TY - JOUR

T1 - Parametric resonance in cantilever beam and energy harvesting outlooks

AU - Bonisoli, Elvio

AU - Scapolan, Matteo

AU - Tehrani, Maryam Ghandchi

N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 2014

Y1 - 2014

N2 - Parametric resonances can occur in internally stressed systems due to the periodic variation of the stiffness in time. Parametric resonance can lead to unstable dynamic behaviour; however, their response is limited by existing nonlinearities in the system, thus resulting in limit cycle oscillations (LCOs).This phenomenon can be exploited in the design of energy harvesters. The amplitude and frequency of the parametric excitation can be adjusted so that the vibration response of internally stressed systems is close to instability. In this paper, a cantilever beam is considered in vertical position and an axial excitation is applied to the base of the beam. The imposed kinematics of the base leads to internal stress along the beam, which produces a variation of the bending stiffness. If the frequency of the base excitation is twice the first natural frequency of the beam, the principal parametric resonances can occur. A quasi-linear FEM approach is adopted, together with a simplified single-degree-of-freedom model of the beam, in order to numerically simulate its dynamic behaviour, to identify unstable conditions and to obtain the Floquet diagram. An analytical approach is developed as well, using a multidegree- of-freedom model of the beam, considering the system as autoparametric. Harmonic balance method is used to determine the Floquet diagram and to validate the numerical model. Principal parametric resonance is observed experimentally. Harvesting energy from parametric resonance is therefore potentially very efficient, especially if the external source is not directly exploitable. Parametric resonance in this case acts as a power amplification.

AB - Parametric resonances can occur in internally stressed systems due to the periodic variation of the stiffness in time. Parametric resonance can lead to unstable dynamic behaviour; however, their response is limited by existing nonlinearities in the system, thus resulting in limit cycle oscillations (LCOs).This phenomenon can be exploited in the design of energy harvesters. The amplitude and frequency of the parametric excitation can be adjusted so that the vibration response of internally stressed systems is close to instability. In this paper, a cantilever beam is considered in vertical position and an axial excitation is applied to the base of the beam. The imposed kinematics of the base leads to internal stress along the beam, which produces a variation of the bending stiffness. If the frequency of the base excitation is twice the first natural frequency of the beam, the principal parametric resonances can occur. A quasi-linear FEM approach is adopted, together with a simplified single-degree-of-freedom model of the beam, in order to numerically simulate its dynamic behaviour, to identify unstable conditions and to obtain the Floquet diagram. An analytical approach is developed as well, using a multidegree- of-freedom model of the beam, considering the system as autoparametric. Harmonic balance method is used to determine the Floquet diagram and to validate the numerical model. Principal parametric resonance is observed experimentally. Harvesting energy from parametric resonance is therefore potentially very efficient, especially if the external source is not directly exploitable. Parametric resonance in this case acts as a power amplification.

KW - Energy harvester

KW - Floquet diagram

KW - Parametric resonance

UR - http://www.scopus.com/inward/record.url?scp=84944056430&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84944056430

SN - 1590-8844

VL - 15

SP - 23

EP - 30

JO - International Journal of Mechanics and Control

JF - International Journal of Mechanics and Control

IS - 2

ER -