It has been proven that tapering the piezoelectric beam through its length optimizes the power extracted from vibration based energy harvesting. This phenomenon has been investigated by some researchers using semianalytical, finite element and experimental methods. In this paper, an exact analytical solution is presented to calculate the power generated from vibration of exponentially tapered unimorph and bimorph with series and parallel connections. The mass normalized mode shapes of the exponentially tapered piezoelectric beam with tip mass are implemented to transfer the proposed electromechanical coupled equations into modal coordinates. The steady states harmonic solution results are verified both numerically and experimentally. Results show that there exist values for tapering parameter and electric resistance in a way that the output power per mass of the energy harvester will be maximized. Moreover it is concluded that the electric resistance must be higher than a specified value for gaining more power by tapering the beam.
It has been shown that exponentially tapering the width of a vibration-based piezoelectric energy harvester will result in increasing electric power per mass in a specified frequency. In this paper, a nonlinear solution of an exponentially decreasing width piezoelectric energy harvester is presented. Piezoelectric, inertial, and geometric nonlinearities are included in the presented model, while the exponentially tapered piezoelectric beam's mass normalized mode shapes are utilized in Galerkin discretization. The developed nonlinear coupled equations of motion are solved using method of multiple scales (MMS), and the steady states results are verified by experiment in high amplitude excitation. Finally, the exponentially tapering parameter effect is studied, and it is concluded that the voltage per mass of the energy harvester is improved by tapering at high exciting acceleration amplitudes.
An explicit hybrid stabilization method is utilized together with a reduced order integration scheme to stabilize spurious zero energy modes from the sub-integrated degenerated shell element. This stabilization is achieved after employing appropriate contravariant higher order stress modes. The relevant finite element formulation of the piezolaminated ninenodded shell element is then derived to analyze smart structures behaviors.To show the capabilities of the presented formulation, it has been implemented in a finite element code. The developed code is used to analyze some typical problems. The results are compared with those obtained from other schemes in the literature and experiment.
During the past years, the development of piezoelectric energy harvesters is extensively increased for providing the required energy of sensor nodes. It has been proven that changing the beam’s cross-section along its length direction may lead to extract more power with less mass. In this article, a hybrid metaheuristic algorithm called tabu continuous ant colony system is employed to optimize the tapered piezoelectric energy harvester in a fast and course manner. The exponential and fourth-order polynomial functions are considered as shaping functions for tapering the beam’s width along its length direction. An experiment is also set up to evaluate the performance of the optimization algorithm for the case of exponential shaping function. Finally, the algorithm is applied to optimize the voltage and power per mass of both shaping functions of the tapered piezoelectric energy harvester at the specified excitation frequency.
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