Distributed Parameter Modelling and Experimental Validation

Abstract

This chapter presents an experimentally validated distributed parameter model, of a base-excited cantilever bimorph, without any tip mass. Euler–Bernoulli beam theory and the well-known constitutive piezoelectric equation are used to derive the model. The main features of this chapter relative to [1, 2] are illustrated as below: As no tip mass is used in the present study, this is known to be a more stringent validation of the distributed parameter piezoelectric beam model since the presence of a tip mass reduces the influence of the distributed inertia of the beam and restricts effective operation to low frequencies (e.g. 45–50 Hz resonance in) [4]. This study covers the relatively higher resonance frequency range, 120–130 Hz, for which most harvesters are designed for. The graphs showing variation in resonance frequency, resonant voltage amplitude, resonant power and resonant deflection amplitude with respect to change in electrical load are presented. These graphs give a deeper insight into the electromechanical interaction and also provide useful insight into theory and experimental results. Nyquist plots of the FRFs are presented. The Nyquist plots are more descriptive than the usual magnitude graphs. Nyquist plots are used for two purposes here: To determine the mechanical damping. To observe the evolution of the FRFs as the electrical load is changed. The measured FRFs are obtained through the application of random excitation, also known as band-limited white noise, rather than a sine sweep [4]. The MatLab code, modelling and simulating the complex equations, of the mathematical model presented in this chapter is attached in Appendix-A of the book.