### ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06

## 3aSA3. Active control of structural intensity in an elastic plate.

**S. I. Hayek
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M.-Y. Nam
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*Dept. of Eng. Sci. and Mech., Penn State Univ., University Park, PA 16801
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**S. Sommerfeldt
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*Penn State Univ, University Park, PA 16801
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Active control of structural intensity (SI) in a finite elastic plate
coupled to a point damper is achieved through the use of a judiciously located
actuator. An algorithm was developed using the magnitude of the structural
intensity vector to achieve local or global reduction of SI. The control
algorithm showed that controlling each component of the intensity vector (I[sub
x] or I[sub y]) generates a parabolic surface, which may or may not intersect
the null plane. Under certain conditions based on the locations of the primary
mechanical source and the error sensors, as well as the dynamic parameters of
the plate, the surface intersects the null plane. If the surface intersects
with the null plane, then the intersection generates a circle of possible
actuator magnitudes and phases that will make either I[sub x]=0 or I[sub y]=0.
If the circles exist for both I[sub x]=0 and I[sub y]=0, then inequalities were
derived that will indicate when and if these circles will intersect. The
intersection of these circles allows only two possible control solutions that
will make the magnitude of the vector SI at the error sensor vanish. When the
intersections do not occur, then minimization rather than extinction is
achieved. These control strategies are explored and applied to an elastic
simply supported plate coupled to a point damper and excited to vibration by a
point force. The role of structural damping on control strategies is fully
explored.