Extensive research has been conducted on vibration energy harvesting utilizing a distributed piezoelectric beam structure. A fundamental issue in the design of these harvesters is the understanding of the response of the beam to arbitrary external excitations (boundary excitations in most models). The modal analysis method has been the primary tool for evaluating the system response. However, a change in the model boundary conditions requires a reevaluation of the eigenfunctions in the series and information of higher-order dynamics may be lost in the truncation. In this paper, a frequency domain modeling approach based in the system transfer functions is proposed. The transfer function of a distributed parameter system contains all of the information required to predict the system spectrum, the system response under any initial and external disturbances, and the stability of the system response. The methodology proposed in this paper is valid for both self-adjoint and non-self-adjoint systems, and is useful for numerical computer coding and energy harvester design investigations. Examples will be discussed to demonstrate the effectiveness of this approach for designs of vibration energy harvesters.

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