Abstract
We examine regular and chaotic responses of a vibrational energy harvester composed of a vertical beam and a tip mass. The beam is excited horizontally by a harmonic inertial force while mechanical vibrational energy is converted to electrical power through a piezoelectric patch. The mechanical resonator can be described by single or double well potentials depending on the gravity force from the tip mass. By changing the tip mass we examine bifurcations from single well oscillations, to regular and chaotic vibrations between the potential wells. The appearance of chaotic responses in the energy harvesting system is illustrated by the bifurcation diagram, the corresponding Fourier spectra, the phase portraits, and is confirmed by the 0–1 test. The appearance of chaotic vibrations reduces the level of harvested energy.
Highlights
Broadband energy harvesting systems for many applications are often nonlinear, exhibiting such nonlinear phenomena as material nonlinearities, geometrical nonlinearities, multi-scale responses and the appearance of multiple solutions
For nonlinear energy harvesting an inverted elastic beam is considered with a tip mass and the base is harmonically excited in the transverse direction
These expressions assume a monolithic piezoceramic actuator perfectly bonded to the beam; Bilgen et al [29] considered the effect of the structure of a Macro-Fiber Composite (MFC) on the coupling coefficient, and the effect of the bond and the insulating Kapton layers
Summary
Broadband energy harvesting systems for many applications are often nonlinear, exhibiting such nonlinear phenomena as material nonlinearities, geometrical nonlinearities, multi-scale responses and the appearance of multiple solutions. These phenomena can be observed from the nonlinear time series analysis of simulated mathematical models or from measured system responses in experiments. The key aspect of nonlinear harvesters is the use of a double well potential function, so that the device will have two equilibrium positions [7,8,9,10,11,12]. Intra- and interwell oscillations as well as periodic and chaotic vibrations lead to different efficiency in the energy harvesting. We identify the properties of given solutions by using nonlinear methods
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