Spectral analysis of a coupled bending-torsion beam energy harvester: asymptotic results

TL;DR

This paper analyzes the spectral properties of a piezoelectric coupled bending-torsion beam energy harvester, deriving asymptotic spectrum approximations and showing that energy harvesting acts as a weak perturbation to the beam's dynamics.

Contribution

It provides the first asymptotic spectral analysis of a coupled piezoelectric beam model, revealing the perturbative effect of energy harvesting parameters.

Findings

Spectral operator is nonselfadjoint with discrete spectrum.

Energy harvesting acts as a weak perturbation in spectral approximation.

No piezoelectric parameters appear in the first two orders of the spectrum.

Abstract

This work is concerned with the spectral analysis of a piezoelectric energy harvesting model based on a coupled bending-torsion beam. After building the problem's operator setting and showing that the governing operator is nonselfadjoint with a purely discrete spectrum, we derive an asymptotic approximation of its spectrum. In doing so, we also prove that the addition of energy harvesting can be viewed as a weak perturbation of the underlying beam dynamics, in the sense that no piezoelectric parameters appear in the spectral approximation's first two orders of magnitude. We conclude by outlining future work based on numerical simulations.