Semi-analytical solution of random response for nonlinear vibration energy harvesters

Stochastic response analysis for nonlinear vibration systems with adjustable stiffness property under random excitation

“…The first example considers the model of a generic piezoelectric vibration energy harvester [ 8 , 32 – 35 ] to be simplified as a base-excited one-degree-of-freedom system coupled to a capacitive energy harvesting circuit, as shown in Fig 1 .…”

“…Xu et al [ 7 ] used the same approach to investigate the random vibration with inelastic impact subject to Gaussian white noise, so as to analytically obtain the joint probability density of nonlinear system and the statistics of system response. Jin et al [ 8 ] also employed the equivalent nonlinearization technique and imported the generalized harmonic transformation to establish a semi-analytical solution of random response for nonlinear vibration energy harvesters subjected to Gaussian white noise excitation. One of the benefits of this approach was the applicability to the strongly nonlinear, self-excited or parametric systems compared with the equivalent linearization technique.…”

“…From the investigations and results in previous studies, the equivalent nonlinearization technique [ 6 – 8 ] and the stochastic averaging method [ 12 – 17 ] have been widely applied in the random response evaluation due to their accuracy and simplicity. However, both of them have disadvantages that the approximate equivalent exists and is required necessarily, which may influence the applicability of these methods and the accuracy of the results.…”

A review on performance enhancement techniques for ambient vibration energy harvesters

“…A bi stable energy harvester can be modelled with k > 0 presented in the Duffing equation, the effective bandwidth of the vibration energy harvester can be extended when they possess nonlinear potential functions. Detailed modelling of nonlinear vibration energy harvesters can be found in [57][58][59][60]. A comparison between bi-stable and mono-stable harvesters found that at small base accelerations the mono-stable harvester is more optimal however bi-stable harvester with large base accelerations need to be coupled with appropriate potential functions [61,62], but in general bi-stable harvesters have a broader bandwidth [63] and their harvester output power is not influenced under white noise [64,65].…”

Time-Delayed Feedback Control in the Multiple Attractors Wind-Induced Vibration Energy Harvesting System

“…In the early stages, different types of linear vibration energy harvesters have been designed to generate electrical energy [4][5][6]. These systems, however, were found to be effective within a limited bandwidth near their resonant frequencies, thus limiting their application to frequency variant, amplitude variant, broadband, and random excitation sources which are typical excitation types in real applications [2,7,8]. In order to solve this critical challenge, a burst of research activities have been devoted to widen the working frequency of energy harvesters by using nonlinear phenomenon [9][10][11][12][13][14].…”