Consider a simply supported deep beam, where both shear and rotary inertia may be considered...

Consider a simply supported deep beam,
where both shear and rotary inertia may be considered important. For certain
applications, it is necessary to actively and effectively clamp both ends of
the beam by applying suitable feedback control forces along the length of the
beam. (i) Design a generic controller capable of clamping a simply supported
beam so its first three modes have the same natural frequencies as those of a
beam clamped at both ends. (ii) How many actuators and sensors would you need
if it is essential to avoid spillover effects in the next three modes? (iii) If
only a maximum of four actuators are available, investigate the effects of
spillover on the closedloop frequency response. Assume that J mL2 = I AL2 =
0.06, E KG = 1.88. (You may find it convenient to use the finite element model
developed or use a finite element analysis package such as ABACUS.)