As an advanced sensing technique, modal sensors have been attracting a lot of research interest in modal filtering and active control fields. Most of the existing investigations are mainly focused on the static structure. In contrast, there is little effort made for its rotating counterpart, which is frequently encountered in various power machineries. Motivated by such limitation, a unified framework for the distributed piezoelectric modal sensor design of rotating beams with elastic boundary restraints is proposed using polyvinylidene fluoride piezoelectric integral equation and the second-order structural modal functions. A boundary smoothed Fourier series is used to obtain the modal information of rotating beams by solving the differential governing equation and elastic boundary conditions, simultaneously. Modal sensor shape of rotating beams can be determined for any boundary condition by simply setting the elastic restraining coefficients accordingly, instead of reformulating the equation or rewriting the codes like other approach usually does. Numerical examples are presented to demonstrate the correctness and effectiveness of the proposed framework. Modal sensitivity coefficient and charge output frequency response under external excitation are calculated to demonstrate the performance of the designed piezoelectric modal sensors. Influence of rotation speed and boundary restraining stiffness on the modal sensing accuracy of the shaped polyvinylidene fluoride sensor is analyzed and addressed. To our best knowledge, this work represents the first time that an analytical solution for the distributed piezoelectric modal sensor design of a rotating beam with general boundary conditions is derived, which can shed some new lights on further design and implementation of polyvinylidene fluoride modal sensing technique for rotating structures.
