Effect of uncertain boundary conditions and uncertain axial loading on lateral vibration attenuation of a beam with shunted piezoelectric transducers

Undesired vibration may occur in lightweight structures due to excitation and low damping. For the purpose of vibration attenuation, resonantly shunted piezoelectric transducers can be an appropriate measure. In this paper, uncertainty in design and application of resonantly shunted piezoelectric patch transducers to attenuate the vibration of a beam due to uncertain rotational support stiffness and uncertain static axial loading is investigated. A linear mathematical model of a beam with piezoelectric patch transducers using RITZ formulation is used to calculate the vibration attenuation potential under uncertainty. Variation in the support stiffness and variation static axial loading lead to detuning and cause the resonant shunt to work off the desired frequency, resulting in higher vibration amplitudes. For a beam that is pinned or fixed at both ends, the attenuation effect is less sensitive to uncertainty in the support stiffness than in case of an elastic support that is neither fully pinned nor fully fixed at both ends. A beam fixed at both ends is most robust against uncertainty in static axial loading.