Document Type : Research Paper


1 Young Researchers and Elite Club, South Tehran Branch, Islamic Azad University, Tehran, Iran

2 Professor, Faculty of Mechanical Engineering, University of Tehran, Tehran


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.

Graphical Abstract

Resonant frequency of bimorph triangular V-shaped piezoelectric cantilever energy harvester


Main Subjects

[1]     T. A. Anderson and D. W. Sexton, "A vibration energy harvesting sensor platform for increased industrial efficiency,", vol. 6174, Smart structures and materials, pp. 61741Y-61741Y-9, (2006).

[2]     S. P. Beeby, M. J. Tudor, and N. White, "Energy harvesting vibration sources for microsystems applications,", Measurement science and technology, Vol. 17, No.12, p. R175, (2006).

[3]     A. Erturk and D. J. Inman, Piezoelectric energy harvesting, John Wiley & Sons, (2011).

[4]     S. Priya and D. J. Inman, Energy harvesting technologies, Springer, (2009).

[5]     A. G. Muthalif and N. D. Nordin,"Optimal piezoelectric beam shape for single and broadband vibration energy harvesting: Modeling, simulation and experimental results," Mechanical Systems and Signal Processing, Vol. 54, No. 3, pp. 417-426, (2015).

[6]     L. Tang, Y. Yang, and C. K. Soh,            " Toward   broadband   vibration  -  based

 energy harvesting,", Journal of Intelligent Material Systems and Structures,   Vol.   21,  No. 18,  pp.  1867-1897, (2010).

[7]     S. Shahruz, "Limits of performance of mechanical band-pass filters used in energy scavenging," Journal of sound and vibration, Vol. 293, No.1, pp. 449-461, (2006).

[8]     Z. Yang and J. Yang,"Connected vibrating piezoelectric bimorph beams as a wide-band piezoelectric power harvester,", Journal of Intelligent Material Systems and Structures, Vol. 20, No. 5, pp. 569-574, (2009).

[9]     R. Hosseini and M. Hamedi,"An investigation into resonant frequency of trapezoidal V-shaped cantilever piezoelectric energy harvester", Microsystem Technologies, Vol. 21, No. 6, pp. 1-8, (2015).

[10]   R. Hosseini and M. Hamedi,"Improvements in energy harvesting capabilities by using different shapes of piezoelectric bimorphs", Journal of Micromechanics and Microengineering, Vol. 25, No. 12, (2015).

[11]   K. Yang, Z. Li, Y. Jing, D. Chen, and T. Ye,"Research on the resonant frequency formula of V-shaped cantilevers", 4th IEEE International Conference on Nano/Micro Engineered and Molecular Systems, pp. 59-62, (2009).

[12]   S. D. Senturia, Microsystem design, Vol. 3:Kluwer academic publishers Boston, (2001).

[13]   J. Lubliner and P. Papadopoulos, Introduction to Solid Mechanics: An Integrated Approach, Springer Science & Business Media, (2013).

[14]   S. S. Rao, Vibration of continuous systems: John Wiley & Sons, (2007).

[15]   R. Hosseini and M. Hamedi, "Study of the Resonant Frequency of Unimorph Triangular V-shaped Piezoelectric Cantilever Energy Harvester," International Journal of Advanced Design and Manufacturing Technology, Vol. 8, No. 4, pp. 75-82, (2015).