Polyvinylidene fluoride modal sensor design for elastically restrained beams resting on general non-uniform foundation

In this article, a unified solution of polyvinylidene fluoride modal sensor design for elastically restrained beams resting on general non-uniform foundation is proposed using an improved Fourier series method. Modal sensor shape is determined from the charge output equation of polyvinylidene fluoride film and the superposition of the second-order derivative of beam mode shape. With the aim to make the spatial differentials of various order sufficiently continuous in the interval [0, L], Fourier series with auxiliary boundary-smoothed terms are employed to construct the displacement expression. Energy formulation is utilized for system dynamic description, with all the unknown expansion coefficients solved in conjunction with Rayleigh–Ritz procedure. The proposed model is validated through the comparison of modal parameters of simply supported beam resting on elastic foundation with those available in literature. Correctness and effectiveness of the designed polyvinylidene fluoride modal sensor are verified by calculating the modal sensitivity coefficients and the charge output frequency response under external excitation. Based on the model established, the perturbation of practical boundary restraining stiffness on sensing accuracy of such polyvinylidene fluoride sensor is studied, and the influences of boundary condition on polyvinylidene fluoride modal sensor design are investigated for the beam structure resting on general non-uniform foundation.