Vibration
Rouhollah Hosseini; Mohsen Hamedi
Abstract
The concept of “energy harvesting” is to design smart systems to capture the ambient energy and to convert it to usable electrical power for supplying small electronics devices and sensors. The goal is to develop autonomous and self-powered devices that do not need any replacement of traditional ...
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The concept of “energy harvesting” is to design smart systems to capture the ambient energy and to convert it to usable electrical power for supplying small electronics devices and sensors. The goal is to develop autonomous and self-powered devices that do not need any replacement of traditional electrochemical batteries. Now piezoelectric cantilever structures are being used to harvest vibration energy for self-powered devices. However, the geometry of a piezoelectric cantilever beam will greatly affect its vibration energy harvesting ability. This paper deduces a remarkably precise analytical formula for calculating the fundamental resonant frequency of bimorph V-shaped cantilevers using Rayleigh method. This analytical formula, which is convenient for mechanical energy harvester design based on Piezoelectric effect, is then validated by ABAQUS simulation. This formula raises a new perspective that, among all the bimorph V-shaped cantilevers and in comparison with rectangular one, the simplest tapered cantilever beam can lead to maximum resonant frequency and highest sensitivity. The derived formula can be commonly used as a relatively precise rule of thumb in such systems.
Perturbation Technique
M. Zamanian; M. Hadilu; B. Firouzi
Abstract
In this paper, a comparison is made between direct and indirect perturbation approaches to solve the non-linear vibration equations of a piezoelectrically actuated cantilever microbeam. In this comparison, the equation of motion is considered according to Euler-Bernoulli theory with considering the non-linear ...
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In this paper, a comparison is made between direct and indirect perturbation approaches to solve the non-linear vibration equations of a piezoelectrically actuated cantilever microbeam. In this comparison, the equation of motion is considered according to Euler-Bernoulli theory with considering the non-linear geometric and inertia terms resulted from shortening effect. In the direct perturbation approach, the multiple scales method is directly applied to the partial differential equation of motion. In the indirect approach, the multiple scales perturbation technique is applied to the discretized equation of motion. It is shown that, if the equation of motion is discretized using one non-uniform microbeam mode shape as a comparison function, then the results of indirect perturbation approach will be identical to those of the direct perturbation approach. Moreover, it is observed that discretization using one uniform microbeam mode shape as a comparison function results in a different output. The concept of non-uniform microbeam mode shape is the linear mode shape of the microbeam by considering the geometric and inertia effects of the piezoelectric layer.
