective length of magnetizing coil and w_c – 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.

Figure 28.3: Distributed control of a composite beam