## Abstract

This paper uses the method of Quadratures in conjunction with the Maximum Entropy principle to investigate the effect of parametric uncertainties on the mean power output and root mean square deflection of piezoelectric vibrational energy harvesting systems. Uncertainty in parameters of harvesters could arise from insufficient manufacturing controls or change in material properties over time. We investigate bimorph based harvesters that transduce ambient vibrations to electricity via the piezoelectric effect. Three varieties of energy harvesters-Linear, Nonlinear monostable and Nonlinear bistable are considered in this research. This analysis quantitatively shows the probability density function for the mean power and root mean square deflection as a function of the probability densities of the excitation frequency, excitation amplitude, initial deflection of the bimorph and magnet gap of the energy harvester. The method of Quadratures is used for numerically integrating functions by propagating weighted points from the domain and evaluating the integral as a weighted sum of the function values. In this paper, the method of Quadratures is used for evaluating central moments of the distributions of rms deflection and mean harvested power and , then, in conjunction with the principle of Maximum Entropy (MaxEnt) an optimal density function is obtained which maximizes the entropy and satisfies the moment constraints. The The computed nonlinear density functions are validated against Monte Carlo simulations thereby demonstrating the efficiency of the approach. Further, the Maximum Entropy principle is widely applicable to uncertainty quantification of a wide range of dynamic systems.

Original language | English (US) |
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Title of host publication | Integrated System Design and Implementation; Structural Health Monitoring; Bioinspired Smart Materials and Systems; Energy Harvesting |

Publisher | American Society of Mechanical Engineers |

ISBN (Electronic) | 9780791857304 |

DOIs | |

State | Published - Jan 1 2015 |

Event | ASME 2015 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, SMASIS 2015 - Colorado Springs, United States Duration: Sep 21 2015 → Sep 23 2015 |

### Publication series

Name | ASME 2015 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, SMASIS 2015 |
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Volume | 2 |

### Other

Other | ASME 2015 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, SMASIS 2015 |
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Country | United States |

City | Colorado Springs |

Period | 9/21/15 → 9/23/15 |

## All Science Journal Classification (ASJC) codes

- Civil and Structural Engineering
- Control and Systems Engineering
- Mechanics of Materials
- Building and Construction