Theoretical prediction and experimental verification of shape control of beams with piezoelectric patches and resistive circuits

This paper presents one-dimensional analytical, three-dimensional numerical and experimental results for shape control of beam-type structures. The beam structures under consideration are assumed to be slender and the surface of the elastic substrate is covered by several piezoelectric patches whose electrodes are connected by a resistor network. In general, the structure will deform, if an external load acts on the system and no control action is present. Therefore, the question arises how to choose the network configuration, in order to completely suppress deflections or vibrations at several desired locations along the beam axis. This aim is also known as shape control. As a practical example, a cantilever beam subjected to a tip-force is considered. First we present shape control results for the one-dimensional extended Bernoulli-Euler theory and three-dimensional finite element calculations with ANSYS for static loads and time-harmonic excitations. Then the theory is verified by an experimental setup and it is shown by several frequency sweep excitations and by a monofrequent harmonic excitation close to the first eigenfrequency that shape control may be achieved approximately, proving the applicability of the proposed control method.