The analysis of a piezoelectric bimorph beam with two input base motions for power harvesting

Abstract

The exploitation of usable power from vibration environments shows potential benefit for recharging batteries and powering wireless transmission. In this paper, we present a novel technique for simulating the electromechanical cantilevered piezoelectric bimorph beam system with two input base transverse and longitudinal motions for predicting power harvesting. The piezoelectric bimorph beam with tip mass was modelled using the Euler-Bernoulli beam assumptions. The strain fields from transverse bending and longitudinal forms can affect the physical behaviour of the polarity and electric field in terms of the series and parallel connections of the piezoelectric bimorph, in such way that each connection has two vector configurations of X-poling and Y-poling due to input base motions. This situation must be correctly identified to form the piezoelectric couplings. The piezoelectric couplings can create the electrical force and moment of each piezoelectric layer in the mechanical domain. At this point, we introduce a new method of modelling the piezoelectric bimorph beam under two input base-motions using coupling superposition of the elastic-polarity field for predicting power harvesting. The constitutive dynamic equations were derived using the weak form from the Hamiltonian theorem, with Laplace transforms being used to obtain the multi-mode frequency response functions (FRFs) relating the input mechanical vibrations with the output dynamic displacement, velocity and power harvesting. The power harvesting predictions under parallel connection at frequencies close to the fundamental bending frequency demonstrate a possibility of being able to produce around 0.4 mW per unit input base transverse acceleration of 3 m/s2. Furthermore, it is shown that varying the load resistance from 20 kΩ to 200 kΩ affects the amplitude of power harvesting as well as resulting in a shift of the first natural frequency from 76 Hz to 79 Hz.