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1 August 2003 Piezoelectic actuation of thin shells with support excitation
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The present contribution is concerned with a thin shell, which is excited to elastic vibrations by an imposed motion of a supporting boundary. Piezoelectric actuation is used to generate an additional actuation of the shell. As a practical application of dynamic shape control, we consider the suppression of flexural and extensional elastic vibrations, such that the shell performs a rigid body motion only. The idea of this procedure is to eliminate the disturbing acoustic noise caused by elastic deformations. We first point out that a suppression of the elastic vibrations can be achieved provided the distributed piezoelectric actuation coincides with a statically admissible (quasi-static) membrane force and bending moment distribution due to a fictitious inertial body force loading of the shell. For practical applications we assume the exciting support motion to be either translational or rotational, and to be given in advance. As an example of practical relevance, noise radiation of the support-excited shell-type funnel of a magnetic resonance tomograph is considered. Due to the complex geometry of this thin shell made of plastics, numerical methods are used in order to treat the shape control problem. The statically admissible membrane forces and bending moments due to the fictitious body force loading are computed by means of the Finite-Element-Code ANSYS. A distributed piezoelectric actuation coinciding with these forces and moments is derived and is approximated by a sparse distribution of piezoelectric patches. It is numerically demonstrated that this sparse distribution is able to suppress the elastic vibrations caused by the support excitation of the funnel.
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Manfred Nader, Michael Krommer, Hans-Georg von Garssen, and Hans Irschik "Piezoelectic actuation of thin shells with support excitation", Proc. SPIE 5049, Smart Structures and Materials 2003: Modeling, Signal Processing, and Control, (1 August 2003);


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