Non-linear dynamics of a vibration energy harvester by means of the homotopy analysis method

2013 ◽  
Vol 25 (13) ◽  
pp. 1605-1613 ◽  
Author(s):  
Luke A Vandewater ◽  
Scott D Moss
2013 ◽  
Vol 102 (15) ◽  
pp. 153901 ◽  
Author(s):  
M. López-Suárez ◽  
J. Agustí ◽  
F. Torres ◽  
R. Rurali ◽  
G. Abadal

Author(s):  
S. D. Moss ◽  
L. A. Vandewater ◽  
S. C. Galea

This work reports on the modelling and experimental validation of a bi-axial vibration energy harvesting approach that uses a permanent-magnet/ball-bearing arrangement and a wire-coil transducer. The harvester’s behaviour is modelled using a forced Duffing oscillator, and the primary first order steady state resonant solutions are found using the homotopy analysis method (or HAM). Solutions found are shown to compare well with measured bearing displacements and harvested output power, and are used to predict the wideband frequency response of this type of vibration energy harvester. A prototype harvesting arrangement produced a maximum output power of 12.9 mW from a 12 Hz, 500 milli-g (or 4.9 m/s2) rms excitation.


Author(s):  
Onur Bilgen ◽  
S. Faruque Ali ◽  
Michael I. Friswell ◽  
Grzegorz Litak ◽  
Marc de Angelis

An inverted cantilevered beam vibration energy harvester with a tip mass is evaluated for its electromechanical efficiency and power output capacity in the presence of pure harmonic, pure random and various combinations of harmonic and random base excitation cases. The energy harvester employs a composite piezoelectric material device that is bonded near the root of the beam. The tip mass is used to introduce non-linearity to the system by inducing buckling in some configurations and avoiding it in others. The system dynamics include multiple solutions and jumps between the potential wells, and these are exploited in the harvesting device. This configuration exploits the non-linear properties of the system using base excitation in conjunction with the tip mass at the end of the beam. Such nonlinear device has the potential to work well when the input excitation does not have a dominant harmonic component at a fixed frequency. The paper presents an extensive experimental analysis, results and interesting conclusions derived directly from the experiments supported by numerical simulations.


Sensors ◽  
2021 ◽  
Vol 21 (16) ◽  
pp. 5517
Author(s):  
Nathan Jackson ◽  
Luis A. Rodriguez ◽  
Rahul Adhikari

One of the biggest challenges associated with vibration energy harvesters is their limited bandwidth, which reduces their effectiveness when utilized for Internet of Things applications. This paper presents a novel method of increasing the bandwidth of a cantilever beam by using an embedded transverse out-of-plane movable mass, which continuously changes the resonant frequency due to mass change and non-linear dynamic impact forces. The concept was investigated through experimentation of a movable mass, in the form of a solid sphere, that was embedded within a stationary proof mass with hollow cylindrical chambers. As the cantilever oscillated, it caused the movable mass to move out-of-plane, thus effectively altering the overall effective mass of the system during operation. This concept combined high bandwidth non-linear dynamics from the movable mass with the high power linear dynamics from the stationary proof mass. This paper experimentally investigated the frequency and power effects of acceleration, the amount of movable mass, the density of the mass, and the size of the movable mass. The results demonstrated that the bandwidth can be significantly increased from 1.5 Hz to >40 Hz with a transverse movable mass, while maintaining high power output. Dense movable masses are better for high acceleration, low frequency applications, whereas lower density masses are better for low acceleration applications.


2019 ◽  
Vol 8 (2S11) ◽  
pp. 3584-3588

In the present investigation a two species commensalism model was taken up for detailed analytical study in which commensal species was harvested at a rate proportional to its strength. The system under investigation was represented by a coupled non linear ordinary differential equations. The series solution of the non-linear system was approximated by Homotopy Analysis Method.


2012 ◽  
Vol 09 (03) ◽  
pp. 1250039 ◽  
Author(s):  
S. S. MOTSA

In this work, we demonstrate the efficiency of the newly developed spectral homotopy analysis method (SHAM) in solving non-linear heat transfer equations. We demonstrate the applicability of the method by solving the problem of steady conduction in a slab and the convective fin equation with variable thermal conductivity. New closed form explicit analytic solutions of the governing non-linear equations are obtained and compared with the SHAM results and numerical solutions. The results reveal that the new SHAM approach is very accurate and efficient and converges much faster than the standard homotopy analysis method.


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