Control of flexible structures by applied thermal gradients

Thermal, elastic, and feedback analyses are applied to the case of a beam with a distributed thermal actuator. The actuator is capable of producing a thermal gradient across the section of the beam. One candidate for such an actuator uses the Pettier effect, which appears in certain semiconductors. These devices act as heat pumps when a voltage is applied, causing a temperature gradient. It is shown that the thermal gradients can induce deflection in the beam. If the thermal gradients are applied in the proper sense to a vibrating beam, it is possible to increase the vibration damping exhibited by the structure. Experimental results are given for a cantilever beam, whose first vibrational mode damping ratio was increased from 0.81 to 1.4% with simple lead compensation. Nomenclature A = cross-sectional area of beam b = beam width CQV - voltage to heat flow conversion constant C(s) = compensator dynamics c = specific heat d = separation of cap neutral axis from beam centroid E = Young's modulus H = Heaviside step function Gs - sensor gain coefficient g = acceleration of gravity at Earth's surface h = depth of beam cap / = bending moment of inertia / = electric current K = thermal conductivity Kc = compensator gain <£ { j = Laplace transform of { ) £ = length of beam 4 = thermal length of beam section near actuator MT = bending moment induced by applied thermal gradient