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...

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 in or use a finite element analysis package such as ABACUS.)